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Theoretical Investigations of the
Photophysical Properties of Chromophoric
Metal-Organic Frameworks
D I S S E R T A T I O N
zur Erlangung des akademischen Grades
Doctor rerum naturalium
(Dr. rer. nat.)
vorgelegt
dem Bereich Mathematik und Naturwissenschaften
der Technische Universität Dresden
von
M.Sc. Kamal Batra
geboren am 12.01.1991 in New Delhi / India
Verteidigt am 17. Februar 2021
Die Dissertation wurde in der Zeit von Mai 2017 bis Dezember 2020
am Institut für Theoretische Chemie angefertigt.
Dekan: Prof. Dr. Thomas Henle
1. Gutachter: Prof. Dr. Thomas Heine
2. Gutachter: Dr. Renhao Dong
Die Dissertation wurde in der Zeit von Mai 2017 bis Dezember 2020 an der Technischen
Universität Dresden unter der Betreuung von Prof. Dr. Thomas Heine durchgeführt.
Ich danke Prof. Dr. Thomas Heine für seine wissenschaftliche und persönliche Unterstützung
sowie für seine ständige Diskussionsbereitschaft.
Contents
Abstract……………………………………………………………………………………...01
1. Introduction………………………………………………………………………………03
1.1 Energy Sources……………………………………………………………………………………03
1.2 Photovoltaics (PVs)……………………………………………………………………………….03
1.3 Porphyrins (PPs) and Porphyrinoids……………………………………………………………....05
1.4 Metal-Organic Frameworks (MOFs)……………………………………………………………...08
1.5 Surface-mounted Metal-Organic Frameworks (SURMOFs)……………………………………...10
1.6 Porphyrin based Metal-Organic Frameworks……………………………………………………..11
Motivation, Objective, and Outline of Thesis…………………………………………………………13
2. Theory and Methods……………………………………………………………………...15
2.1 Quantum Chemistry…………………………………………………………………….................16
2.1.1 The Schrödinger Equation (SE)………………………………………………………...16
2.1.2 The Born-Oppenheimer (BO) Approximation………………………………………….17
2.2 Density Functional Theory (DFT)………………………………………………………………...18
2.2.1 The Hohenberg-Kohn (HK) Theorems………………………………………................19
2.2.2 The Kohn-Sham (KS) Formalism……………………………………………................19
2.2.3 Exchange-Correlation Functionals……………………………………………………...21
2.2.3.1 Local Density Approximation (LDA)………………………………………..22
2.2.3.2 Generalized Gradient Approximations (GGAs)……………………..............23
2.2.3.3 Global Hybrids (GHs)………………………………………………………..23
2.3 Time Dependent Density Functional Theory (TD-DFT)……………………………….................24
2.3.1 The Runge-Gross (RG) Theorem and TD KS Formalism……………………………...25
2.3.2 The Linear Response (LR) Formalism ………………………………………...............27
2.3.2.1 The LR TD-DFT and Tamm-Dancoff Approximation (TDA) ……………...27
2.3.2.2 The simplified TDA and TD-DFT approaches………………………………29
2.4 Density Functional Based Tight Binding (DFTB) ………………………………………………..30
2.5 Periodic Treatment of Crystalline Materials………………………………………………………33
2.6 Applied Computational Chemistry Packages……………………………………………………..37
3. Benchmarking the Performance of Time Dependent Density Functional Theory for
Predicting the UV-Vis Spectral Properties of Porphyrinoids……………………………39
3.1 Introduction………………………………………………………………………………………..41
3.2 Computational Methodologies………………………………………………………….................45
3.3 Results and Discussions…………………………………………………………………………...48
3.3.1 GGA and meta-GGA Functionals……………………………………………................49
3.3.2 Global Hybrid Functionals……………………………………………………………...51
3.3.3 Range Separated Hybrid (RSH) Functionals…………………………………...............53
3.3.4 Double Hybrid Functionals and post-Hartree Fock (HF) Approaches…………………57
3.3.5 Influence of Diffuse Basis Set and Ground State Structure…………………………….59
3.4 Conclusions………………………………………………………………………………………..60
4. Computational Screening of Surface-mounted Metal Organic Frameworks
Assembled from Porphyrins………………………………………………………………..63
4.1 Introduction………………………………………………………………………………………..66
4.2 Computational Methodologies………………………………………………………….................69
4.3 Results and Discussions…………………………………………………………………………...70
4.4 Conclusions………………………………………………………………………………………..74
5. The Proximity effect in Porphyrin-based Surface-mounted Metal-Organic
Frameworks…………………………………………………………………………………77
5.1 Introduction………………………………………………………………………………………..79
5.2 Computational Methodologies………………………………………………………….................83
5.3 Results and Discussions…………………………………………………………………………...84
5.4 Conclusions………………………………………………………………………………………..86
6. Computational Screening of Phthalocyanine-based Surface-mounted Metal-Organic
Framework…………………………………………………………………………………..89
5.1 Introduction………………………………………………………………………………………..91
5.2 Computational Methodologies………………………………………………………….................94
5.3 Results and Discussion………………………………………………………………….................95
5.4 Conclusions………………………………………………………………………………………..99
7. Summary………………………………………………………………………………...101
A. Acronyms………………………………………………………………………………..109
B. Appendices………………………………………………………………………………111
B.1 Supporting Information of Chapter 3…………………………………………………...111
B.2 Supporting Information of Chapter 4…………………………………………………...129
C. Bibliography…………………………………………………………………………….145
D. Acknowledgement………………………………………………………………………161
1
Abstract
For inorganic semiconductors such as silicon, crystalline order leads to bands in the electronic structure
which give rise to drastic differences with respect to disordered materials. Distinct band features lead
to photo-effect, and the band structure can be tuned to optimize the performance of the photovoltaic
(PV) device. An example is the presence of an indirect band gap. For organic semiconductors, such
effects are typically precluded, since most organic materials employed are disordered, which hampers
their characterization and theoretical analysis.
The inspiration for this thesis came from the very first evidence of an indirect band gap exhibited by
highly ordered and crystalline porphyrin-based surface-mounted metal-organic framework (PP-based
SURMOF) material [J. Liu et al. Angew. Chem. Int. Ed. 2015, 54, 7441]. The presence of an indirect
band gap should in principle result in suppressed charge recombination and efficient charge separations
which would significantly enhance the PV device performance. However, the energy gain from the
electronic band dispersion in the reported Pd-PP-Zn-SURMOF is far too low (≈5 meV) and results in a
very low photocurrent generation (efficiency 0.2%), which is certainly not sufficient for the application.
Another noticeable shortcoming is the weakly absorbing Q-bands of the employed PP chromophore
(Pd-metal containing porphyrinoid, Pd-PP) in the visible region of the solar spectrum. Nevertheless,
this novel research has highlighted the potential to improve the photophysical properties of PP-based
SURMOFs by (i) introducing various functional groups or metal ions to the PP-core and (ii) controlling
the PP-stacking behavior in layered materials.
To overcome the posed shortcomings of the PP-MOF prototype PV material and to exploit the potential
of PP-based SURMOFs, we have employed the following approach to increase the light absorption and
the electronic band dispersion. Firstly, we proposed a computationally feasible simplified time-
dependent approach to investigate the light absorption properties of PP derivatives or related PP-
containing materials. Secondly, we predicted the light absorption properties of multi-functionalized PPs
(i.e. tuning the weakly absorbing Q-bands), thus allowing us to identify different PP linkers with
different light absorption properties, allowing to bridge the so-called green gap. Finally, we
incorporated the most promising PP linkers for the construction of SURMOFs and applied state-of-the-
art DFT methods in various approximations to optimize the PP-stacking behavior to achieve the desired
photophysical properties. Besides PPs, we have extended our investigations to phthalocyanines (PCs)
as alternative individual SURMOF building blocks, because they do not only exhibit structural
robustness and stability but also possess enhanced absorption in the visible and the near IR spectral
regions in comparison to PPs. Hence, the exploitation of PCs could enrich the library of SURMOFs
with the desired optical quality.
2
3
Chapter 1
Introduction
"I’d put my money on the sun and solar energy. What a source of power!
I hope we don’t have to wait until oil and coal run out before we tackle that." – Thomas Edison
1.1 Energy Sources
Energy has been one of the fundamental prerequisites for human activity and has played a
crucial role in human history. The development and success of human industrialization have
mainly been driven by using fossil fuels as an energy source. However, the continued use of
fossil energy is linked to harmful impacts on the global climate and has forced us to examine
alternative forms of energy sources that are eco-friendly, sustainable, and economical.
Prominent and possible resources that are alternative to fossil fuels include biomass, solar,
wind, geothermal, and nuclear energy. All these possible energy sources can certainly assist us
in reducing our dependence on fossil fuels. However, among all, solar energy has the unique
potential as it is readily available and renewable at the same time to meet a broad scope of
current global energy demand and remains an attractive source of energy.
1.2. Photovoltaics
Harnessing solar energy, to create an artificial source of energy in the form of electricity or as
fuel is one of the top priorities in the 21st century. The direct capture of solar energy by green-
clean technology is a valuable option to reduce human dependence on fossil fuels as an energy
source. Therefore, there is a rapidly growing demand for devices that convert solar energy into
4
electrical energy. Today the highest conversion efficiencies are achieved with photovoltaic
(PV) devices based on inorganic semiconductors like silicon.1 Apart from that, there are many
other promising PV technologies in their rising stage. These mainly include dye-sensitized
solar cells,2 organic solar cells,3 and perovskite solar cells.4 Organic solar cells, also known as
organic photovoltaics (OPVs), are very promising as there is huge interest in the use of organic
materials because they offer a less expensive and non-toxic alternative to silicon and other thin-
film PV technologies.
Although the first successful OPV device was reported in 1986 by Tang et al.5, progress in
improving their efficiency, stability, and scalability is slow, since the search for organic
molecules that are suited as active material in OPV devices is to a large extent still controlled
by empirical approaches. Most organic materials employed in OPV devices are disordered,
which hampers their characterization and theoretical analysis. To overcome these problems,
the employment of suitable crystalline systems with well-defined structure is sought after, as
this would enable the OPV device characteristics to be understood on the grounds of high-level
Figure 1.1 Schematic representation of recombination process of free electrons and holes in a
solid with an indirect and direct band gap. The hole-electron recombination is suppressed in an
indirect band gap solid.
5
electronic structure calculations. Finding such well-defined structures will unlock a promising
new path to the design of optoelectronic materials. The most relevant earlier work6 has
suggested that the formation of an indirect band gap (as schematically shown in Figure 1.1)
might be indeed possible for highly ordered organic materials and represents a condition which
is anticipated to significantly enhance the device performance. It is important to note that in
the case of an indirect band gap, there is fast and highly efficient charge separation and the
charge carrier recombination is strongly suppressed. The advantage of having a regular
arrangement of organic molecules for light-harvesting is demonstrated by exploiting
porphyrins, a class of organic molecules, which are present in many biological systems and
have attracted much attention in light-harvesting or PV applications.7-10
1.3 Porphyrins and Porphyrinoids
Porphyrins (PPs) and their derivatives (also called as Porphyrinoids) are a group of heterocyclic
macrocycle organic compounds derived from the simplest free base PP named “porphin”, to
which a variant of substituents can be connected. Porphin consists of four modified pyrroles
(5-membered organic ring) subunits connected by methine bridges (=CH-) as shown in Figure
1.2. The structure of PP has a stable configuration of single and double bonds with aromatic
Figure 1.2 The unsubstituted porphyrin macrocycle (porphin).
6
character, resulting in a highly conjugated molecule containing 18π-electrons. The PP core is
a tetradentate ligand in which the space available for metal coordination has a maximum
diameter of approximately 3.7 Å. During the metalation of the PP macrocycle, two protons are
removed from the pyrrole nitrogen atoms, leaving two negative charges,11 which could bind
with transition metal ions to form metal-porphyrins (M-PPs). In the PP macrocycle, there are
two distinct sites, the so-called meso- and β-pyrrole positions (Figure 1.2), where electrophilic
substitution can take place with different reactivity.12
The light absorbing properties of PPs constitute one of their most fascinating attributes, which
can be examined by Ultraviolet-Visible (UV-Vis) spectroscopy. The typical absorption
spectrum of PPs (e.g. tetraphenyl PP as shown in Figure 1.3a) consists of a sharp, strongly
intense Soret-band, which is typically located in the near UV region (350 to 450 nm), and four
weakly intense Q-bands located in the visible region (450 to 700 nm). In principle, all the
transitions between the frontier orbitals are allowed based on symmetry rules. However, as the
both highest occupied molecular orbitals (HOMO-1 and HOMO) as well as both lowest
unoccupied molecular orbitals (LUMO and LUMO+1) are nearly degenerated, the electronic
Figure 1.3 a) Typical spectrum of a porphyrinoid consists of a strong Soret-band and four weak Q-
bands in which two of them are transition between the ground states Qx,y(00) and two from the
ground state to the single-excited vibrational state Qx,y(01). Blue lines in the Lewis structure
highlight the π-electrons on which a 18π cyclic polyene model is reasonable; b) Comparison of the
frontier orbitals obtained from DFT calculations of porphyrin and the 18π cyclic polyene model.
7
structure can be approximated by a 18π cyclic polyene model, as suggested by Gouterman,13
where two transitions are allowed between the degenerated frontier orbitals, while two are
forbidden (Figure 1.3b). In Gouterman’s model, the Q-band intensity is almost negligible. Any,
Q-band intensity is due to the distortion of Gouterman’s perfect 18π-electron system. Thus,
two bands arise due to the transition between the ground states Q(0,0) and from the ground
state to the single-excited vibrational state Q(0,1). The presence of the NH protons breaks the
symmetry and further split into two bands each in the no longer degenerated x and y
components: Qx(0,0), Qy(0,0), Qx(0,1), and Qy(0,1) as indicated in Figure 1.3a. The Q-bands
arise from the vibrational coupling are not visible in a standard calculation. Furthermore, a
strong mixing of the transitions was observed for Soret and Q-bands by quantum chemical
studies.14-15 In order to adjust the positions and intensities of characteristic Q-bands, the energy
levels and shapes of frontier orbitals must be tuned. The larger the energy gap between HOMO-
1 and HOMO as well as LUMO and LUMO+1, the stronger will be the absorption intensity of
the Q-bands and vice-versa. Hence, the tuning of energy level can be performed through the
rational design of PP skeleton by modifying the π-conjugation, ring functionalization as well
as inclusion/change of a central metal atom.
Compared to many other photoactive molecules, PPs are not only very effective in
transforming photons into electronic excitations but are also rather stable. In the natural
photosystems, the PPs are usually stacked to yield extended columns along which the excitons
can be transported and the most important operation takes place at a target chlorophyll center,16
where dissociation of the exciton yields an electron and a hole through a process known as
charge separation. Given all that, PPs are among the best-performing organic molecules
regarding photon absorption and charge separation. Numerous previous investigations with
variant approaches17-19 (e.g. vapor phase deposition or self-assembly) have been performed
with the goal to develop well-defined, thin PP layers on various substrates, but the resulting
8
systems do not exhibit a high degree of ordering. In the present thesis, we propose to use a
rather unconventional approach based on metal-organic frameworks (MOFs). The basic idea is
to use PP-containing organic linkers, which are coordinated to metal-or-metal/oxo nodes to
yield crystalline, porous MOFs. In addition to PPs, we would like to extend our studies and
introduce phthalocyanine (PC) as an alternative organic linker. PCs are consisting of four iso-
indole units linked together through nitrogen atoms. PCs possess a 18π-electron aromatic cloud
delocalized over an arrangement of alternating carbon and nitrogen atoms. The replacement of
the meso carbons in PPs by nitrogen linkages, combined with four fused benzo rings
significantly breaks the degeneracy of the frontier orbitals. PCs are not only owing structural
robustness and stability but also possess red-shift of the Q-bands with a significantly increased
absorption intensity as compared to PPs (more details are described in Chapter 6). Also, it is
worth mentioning that the synthesis of PCs is more exhausting and challenging than that of
PPs. This is reflected by the rough numbers of successful PC syntheses, which amounts to over
100,000 for PPs (according to Sci-Finder), but only to 20,000 for PCs. Given all the facts and
figures, we propose to extend the idea of PP-MOF to PC-MOF. This will enable the extension
of MOF application areas to photo-electrochemistry, where the conditions are much harsher.
In the following section, the MOF approach will be described in more detail.
1.4 Metal-Organic Frameworks
Metal-Organic Frameworks (MOFs), also known as porous coordination polymers (PCPs), are
a class of two- or three-dimensional (2D or 3D) materials assembled through coordination
bonds between organic linkers and inorganic connectors of metal ions or clusters (Figure
1.4).20-22 Although the first 3D coordination polymer was published by Saito and co-workers
in 1959,23 the first MOF constructed by organic linkers and metal-ions resulting in a structure
with potential voids was introduced by Yaghi et al.24-26 in the late 1990s. Since then, thousands
9
of MOF structures have been reported with a variety of constituents, geometry, size, and
functionality.27
MOFs show an extraordinarily high porosity with up to 9.000 m2/g combined with a high
crystallinity has not been surpassed by any other porous material till date.28 These unique
properties have opened the door for the MOF research to grow significantly, and consequently,
MOFs have attracted considerable attention in many applications, including gas storage,29-30
gas separation,31-33 sensing,34-35 catalysis,36-38 and drug-delivery.39 Besides conventional
applications of 3D (bulk) MOFs as materials for gas storage or separation, recently their
optical,40-42 electrical,43-45 and magnetic properties46-48 have attracted increasing attention.
However, the bulk MOF materials are not well suited for investigating the optical properties
since the light scattering by the powder particles/pellets hamper a thorough optical
characterization. For these purposes, MOF thin films are much better suited and rapidly
growing area. Recently, in a review article Fischer et al.49 distinguished the MOF thin films
into two classes: polycrystalline and surface-mounted MOFs (SURMOFs). The polycrystalline
films are generally regarded as an assembly of randomly oriented MOF crystals on a surface.
The thickness of these films is usually related to the size of MOF crystals/particles and ranging
up to micrometers. The second class of MOF thin film is emerging, referred to as SURMOFs.
These films consist of ultrathin (in the nanometer range) MOF multilayers that are perfectly
Figure 1.4 Schematic of the construction of a 3D MOF via the reticular chemistry approach:
stitching of organic linkers and metal connectors to build metal-organic frameworks.
10
oriented and homogeneously deposited on the surface. In the following section, the SURMOF
approach will be described in some more details.
1.5 Surface-mounted Metal-Organic Frameworks
SURMOFs are crystalline, highly oriented MOF thin films which are deposited on the surface
of a given substrate by employing Liquid Phase Epitaxial (LPE) growth scheme in layer-by-
layer (LbL) fashion, introduced by Wöll and Fischer50-51 in 2007. The most notable difference
of LPE-approach compared to the conventional solvothermal method52 yielding MOF powder
is the stepwise growth of the MOFs on a –COOH-functionalized surface, by repeated
immersion cycles, first in a solution of the metal precursor and subsequently in a solution of an
organic linker, as shown in Figure 1.4. Another notable difference, it is mandatory to deposit
the MOFs on conducting and, if possible, transparent substrates for being able to investigate
photophysical properties. Also, it is worth mentioning that not all MOF types are well-suited
for the LPE-approach. For example, attempts to grow ZIF-8 thin films were unsuccessful unless
a special synthetic route had to be formulated (replacing the ethanol solvent, used in most other
MOF thin film syntheses by methanol).53 Nonetheless, in the case of PP-based SURMOFs, the
LPE approach has already been successfully applied to fabricate thin films, first by J. Hupp
and co-workers, and later by C. Wöll and co-workers. To extend the idea of PP-MOF thin films,
only very few papers concerning PC-MOFs have been published to date54-56 and as per our
knowledge, no previous literature was found for PC-MOF thin films. To highlight the fact of
insufficient results is substantial experimental effort requires to synthesize PC compounds, and
especially functionalized PCs (more details are described in Chapter 6).
In contrast to other MOF thin films synthesized by different techniques (e.g. mother-solution,
dip coating, electrochemical growth, etc.), SURMOFs exhibit several unique properties,57-59
11
namely: (a) monolithic, crystalline, and highly-oriented MOF layers; (c) smooth and
homogeneous morphologies; (b) controllable thickness and growth orientations; (d) low
defects densities; (e) allows well-defined MOF-on-MOF multilayer systems. It is also worth to
mention that the templating effect gives typically higher-symmetry structures compared to the
solvothermal approach (e.g. P4 for SURMOF-2).60 These properties of SURMOFs make them
perfectly suitable candidates for membrane separations, sensor techniques, electronic devices
etc.61-63 More importantly, recent works in the groups of Wöll and Heine have demonstrated
the successful fabrication of crystalline, highly orientated PP-MOF thin films and their use as
a platform in the application of light-harvesting and conversion of solar energy. In the
following section, a state of art for PP-MOF thin films will be discussed in a detailed manner.
1.6 Porphyrin based Metal Organic Frameworks
In the past decades, PPs and their derivatives have attracted much attention as an interesting
platform in the construction of MOFs. The first PP-based coordination polymer was reported
in 1991,64 however the first PP-MOF was successfully synthesized in 2006 by self-assembly
of a 2D coordination network. The characteristics of N2 adsorption has indicated that this
coordination network has uniform micropores and gas adsorption cavities.65 Since then, an
exponential increase in the synthesis of various kinds of PP-MOF structures has been
Figure 1.4 Schematic of the layer-by-layer (LbL) growth of MOFs on a functionalized substrate by
repeated cycles of immersion in solution of metal precursor and subsequently solution of an organic
linker. Between steps, the material is rinsed with solvent and typical thickness range is 100-200 nm.
12
observed.66 As discussed earlier, we are interested in a particular class of MOF thin films,
known as SURMOFs, with regard to their electrical and optical properties and applications. An
excellent description of the present status regarding applications exploiting electrical and
optical properties of MOFs is provided by the review from Falcaro, Allendorf, and Ameloot,67
while in the review by Liu and Wöll, the focus is on MOF thin films.68
H. Kitagawa and co-workers reported the fabrication of a perfect preferentially oriented
nanofilm of MOFs on surface-no.1 (NAFS-1), consisting of Co2+ substituted PP building units.
This was achieved by applying the layer-by-layer growth technique coupled with the Langmuir
Blodgett (LB) method.69 Subsequently, the authors have applied the same technique to prepare
NAFS-2 consisting of free base substituted PP building units coupled with Cu2 paddlewheel
dimers on a surface. The interlayer spacing in NAFS-2 varied while retaining the same in-plane
molecular arrangement by employing different molecular building units than for the previously
reported NAFS-1, and maintains its highly crystalline order above 200 °C.70
J. Hupp and co-workers have fabricated pillar-layered paddlewheel type PP-based MOFs on
functionalized surfaces using the LbL growth technique. The obtained PP-MOF thin films are
preferentially oriented, highly porous, and have controlled thickness. Long-range energy
transfer has been demonstrated for MOF films and the reported findings offer useful insights
for the subsequent fabrication of MOF-based solar energy conversion devices.71
In 2015, a study co-authored by C. Wöll and T. Heine72 reported the first evidence of an indirect
band gap formation in an epitaxial MOF/SURMOF. The investigated SURMOF constructed
by Zn-paddlewheel units and Pd-porphyrinoid linkers using LbL growth technique, and exhibit
photocarrier generation efficiency of 9.510-2. The electronic structure calculation for such a
system displays that layers are stacked in AAA fashion within a square lattice. Furthermore,
this MOF-system reveals a small but distinct dispersion (≈5 meV) in both conduction and
13
valence band leading to the formation of an indirect band gap. This novel finding demonstrates
that the solid-state properties of PP-based SURMOFs offer a huge potential for OPVs.
Subsequently, C. Wöll and co-workers73 have demonstrated the fabrication of a new class of
epitaxial PP-based SURMOF incorporating electron donor diphenylamine (DPA) groups into
the PP-macrocycle, which exhibits the highest photocarrier generation efficiency of up to
3.010-1 reported so far. Although this value is still rather low, the study has highlighted the
potential for improving the performance of these systems by adding electron donor or acceptor
groups to the PP linkers and by optimizing the device architecture.
Motivation, Objective, and Outline of the Thesis
The motivation of the thesis is led by the very first evidence of an indirect band gap exhibited
by highly ordered and crystalline PP-SURMOF. The photovoltaic efficiency of the reported72
PP-SURMOF amounts to only 0.2% and is thus far too low for realizing a competitive device.
However, the study has highlighted the potential to improve the photophysical properties of
PP-SURMOFs by functionalizing PP-core and optimizing their layered stacks within material.
The overarching focus of the thesis to proceed with an interesting class of photoactive organic
molecules, PPs and their derivatives as organic linkers and to utilize the SURMOF approach
for designing crystalline, highly ordered, and well-defined organic thin films. Considering the
light-harvesting properties of PPs, they can be tuned to maximize the light-to-electricity
conversion (i.e. tuning the positions and intensities of weakly Q-bands). However, tuning of
PPs depends on the side groups (e.g. meso and β-positions) at the PP-core or the presence of
central metal ions, different intermolecular interactions can be either supported or blocked, and
by that the photoelectric and photophysical properties. Undoubtedly, there is a huge range of
combinations possible to substitute the variant of PPs and building SURMOFs out of them.
Here, the computational modelling plays a pivotal role, not only to screen a large library of PPs
14
and their corresponding SURMOFs, but also circumvents the huge experimental synthesis
effort and resources. Among the large number of possibilities, three particularly interesting PPs
have been identified by combining rational design using computer simulation methods.
Moreover, the computational modelling and screenings of the anticipated PP-SURMOF
structures will also provide an insight for tailoring their photoelectric and photophysical to
achieve the remarkable efficiency of this novel OPV device.
The thesis is organized as follows: The current Chapter (Chapter 1) has introduced the main
phenomena and systems of interest. Chapter 2 introduces the theoretical background and
methods, as well as the computational protocols that have been applied to investigate the posed
problems and achieve the respective goals. In Chapter 3, we investigate the capability of
various variants of time-dependent density functional theory (TD-DFT) for predicting the UV-
Vis spectra of porphyrinoids having a diverse extent of conjugation, ring functionalization, as
well as inclusion/modification of a central metal atom. Chapter 4 lays out how the molecular
and electronic structure of variously substituted PPs can be tuned for increasing their absorption
efficiency with help of the identified TD-DFT approach in Chapter 3. Subsequently, we
demonstrate the power of computational screening methods for the construction of selected
PP-based SURMOF structures with the desired photophysical properties. Chapter 5 introduces
a promising PP-SURMOF modeled in Chapter 4 to exploit its band dispersion characteristic as
a function of the rotation of the employed functional groups with respect to the PP core (in a
bulk framework). In Chapter 6, we extend our studies from PPs to PCs as alternative SURMOF
building blocks and introduce some of the preliminary calculated results for the same. Finally,
the summary, acronyms, appendices, bibliography, and acknowledgement are presented.
15
Chapter 2
Theory and Methods
"If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet."
– Niels Bohr
In this Chapter, we give a brief survey over quantum chemistry and we review the various
theoretical methods that are utilized in the doctoral studies. In Section 2.1, we introduce the
fundamental Schrödinger equation, which is the basis for nearly all further theories and
methods. Section 2.2 elaborates on the theory behind the quantum chemical ground state
methods. Most importantly, time-independent Kohn-Sham based density-functional theory
(DFT), which is the workhorse for proper description of electronic ground state. Section 2.3
lays out flavors of time-dependent density functional theory (TD-DFT), which can efficiently
and reliably compute the electronic excited states of large molecular or extended biological
systems. In Section 2.4, we discuss the density functional tight binding (DFTB) method which
allows us to determine the electronic structure properties of systems with increasing complexity
such as larger molecules, clusters, and solids. Section 2.5 discusses the treatment of periodic
crystalline solids by exploiting their lattice periodicity in order to calculate their electronic
structure properties efficiently. Finally, in Section 2.6, applied computational chemistry
toolbox are briefly discussed.
16
2.1 Quantum Chemistry
Quantum chemistry applies quantum mechanics to address numerous aspects and phenomena
associated with the behavior of electrons and thus of chemistry. It aims, in principle, to solve
the Schrödinger equation, postulated by the Nobel Laureate Erwin Schrödinger in 1925, later
published in 1926.74 It represents the most significant landmark in the given field. However,
its complexity for all but the simplest of atoms or molecules requires simplifying assumptions
and approximations, establishing a balance between accuracy and computational effort.
2.1.1 The Schrödinger Equation
In general, the time-independent Schrödinger Equation (SE) is the basis for almost all quantum
chemical methods and used for the estimation of the electronic structural properties of the
molecular and solid-state systems. It can be expressed in equation 2.1 as follows:
𝐻𝛹 = 𝐸𝛹 (2.1)
Here, H is the Hamiltonian operator, which defines all the properties of the system, 𝛹 is the
wave function of the system comprising of n electrons and N nuclei in terms of atomic units,
and E is the total energy of the system. The typical form of the Hamiltonian takes into account
five contributions to the total energy of the system: the kinetic energy of the electrons (𝑇𝑛) and
the nuclei (𝑇𝑁), the attractive potential between the electrons and the nuclei (𝑉𝑛𝑁), and the inter-
electronic (𝑉𝑛𝑛) and the inter-nuclear (𝑉𝑁𝑁) repulsive potentials. Thus, for a system of n+N
interacting particles (electrons and nuclei), the Hamiltonian can be expressed as:
𝐻 = 𝑇𝑛 + 𝑇𝑁 + 𝑉𝑛𝑁 + 𝑉𝑛𝑛 + 𝑉𝑁𝑁 (2.2a)
or
17
𝐻 = −∑1
2∇𝑖
2𝑛𝑖 − ∑
1
2𝑀𝐼∇𝐼
2𝑁𝐼 − ∑ ∑
𝑍𝐼
ǀ𝑟𝑖 −𝑅𝐼 ǀ 𝑁
𝐼𝑛𝑖 + ∑
1
ǀ𝑟𝑖 −𝑟𝑗 ǀ
𝑛𝑖≠𝑗 + ∑
𝑍𝐼𝑍𝐽
ǀ𝑅𝐼 −𝑅𝐽 ǀ𝑁𝐼≠𝐽 (2.2b)
where ∇2 is the Laplacian acting on particles, 𝑟 stands for the particle position, whereas M, Z
and R stand for the nuclear mass, charge, and positions, respectively. Indices i and j denote
electrons with different spatial positions, while I and J are used for nuclei of different type and
spatial positions.
For any kind of property, the SE (Eq. 2.1) must be solved. However, the analytical solutions
for the SE are only possible for a few simple one-particle systems. While in the case of many-
particle systems, the number of nuclei and electrons are very high, leading to a complex
Hamiltonian operator. In fact, accurate wave function description of such systems is then
practically impossible because of the correlated motion of particles. That is, the Hamiltonian
in equation 2.2 includes pairwise interactions (attraction and repulsion) which means no
particle is moving independently. To simplify the problem, it is important to employ some
approximations, and in this context, the Born-Oppenheimer approximation is quite useful.
2.1.2 The Born-Oppenheimer Approximation
In Born-Oppenheimer (BO) approximation, we consider the speed of the nuclei and electrons.75
The nuclei speed is very less compared to the electrons as the nucleus is ~1800 times much
heavier than the mass of the electron for a hydrogen-like atom. Hence, the nucleus is presumed
to be stationary (or in rest) with respect to electrons. As a result, the total wave function can be
separated into two components: one is electronic and other nuclear wave function.
Consequently, we focus on the electronic wave function in which the electronic Hamiltonian
operates can be expressed as:
𝐻 = 𝑇𝑛 + 𝑉𝑛𝑛 + 𝑉𝑛𝑁 (2.3a)
18
or
𝐻 = −∑1
2∇𝑖
2𝑛𝑖 + ∑
1
ǀ𝑟𝑖 −𝑟𝑗 ǀ
𝑛𝑖≠𝑗 − ∑ ∑
𝑍𝐼
ǀ𝑟𝑖 −𝑅𝐼 ǀ 𝑁
𝐼𝑛𝑖 (2.3b)
In general, the BO approximation is an extremely mild one and not fully sufficient to solve of
the SE for larger, more realistic, but also computationally demanding many-electron systems.
Hence, the equation 2.3 requires even further modifications. In this context, other
approximations76-77 such as Hartree-Fock theory (HF theory), density functional theory (DFT)
etc. are extremely useful. In HF theory, the wave function for an n-electron system is generally
approximated by the linear combination of Hartree products of orbitals within a Slater
determinant78 which is essential for fulfilling the anti-symmetric behavior of particles.
However, the major drawback of HF theory is the absence of electron-electron correlation in
its single determinant wave function, which results in large deviations when it comes to
comparing with experimental data. To address this drawback, more accurate wave function-
based methods such as configuration interaction (CI) and other post-HF methods are available
which explicitly include electron-electron correlation. However, the high computational cost
to accuracy ratio limits their further usage. In this case, the DFT is an alternative method that
not only recovers the electron-electron correlation but quite efficient as well.
2.2 Density Functional Theory
DFT is a well-established quantum-mechanical method for efficiently solving the SE of
complex many-electron systems. It has gained huge popularity among theoreticians, to
calculate the electronic structure and properties of the many-electron system by consideration
of its electron density. Moreover, it has proven based on the pragmatic observation that it is
less computationally demanding than other methods with similar accuracy for various
applications in physics and chemistry. This section provides a detailed introduction to the
19
basics of DFT as it is used extensively in this thesis to calculate the electronic structure
properties of molecular and extended systems with respect to their light-harvesting properties
and solar energy conversion-based applications.
2.2.1 The Hohenberg-Kohn Theorems
The theoretical background of DFT was first established in 1964 by two major Hohenberg-
Kohn (HK) based theorems.79 The 1st HK theorem states that the ground state properties of
many-electron system are uniquely determined by the ground state electron density ρ(r ) that
relies on only three spatial coordinates. It sets down the basis for reducing the many-body
problem of n electrons with 3n spatial coordinates to three spatial coordinates, through the use
of functionals of the electron density. The 2nd HK theorem introduces a term universal total
energy functional 𝐸[𝜌(𝑟 )] with respect to electron density 𝜌(𝑟 ) under the external potential of
𝑉𝑒𝑥𝑡(𝑟 ). The term 'universal' means that this functional can be applied to any electronic system
independently of 𝑉𝑒𝑥𝑡(𝑟 ). The functional is written in equation 2.4 as follows:
𝐸[𝜌(𝑟 )] = 𝐹𝐻𝐾[𝜌(𝑟 )] + ∫𝑉𝑒𝑥𝑡(𝑟 )𝜌(𝑟 )𝑑𝑟 (2.4)
where, 𝐹𝐻𝐾[𝜌(𝑟 )] contains the kinetic energy and the electron-electron interactions. To sum-
up, from the above-equation, the exact ground-state energy of the many-body system can be
determined variationally by minimizing the total energy as a functional of the electron density.
However, the explicit forms of the two terms which compose the functional 𝐹𝐻𝐾[𝜌] are
unknown. Therefore, further improvement of the theory is needed.
2.2.2 The Kohn-Sham Formalism
In 1965, Kohn and Sham proposed a new formalism80 by introducing the concept of a fictitious
system of non-interacting particles. The scheme was to map a system of interacting electrons
onto a system of non-interacting electrons in an effective potential 𝑉𝑒𝑓𝑓(𝑟 ), known as the Kohn-
20
Sham (KS) potential, which is constructed such that the density of the fictitious system equals
the density of the real, interacting system. Thus, in KS-DFT, the electronic wave function of
the fictitious system is then represented by a single Slater determinant, consisting of the single
electron wave functions or KS orbitals 𝜓𝑖(𝑟 ). The electron density can thus be expressed in
equation 2.5 as follows:
𝜌(𝑟 ) = ∑ |𝜓𝑖(𝑟 )|2
𝑖 (2.5)
According to the KS-DFT scheme, the total energy functional can then be calculated as follows:
𝐸𝐾𝑆−𝐷𝐹𝑇 = 𝑇𝐾𝑆 + 𝐸𝐻 + 𝐸𝑥𝑐 + 𝐸𝑒𝑥𝑡 (2.6)
Figure 2.1 Flow chart of a typical time-independent KS-DFT calculation
Initial Guess
Calculate Effective Potential
Solve Kohn Sham Equation
Calculate Electron Density
Convergence ?No
Yes
Output
Time-Independent Properties
21
Here, 𝑇𝐾𝑆 is the kinetic energy of the non-interacting system of electrons, 𝐸𝐻 is the classical
Coulomb (or Hartree) energy corresponding to electron-electron interaction, 𝐸𝑥𝑐 is the
unknown exchange-correlation interaction that considers all non-classical many-body effects
between electrons, and 𝐸𝑒𝑥𝑡 is the energy from the external field due to the positively charged
nuclei. Furthermore, one can rewrite the KS equation in a wave function form as follows:
[−1
2∇2 + 𝑉𝑒𝑓𝑓(𝑟 )]𝜓𝑖(𝑟 ) = 𝐸𝑖𝜓𝑖(𝑟 ) (2.7)
Here, the effective single-particle potential, 𝑉𝑒𝑓𝑓(𝑟 ) represents the addition of classical
Coulomb potential 𝑉𝐻(𝑟 ), exchange-correlation potential 𝑉𝑥𝑐(𝑟 ) =𝛿𝐸𝑥𝑐[𝜌(𝑟 )]
𝛿𝜌(𝑟 ), and the external
potential 𝑉𝑒𝑥𝑡(𝑟 ). To sum-up, the KS formalism allows to calculate the ground-state energy
and density exactly (see flow-chart in Figure 2.1). However, the exact form of the exchange-
correlation energy, 𝐸𝑥𝑐, is unknown yet, so further approximations are needed to enable
calculations practically in the framework of KS-DFT.
2.2.3 Exchange-Correlation Functionals
The exchange-correlation (XC) energy functional, 𝐸𝑥𝑐[𝜌(𝑟 )], defined in the KS-DFT can be
expressed as a sum of two terms. One is exchange 𝐸𝑥[𝜌(𝑟 )] and another is correlation part
𝐸𝑐[𝜌(𝑟 )] as follows in equation 2.8.
𝐸𝑥𝑐[𝜌(𝑟 )] = 𝐸𝑥[𝜌(𝑟 )] + 𝐸𝑐[𝜌(𝑟 )] (2.8)
There are different approximations to the XC energy functional available and in the following
subsection, we will describe them in an order of increasing complexity.
22
2.2.3.1 Local Density Approximation
The simplest XC functional depends only on the electron density and occupies the first rung of
Jacob’s Ladder (as shown in Figure 2.2) known as local density approximation (LDA). In this
approximation, a homogeneous electron gas (HEG) is considered, and can be expressed in
equation 2.9 as follows:
𝐸𝑥𝑐[𝜌(𝑟 )] ≈ 𝐸𝑥𝑐𝐿𝐷𝐴[𝜌(𝑟 )] = ∫𝑑3𝑟 𝜌(𝑟 ) Ɛ𝑥𝑐
𝐻𝐸𝐺[𝜌(𝑟 )] (2.9)
where, Ɛ𝑥𝑐𝐻𝐸𝐺[𝜌(𝑟 )] is the XC energy density for a homogeneous electron gas that can, then, be
solved individually as follows:
Ɛ𝑥𝑐𝐻𝐸𝐺 = Ɛ𝑥
𝐻𝐸𝐺 + Ɛ𝑐𝐻𝐸𝐺 (2.10)
LDA mostly works well for materials, where electron density varies slowly, but also displays
shortcomings and large inaccuracies in cases of energetics details, since most real systems have
inhomogeneous density distributions. Therefore, an attempt to correct shortcoming of the LDA,
is addressed by the so-called Generalized Gradient Approximation (GGA).
Figure 2.2 Schematic representation of five different rungs of Jacob’s Ladder (1-5)
23
2.2.3.2 Generalized Gradient Approximations
GGA employs an ingredient that can account for inhomogeneities in the density distributions:
the density gradient, 𝛻ρ in real systems. The GGA functionals occupy the second rung of
Jacob’s Ladder (see Figure 2.2) and the general form is given in equation 2.11 as follow:
𝐸𝑥𝑐𝐺𝐺𝐴[𝜌(𝑟 )] = ∫ 𝑑3𝑟 𝜌(𝑟 ) Ɛ𝑥𝑐
𝐺𝐺𝐴(𝜌(𝑟 ), 𝛻𝜌(𝑟 )) (2.11)
where, Ɛ𝑥𝑐𝐺𝐺𝐴(𝜌(𝑟 ), 𝛻𝜌(𝑟 )) is the XC energy per electron gradient that can, then, be solved
individually as follows:
Ɛ𝑥𝑐𝐺𝐺𝐴 = Ɛ𝑥
𝐺𝐺𝐴 + Ɛ𝑐𝐺𝐺𝐴 (2.12)
The GGA functionals are improved significantly over the LDA and work well for the real
systems, where electron density varies rapidly. However, to further improve their accuracy,
two additional local ingredients such as either the Laplacian of the electron density, ∇2𝜌(𝑟 ), or
the kinetic energy density, 𝜏(𝑟 ) = ∑1
2|∇ 𝜓𝑖
(𝑟 )|2𝑖 can be utilized. From a chemical point of
view, the kinetic energy density is by far more popular and useful ingredient for predicting
charge delocalisation.81 To sum up, XC functionals that rely on either of above-mentioned local
ingredients are known as meta-generalised gradient approximations (meta-GGA or mGGA)
and occupy the third rung of Jacob’s Ladder (see Figure 2.2).
2.2.3.3 Global Hybrids
Despite the systematic improvement offered by the inclusion of physical ingredients (𝛻𝜌, ∇2𝜌,
and 𝜏), gradient corrected functionals are still prone to originate systematic errors due to self-
interaction error (SIE) limitation. 82 The simplest way to explain self-interaction (i.e. electrons
interact with themselves) is to consider the HF description of the one-electron system (e.g. H-
atom), where the electron-electron interaction energy should be zero. That is, the classical
24
“Coulomb” and the non-classical “exchange” energy terms cancel out exactly, making HF one-
electron SIE-free. In case of KS-DFT, since the exact exchange term is replaced by the XC
functional, most functionals are not SIE-free (i.e. 𝐸𝐻[𝜌(𝑟 )] + 𝐸𝑥𝑐[𝜌(𝑟 )] ≠ 0 for the H-atom)
To address the SIE problem, an alternative scheme is to replace the local exchange functional
with the exact exchange functional, while taking a local correlation functional that yields
correlation energy exactly zero for one-electron systems. However, early trials to combine
exact exchange with local correlation of DFT were unsuccessful. In the early 1990s, Becke
introduced an imperfect yet highly effective scheme83 of mixing only a global fraction of exact
exchange with the XC functional from considerations of the adiabatic connection formula.84-87
This successful functional scheme defines the Rung 4 of Jacob’s Ladder (Figure 2.2) and
known as the global hybrid (GH) which take the form given in equation 2.13,
Ɛ𝑥𝑐𝐺𝐻 = 𝑐𝑥Ɛ𝑥
𝐻𝐹 + (1 − 𝑐𝑥) Ɛ𝑥𝐷𝐹𝑇 + Ɛ𝑐
𝐷𝐹𝑇 (2.13)
While given the ongoing rapid pace of functionals development, there is a plethora of XC
functionals available in most of the quantum chemistry codes, so many, in fact, that it would
be impossible to cover all of them in this thesis. The choice of functional mostly depends on
the system of interest and the property to be evaluated. Here, for an overview and extensive
assessment of different rungs of XC functionals (including range-separation or double hybrids),
we would like to refer this excellent review article by N. Mardirossian and M. Head-Gordon.88
2.3 Time-Dependent Density Functional Theory
As mentioned in the previous section, time-independent KS-DFT provides quite an accurate
ground-state electronic structure. So, basic questions from a theoretical chemist and physicist
perspective would be: Is there any time-dependent analogue of the most fundamental HK
theorems and KS equation? Also, what about the characteristic properties which are evolving
25
with time, to name a few, such as UV-Vis spectroscopy, non-linear optics, and photochemistry?
To address these questions, time-dependent density functional theory (TD-DFT) extends the
ideas based on ground-state DFT for the treatment of excited-state and the time-dependent
phenomena.89 In the following, two possible strategies to obtain the excited-state energies and
spectra are discussed. The first one is to propagate the time-dependent KS formalism, referred
to as real-time TD-DFT,90-91 and the other one is the time-dependent linear-response
formalism,92 which rapidly took off the application of TD-DFT.
2.3.1 The Runge-Gross Theorem and Time-Dependent Kohn Sham Formalism
The first theoretical foundation of TD-DFT was established in 1984 by the Runge-Gross (RG)
theorem,93 which is a time-dependent analogue of the HK theorem. It states that for a system
initially in its stationary ground-state exposed to time-dependent perturbation, the time-
dependent charge density, 𝜌(𝑟 , 𝑡), determines the time-dependent external potential, 𝑉𝑒𝑥𝑡(𝑟 , 𝑡)
up to a spatially constant function of time, 𝐶(𝑡), and thus a time-dependent wave function can
be expressed as follows:
𝛹(𝑟 , 𝑡) = 𝛹[𝜌(𝑡)](𝑡)𝑒−𝑖𝛼(𝑡) with (𝑑
𝑑𝑡)𝛼(𝑡) = 𝐶(𝑡) (2.14)
The RG theorem implies that there is one-to-one correspondence of the time-dependent
external potential and time-dependent density, which constitutes the foundation for the time-
dependent KS equations, (analogy to the time-independent KS equations 2.7) as follows:
𝑖𝜕
𝜕𝑡𝜓𝑖(𝑟 , 𝑡) = [−
1
2∇2 + 𝑉𝑒𝑓𝑓
𝑇𝐷 (𝑟 , 𝑡)] 𝜓𝑖(𝑟 , 𝑡) (2.15)
Here 𝑉𝑒𝑓𝑓𝑇𝐷 is the effective single-particle potential (extended from time-independent KS-DFT)
evolving with time is the sum of classical Coulomb potential 𝑉𝐻(𝑟 , 𝑡), exchange-correlation
potential 𝑉𝑥𝑐(𝑟 , 𝑡), and the external potential 𝑉𝑒𝑥𝑡(𝑟 , 𝑡). It can be expressed as follows:
26
𝑉𝑒𝑓𝑓𝑇𝐷 (𝑟 , 𝑡) = 𝑉𝐻(𝑟 , 𝑡) + 𝑉𝑥𝑐(𝑟 , 𝑡) + 𝑉𝑒𝑥𝑡(𝑟 , 𝑡) (2.16)
The time-dependent density can thus be calculated from the time-dependent KS equations (see
flow-chart in Figure 2.3) by solving equation 2.15, is given by 𝜌(𝑟 , 𝑡) = ∑ |𝜓𝑖(𝑟 , 𝑡)|2
𝑖 . Like
in DFT, the exact functional form of the time dependent XC potential, 𝑉𝑥𝑐(𝑟 , 𝑡)
𝑉𝑥𝑐(𝑟 , 𝑡) =𝛿𝐸𝑥𝑐[𝜌(𝑟 ,𝑡)]
𝛿𝜌(𝑟 ,𝑡) (2.17)
is not known, therefore approximations are required. To address this problem, the simplest
possible approximation of the time-dependent XC potential is the adiabatic local-density
approximation (ALDA). It employs the functional form of the static LDA with a time-
Figure 2.3 Flow chart of a typical time-dependent KS-DFT calculation
Initial Guess
Calculate Effective Potential
Solve Kohn Sham Equation
Calculate Electron Density
Convergence ?No
Yes
Output
Time-Dependent Properties
27
dependent density, where the value of 𝑉𝑥𝑐(𝑟 , 𝑡) is equal to the time-independent HEG potential.
This approximation allows to use the standard ground-state functionals for the TD-DFT
calculations, i.e. it can also be extended to adiabatic GGA, meta-GGA and hybrids.94
Despite some recent successful applications of the time-dependent KS equations in the
literature,95-96 it is still having the status of an expert’s approach. In the following sub-section,
we introduce the linear response TD-DFT, which is more convenient and easily implemented
in the most standard quantum chemistry codes.
2.3.2 The Linear Response Formalism
2.3.2.1 The Linear Response TD-DFT and TDA Approaches
The RG theorem and the time-dependent KS formalism represents the most essential
ingredients to construct the linear response (LR) formalism for TD-DFT, which was first
developed by M.E. Casida in the mid-1990s.92 The LR-TD-DFT is also referred as Casida’s
equation and can be defined by the linear time-dependent response of the system to a time-
dependent external electric field, which describes the change in electron density in response to
a time-varying external potential. Here, we would like to refer to the excellent review articles
by A. Dreuw et al.97 and M. E. Casida et al.89 for extended details. The TD-DFT response
problem is expressed by the following non-Hermitian eigenvalue equation:
( 𝐴 𝐵𝐵∗ 𝐴∗) (
𝑋𝑌) = 𝜔 (
1 00 −1
) (𝑋𝑌) (2.18)
Here, A and B are excitation and de-excitation matrices, respectively, X and Y are eigenvectors
and ω is the eigenvalue. For hybrids, the elements of matrices A and B are defined as:
Aia,jb = δij δab (ϵa - ϵi) + 2(ia | jb) – ax (ij | ab) + (1 - ax) (ia | fxc | jb) (2.19)
28
Bia,jb = 2(ia | bj) – ax (ib | aj) + (1 - ax) (ia | fxc | bj) (2.20)
The first term in matrix A is the difference of the orbital energies, where δ is the Kronecker
delta, i,j and a,b correspond to occupied and unoccupied orbitals respectively, and ax represents
the amount of non-local Fock exchange (ax = 0 for pure DFT functionals). The last two terms
in matrix A and the elements of matrix B are the two-electron integrals, stem from the linear
response of the Coulomb and XC ( 𝑓xc ) operators. Here 𝑓xc corresponds to second functional
derivative of the XC energy (or XC kernels) and can be written using ALDA:
𝑓xc =𝛿2𝐸𝑥𝑐
𝛿𝜌(r, t) 𝛿𝜌(r´, t´) (2.21)
A popular approximation to the linear response is the Tamm-Dancoff approximation (TDA).98
This approximation corresponds to neglecting the matrix B, thus, instead of solving two
eigenvalue problems as in TD-DFT, only one eigenvalue problem needs to be solved which is
given in equation 2.22:
𝐴𝑋 = 𝜔𝑋 (2.22)
Here, the definition of the matrix elements of A is still the same as in equation 2.19. In the
TDA, the calculated excitation energies are only slightly larger than the full linear response
TD-DFT, but come at lower computational cost (an order of 2).98 Furthermore, the TDA can
be utilized to circumvent the so-called triplet instabilities.99 However, a well-known drawback
of the TDA is that the sum rules are no longer fulfilled, which results in poor description of
calculated oscillator strengths.100 To sum up, the TDA suggests that excitation energies can be
obtained in a good approximation within simplifying scheme of full TD-DFT.
Despite successful applications, TD-DFT on the basis of popular XC functionals and the so-
called adiabatic approximation still suffers accuracy limitations from the electronic SIE which
29
is most evident in the wrong description of charge-transfer (CT), extended π-systems and
Rydberg states.101-105 Thus, like in DFT, it is necessary to include hybrids which employ a large
fraction of HF exact exchange to alleviate the SIE as well as the CT and related problems.
On the other hand, while TD-DFT can efficiently deal with molecular systems beyond the level
of traditional wave function-based methods, the computation of an entire UV-Vis or circular
dichroism (CD) spectrum of larger molecular or extended biological systems remains a
challenge. To address this challenge, the Grimme group has recently reported two advanced
simplifications to TD-DFT response, the simplified Tamm–Dancoff-Approximation106 (sTDA)
and the simplified Time-Dependent Density Functional Theory approach107 (sTD-DFT). Both
approaches allow extremely fast computations of UV-Vis (and CD) spectra for systems with
up to 1000 atoms. The computational bottleneck of the extremely fast sTDA (or sTD-DFT) is
the determination of the ground state KS orbitals and eigenvalues. In the following sub-section,
the sTDA and sTD-DFT approaches will be described in some more detail.
2.3.2.2 The sTDA and sTD-DFT Approaches
The sTDA approach begins by employing step-by-step three unique simplifications into the
TD-DFT/TDA equation 2.22: (1) The response of the XC functional (last term in equation
2.19) is neglected, to avoid the expensive numerical integration. (2) The two electron integrals
in matrix A are approximated by short-range damped Coulomb interactions of transition density
monopoles. (3) The reduction of the single excitation space. Here, we would like to refer to the
original articles by S. Grimme 106 and C. Bannwarth et al.107 for extended details. To sum up,
the elements of the approximated matrix A (denoted as A′) are then given by in equation 2.23:
A′ ia,jb = δij δab (ϵa - ϵi) +∑ (2𝑞𝑖𝑎𝐴𝑁 𝑎𝑡𝑜𝑚𝑠
𝐴,𝐵 𝛤𝐴𝐵𝐾 𝑞𝑗𝑏
𝐵 − 𝑞𝑖𝑗𝐴𝛤𝐴𝐵
𝐽 𝑞𝑎𝑏𝐵 ) (2.23)
30
Here, the transition charge density 𝑞 is obtained from a Löwdin population analysis.108 A, B are
defined as atoms. 𝛤𝐴𝐵 with the Mataga-Nishimoto-Ohno-Klopman109-111 damped Coulomb
operator. Note that the pre-factor 𝛼𝑥 is dropped, but its effect is accounted for in the 𝛤𝐴𝐵𝐽
.
The modifications explained above are consistently applied also in the sTD-DFT approach.
The matrix A is just replaced by the approximate matrix A′ from sTDA and the matrix B is set
up in a consistent, simplified manner. As mentioned above, the term originating from the non-
local Fock exchange is of Coulomb type in matrix A, but of exchange-type in matrix B. Since
fitting the another set of parameters avoided, the exchange-type Mataga-Nishimoto-Ohno-
Klopman damped Coulomb interaction has been exploited, while keeping the scaling factor
𝛼𝑥. The elements of approximated matrix B (denoted as B′) can be expressed as:
B′ ia,jb = ∑ (2𝑞𝑖𝑎𝐴𝑁 𝑎𝑡𝑜𝑚𝑠
𝐴,𝐵 𝛤𝐴𝐵𝐾 𝑞𝑏𝑗
𝐵 − 𝛼𝑥𝑞𝑖𝑏𝐴 𝛤𝐴𝐵
𝐾 𝑞𝑎𝑗𝐵 ) (2.24)
In summary, these three simplifications along with the simple eigenvalue problem allow
extremely fast computations for a broad energy range spectrum of very large molecular and
extended biological systems.
2.4 Density Functional Based Tight Binding
While DFT methods have been successfully applied to systems of increasing size and
complexity, methods that can incorporate approximations to reduce further the computational
demand, without compromise much with accuracy, are still required. In this case, the density
functional tight binding method (DFTB) is quite reliable. In this section, we will briefly
introduce the DFTB method and mainly focus on one of its flavors, the self-consistent charge
DFTB (SCC-DFTB) which is thoroughly utilized in this thesis (see Chapters 4-6).
31
DFTB112-114 is an approximate method based on KS-DFT (see section 2.2) within the Linear
Combination of Atomic Orbitals (LCAO) ansatz. Besides, DFTB is more align towards tight-
binding (TB) scheme and in fact, can be visualized as a non-orthogonal tight-binding scheme
based on DFT parameterization. Since DFTB was first introduced in the 1980s as a non-self-
consistent method112, three major extensions of DFTB have been systematically developed
over the years. These include (1) the self-consistent charge extension,115 known as SCC-DFTB,
(2) the formulation for the spin-dependent calculations116 and (3) the time-dependent treatment
of excited states.117 Generally, TB methods are utilized to calculate the electronic band
structures for solids or periodic systems. However, SCC-DFTB is not restricted to this and can
be utilized for calculating the full electronic structures i.e. total energies. SCC-DFTB
(approximation to KS-DFT) is computationally much faster than DFT and does not demand
multiple empirical parameters. In fact, the parameters are consistently gathered from DFT
treatments of few molecular systems. Since SCC-DFTB (with right parameter set) is
chemically more precise than the force-field methods, it is well utilized for larger systems118-
119 and even at longer time scales than DFT.
The theoretical approximation which is utilized for DFT as a basis for TB method is given by
Foulkes and Haydock,113 where the electronic density 𝜌 is expressed as a reference density 𝜌0,
plus a small fluctuation 𝛿𝜌, and finally expressed in equation 2.25,
𝜌 = 𝜌0 + 𝛿𝜌 (2.25)
This electronic density 𝜌 = [𝜌0 + 𝛿𝜌] is then employed in the KS-DFT total energy (see
equation 2.6) and can be rewritten as:
𝐸𝐾𝑆−𝐷𝐹𝑇[𝜌0 + 𝛿𝜌] = 𝑇𝐾𝑆[𝜌0 + 𝛿𝜌] + 𝐸𝐻[𝜌0 + 𝛿𝜌] + 𝐸𝑥𝑐[𝜌0 + 𝛿𝜌] + 𝐸𝑒𝑥𝑡[𝜌0 + 𝛿𝜌] (2.26)
32
Afterwards, 𝐸𝑥𝑐[𝜌0 + 𝛿𝜌] is expanded in a Taylor series up to the second-order term, and it is
given in equation 2.27 as follows:
𝐸𝑥𝑐[𝜌0 + 𝛿𝜌] = 𝐸𝑥𝑐[𝜌0] + ∫𝛿𝐸𝑥𝑐
𝛿𝜌 𝛿𝜌 𝑑𝑟 +
1
2 ∬
𝛿2𝐸𝑥𝑐
𝛿𝜌𝛿𝜌′ 𝑉𝑥𝑐 𝛿𝜌𝛿𝜌′𝑑𝑟 𝑑𝑟 ′ (2.27)
followed by substitution of equation 2.27 into 2.26 by using the definition, 𝑉𝑥𝑐 =𝛿𝐸𝑥𝑐
𝛿𝜌, with this
total energy can be written as follows:
𝐸𝑡𝑜𝑡 ≈ 1
2 ∬
𝛿2
𝛿𝜌𝛿𝜌′ 𝑉𝑥𝑐 𝛿𝜌𝛿𝜌′𝑑𝑟 𝑑𝑟 ′ + 1
2∬
𝛿𝜌𝛿𝜌′
|𝑟 −𝑟 ′|𝑑𝑟 𝑑𝑟 ′
−1
2∬
𝜌0𝜌0′
|𝑟 −𝑟 ′|𝑑𝑟 𝑑𝑟 ′ + 𝐸𝑥𝑐[𝜌0] − ∫𝑉𝑥𝑐[𝜌0] 𝜌0 𝑑𝑟 + 𝑉𝑛𝑛 (2.28a)
In SCC-DFTB,115 the total energy expression, 𝐸𝑡𝑜𝑡𝑆𝐶𝐶−𝐷𝐹𝑇𝐵 is derived from the second order-
expansion of KS-DFT energy, and can be expressed in equation 2.28b:
𝐸𝑡𝑜𝑡𝑆𝐶𝐶−𝐷𝐹𝑇𝐵 = 𝐸𝑒𝑙𝑒𝑐 + 𝐸𝑟𝑒𝑝 = 𝐸𝐵𝑆 + 𝐸𝑆𝐶𝐶 + 𝐸𝑟𝑒𝑝 (2.28b)
where, 𝐸𝑒𝑙𝑒𝑐 denotes the electronic and 𝐸𝑟𝑒𝑝 the repulsive energy term. The 𝐸𝑒𝑙𝑒𝑐 consists of
the zero order (𝐸𝐵𝑆) and the second order (𝐸𝑆𝐶𝐶) terms. The zero-order term, also known as
the band-structure (BS) term, is the summation of energy over all the occupied eigenstates
represented by LCAO and is given in equation 2.29 as follows:
𝐸𝐵𝑆 = ∑ [𝑛𝑖 휀𝑖]𝑣𝑎𝑙𝑒𝑛𝑐𝑒 𝑒𝑖 = ∑ 𝑛𝑖⟨𝜓𝑖|𝐻0|𝜓𝑖⟩
𝑣𝑎𝑙𝑒𝑛𝑐𝑒 𝑒𝑖 (2.29)
In equation 2.29, 𝑛𝑖 denotes occupation, and, 휀𝑖 is the orbital energy for each of the occupied
electronic eigenstates signified by 𝜓 and the basis-set used for these calculations is minimal.
The diatomic distance related Hamiltonian matrix elements are calculated by DFT and stored
in SCC-DFTB parameter files, called a Slater-Koster tables. Besides 𝐸𝐵𝑆, the second term, i.e.
=𝐸𝑒𝑙𝑒𝑐
=𝐸𝑟𝑒𝑝
33
𝐸𝑆𝐶𝐶 which is derived from the charge density fluctuations is included in total energy
expression. The 𝐸𝑆𝐶𝐶 term is calculated via expansion of the energy corresponding to Coulomb
interaction (taking charge fluctuation into account) is given by,
𝐸𝑆𝐶𝐶 = 1
2∑ [𝛾𝐴𝐵∆𝑞𝐴∆𝑞𝐵]𝑎𝑡𝑜𝑚𝑠
𝐴𝐵 (2.30)
where, 𝛾𝐴𝐵 is the distance-dependent, mainly a Coulomb charge-density interaction functional.
The variables ∆𝑞𝐴 and ∆𝑞𝐵 are induced Coulomb charges on atom A and B respectively,
derived from Mulliken population analysis.120 Here we would like to refer the original article
on SCC-DFTB by Elstner et al.115 for extended details.
To sum up, by utilizing approximations and proper parameterization, SCC-DFTB is well-
qualified method and expected to keep the accuracy of full DFT while computationally faster
and efficient. In this thesis, we have thoroughly used SCC-DFTB for the electronic structure
calculations of extended system of interest. (more details can be found in Chapter 4, 5, and 6)
2.5 Periodic Treatment of Crystalline Materials
To study the electronic structure properties of crystalline materials based on the periodic
arrangement of the atoms, we first must introduce several definitions related to crystal
structure. The fundamental property of a crystal or crystalline material is an ordered repetitive
arrangement of its constituents (atoms, molecules, or ions) forming a crystal lattice that extends
in all the directions. The terms “periodic” and “order” are not equivalent, and most recent
definition by the “International Union of Crystallography” thus states: A material is a crystal
if it has essentially a sharp diffraction pattern.121 This means periodic crystal forms subset and
usually mapped onto itself by a certain translation. Therefore, to describe a system which shows
a well-defined structure such as crystals or surface-mounted MOFs (SURMOFs) periodic
boundary conditions (PBCs) can be studied.
34
In PBCs, periodicity is treated by a set of boundary conditions which are often selected for
approximating a large (infinite) system by using a small repeating unit that reflects the
symmetry of the system, called as unit cell. The periodicity can be 1D (e.g. polymer), 2D (e.g.
a surface) or 3D (e.g. a crystal), with the latter being most common. Every periodic system has
two lattices associated with it. The first one, is known as the real space lattice in which any
periodic distribution of a set of objects can be characterized by a certain translation that repeats
the set of objects periodically. This set of translations generate real space lattice and is defined
by a vector �� ,
�� = 𝑛1𝑎1 + 𝑛2𝑎2 + 𝑛3𝑎3 (2.31)
Here, the set of points defined by �� is called Bravais lattice (as shown in Figure 2.4a) where
𝑛1, 𝑛2, and 𝑛3 are integers and the vectors 𝑎1 , 𝑎2 , and 𝑎3 are the basis vectors in 3D space.
These three vectors are not necessarily orthogonal, and they restrict to angles 𝛼, 𝛽, and 𝛾. The
length of unit cell can be given by 𝑎, 𝑏, and 𝑐 along the axes of three vectors. All the physical
dimension of unit cells such as 𝑎1 , 𝑎2 , 𝑎3 , 𝑎, 𝑏, 𝑐, 𝛼, 𝛽, and 𝛾 in a crystal lattice are collectively
referred as lattice parameters or even unit cell parameters (as shown in Figure 2.4b).
Figure 2.4 (a) A 3D Bravais lattice. The choice of the primitive vectors a1, a2, and a3 is not
unique. (b) represents the lattice parameters includes lattice vectors, lengths, and angles
35
The other lattice is the reciprocal space lattice (also known as k-space),122 which determines
how the periodic structure interacts with waves and plays a fundamental role in most analytic
studies of periodic structures, particularly mapping the diffraction pattern. The reciprocal space
lattice vector, 𝐺 is defined as a linear sum of new set of basis vectors 𝑏1 , 𝑏2
, and 𝑏3 derived
from the 𝑎1 , 𝑎2 , and 𝑎3 vectors of the real cell, and obeying the orthonormality condition
𝑎𝑖𝑏𝑖 = 2𝜋 𝛿𝑖𝑗. The reciprocal lattice vector, 𝐺 then can be expressed as follows:
𝐺 = 𝑚1𝑏1 + 𝑚2𝑏2
+ 𝑚3𝑏3 (2.32)
where 𝑚1, 𝑚2, and 𝑚3 are integers, and �� is real space lattice vector. The equivalent of a unit
cell in reciprocal space is called the (first) Brillouin zone (Figure 2.5a). The point in a reciprocal
space is described by a vector k. Since k has units of inverse length, it is called a wave vector.
The periodicity of the particle in the system means that the square of the wave function must
exhibit the similar periodicity. This is inherent by the Bloch theorem,123 which states that for a
periodic potential with translational symmetry, 𝑉(𝑟 ) = 𝑉(𝑟 + �� ), the corresponding time-
independent SE for a particle yields a set of eigen-functions,
Figure 2.5 (a) Brillouin zone for the face-centered cubic. (b) An illustration of the electronic band
structure diagram for a semiconducting material, Gallium phosphide (GaP)
36
𝛹𝑛�� (𝑟 ) = 𝑢𝑛�� (𝑟 ) 𝑒𝑖�� .�� (2.33)
where 𝑢𝑛�� (𝑟 ) is a periodic function with same periodicity as the potential, 𝑢𝑛��
(𝑟 ) = 𝑢𝑛�� (𝑟 +
�� ), the solution of the SE are characterized by an integer number n (called band index) and the
wave vector �� . The eigenvalues 휀𝑛�� are dependent on the wave vector �� , this dependency is
the basis for the band structure model and forms a continuous spectrum, so called band structure
diagram (see Figure 2.5b). Like in non-periodic system (or molecular system), these bands are
filled with electrons according to energy. The “top” highest occupied filled band is called
valence band (VB) and the “bottom” lowest unoccupied one which is called as conduction band
(CB). The energy difference between the top of the VB and the bottom of CB is called as band
gap and is equivalent to HOMO-LUMO gap in non-periodic system. The band gap values are
generally zero (metallic systems) and finite (insulators or semi-conductors) depending on
whether the band gap is large or small compared with the thermal energy kBT.
The application of Bloch's theorem to the Kohn-Sham wavefunctions greatly facilitates the
treatment of periodic crystals by exploiting their lattice periodicity. Due to this tremendous
computational simplification, DFT has become a working horse for the calculations of
structures and properties of crystalline framework materials. Unfortunately, there is no DFT
software available that concomitantly offers all the required features for above-mentioned class
of materials. In this thesis, we have employed DFT for electronic structure and band structure
calculations for PP-SURMOFs. For this 3D bulk system of interest, we have discovered that
the DFT (GGA-level itself) has not only suffered computationally but also encountered
troubles in their convergence. Furthermore, the well-known shortcomings for electronic
structure calculations using DFT, most notably the too-narrow band gaps were observed. To
overcome these shortcomings, we have employed the DFTB (an approximate-DFT) approach
which keeps the accuracy of the full-DFT while computationally faster and efficient. However,
37
DFT has been proven to efficiently calculate the electronic band structure properties for
SURMOFs at most prominently the GGA-level of approximations, while the band gaps were
improved at hybrid-level.
2.6 Applied Computational Chemistry Packages
In this section, we briefly introduce the computational chemistry packages used to investigate
the electronic structure properties of the molecular and extended systems of interest.
AMS is the Amsterdam Modeling Suite that contains various set of modules for
computationally tackling research problems of various types in diverse areas of chemistry and
materials science. Below we list the AMS modules that have been used in our studies:
ADF, the Amsterdam Density Functional,124 has been used for molecular systems,
particularly in predicting electronic structure and spectroscopy.
AuToGraFS, the Automatic Topological Generator for Framework Structures,125 has
been used for stitching the periodic framework structures from topological information,
and specification of individual linkers and connectors. This coupling framework
generation to a force field is quite essential to produce starting structures that should be
followed by higher-level methods. (see Chapters 4, 6)
UFF, the universal force field,126 is an all atom potential containing parameters for
every atom. It has been used to provide parameters for each atomic type within a
framework to dictate the strength of local chemical bonds / bends. (see Chapters 4, 6)
DFTB, the Density Functional Tight Binding method.127 It is available in three variants,
the DFTB0, DFTB2, and DFTB3. The self-consistent charge (SCC) approximation,
also known as DFTB2, improves the transferability, in particular to polar systems and
38
has been thoroughly used for determining the (3D) bulk structure, stacking, electronic,
including topological, properties in a first screening approach. (see Chapters 4,5 and 6)
TURBOMOLE is an ab initio computational chemistry program.128 It has been used for
ground-state electronic structure calculations for molecular systems of interest (see Chapter 3).
ORCA is a general-purpose quantum chemistry program package.129 It is a molecular code
lacking periodic boundary conditions. It features all modern electronic structure methods with
specific emphasis on spectroscopic properties. It has been thoroughly used for the calculations
of ground-state as well as excited-state electronic structure properties for molecular system of
interest (see Chapters 3, 4, 5 and 6).
CRYSTAL is a general-purpose program for the study of crystalline solids.130 It computes the
electronic structure properties of 0D, 1D, 2D and 3D systems within wave function and density-
based approximations. It has been used for determining the (3D) bulk electronic band gap and
band structure properties within DFT-level (see Chapters 4, 5 and 6).
39
Chapter 3
Benchmarking the Performance of Time-Dependent
Density Functional Theory for Predicting the UV-Vis
Spectral Properties of Porphyrinoids
"Because the theory of quantum mechanics could explain all of chemistry
and the various properties of substances, it was a tremendous success.
But still there was the problem of the interaction of light and matter." – Richard P. Feynman
The studies summarized in this Chapter have been published as:
Benchmark of Simplified Time‐Dependent Density Functional Theory for UV–Vis Spectral
Properties of Porphyrinoids
Kamal Batra, Stefan Zahn, and Thomas Heine
Adv. Theory Simul. 2020, 3, 1900192 © Wiley-VCH Verlag GmbH & Co. KGaA
40
This Chapter investigates the capability of various variants of time-dependent density-
functional theory (TD-DFT) for predicting the UV-Vis spectra (including Soret- and Q-bands)
of porphyrinoids with the aim to identify a computationally feasible approach for large-scale
applications such as molecular framework materials. In the following, we mainly focus on the
characteristic Q-bands because they absorb in the visible light range.
In Section 3.1, after a brief introduction of porphyrinoids followed by the shortcomings of the
ab-initio approaches, we introduce the canonical TD-DFT and the popular Tamm-Dancoff
Approximation (TDA) for predicting the Q-bands of porphyrinoids. Then we summarize the
TD-DFT shortcomings and the state-of-the-art for porphyrinoids. Finally, we present two
highly efficient approaches developed by Grimme et al., namely, the simplified TDA (sTDA)
and the simplified TD-DFT (sTD-DFT).
Section 3.2 lays out a summary of computational methodologies which include various TD-
DFT approaches, basis-sets, density functional flavors (gradient corrected, global hybrids,
range-separated, and double hybrids), and some ab-initio approaches for the comparison.
Besides, we briefly present the benchmark-set of porphyrinoids having a diverse extent of π-
conjugation, ring functionalization, as well as inclusion/modification of a central metal atom.
In Section 3.3, we discuss the performance of the canonical and the simplified version of TD-
DFT approaches by exploiting various basis-sets and density functional flavors with respect to
the experimental references. Furthermore, we discuss some traditional ab-initio e.g. CIS and
CIS(D) approaches with comparable computational cost to density functional flavors.
Finally, in Section 3.4, we discuss the range-separated functional CAM-B3LYP in combination
with the sTDA approach and a basis-set of double-ζ quality, def2-SVP, as an excellent choice
for these calculations. This approach outperforms more expensive approaches, even double
hybrids, and incrementally improves the results by systematic excitation energy scaling.
41
3.1 Introduction
Porphyrins (PPs) and their derivatives can be found in many natural biological systems and
offer potential solutions to a wide range of applications. In plants, PPs are an essential part of
the chlorophyll pigment that converts solar energy into chemical energy.131 Porphyrinoids also
have been proven to be efficient sensitizers132 and catalysts133 in several chemical processes,
including medical applications such as photodynamic therapy.134 They have been incorporated
both as linkers and connectors in metal-organic frameworks (MOFs)72, 135 and covalent-organic
frameworks (COFs).136 A good light-harvesting material efficiently absorbs photons from the
highly abundant visible solar spectrum. This property can be probed by UV-Vis spectroscopy.
The characteristic absorption bands of porphyrinoids are displayed for an example of
tetraphenyl PP, see supporting information (SI) Figure S3.1 in the appendix B.1. The intense
Soret-band, also called B-band, commonly arises in the UV from 350 to 450 nm. In metal free
porphyrins, four transitions with much lower intensity are found in the spectral range from 450
to 800 nm, which are called Q-bands. All transitions between the frontier orbitals are allowed
based on symmetry rules. However, both highest occupied molecular orbitals (HOMO-1 and
HOMO) as well as both lowest unoccupied molecular orbitals (LUMO and LUMO+1) are close
in energy and thus, nearly degenerated as in a simplified model of a 18π cyclic polyene, as
employed by Gouterman13. In this model, two transitions are allowed between the degenerated
frontier orbitals while two are forbidden. Indeed, the frontier molecular orbitals of porphyrin
and the model system show strong similarities. Furthermore, a strong mixing of the transitions
was observed for Soret and Q-bands by quantum chemical calculations.14-15 Opposing
transition dipoles reduce the intensity of the Q-bands while a parallel orientation of both
transition dipoles contributes to the Soret band and thus, a more intense absorption band is
observed for the latter. Therefore, tuning the energy levels of the frontier molecular orbitals
strongly affects the absorption intensity of the characteristic Q-bands. The higher the energy
42
gap between HOMO-1 and HOMO as well as LUMO and LUMO+1, the stronger will be the
absorption intensity of the Q-bands. Nonetheless, predicting the final spectra is challenging.
Obviously, correlated ab-initio approaches such as coupled cluster theory137-139 (CC2, CCSD,
and CC3), the algebraic diagrammatic construction through second order140 (ADC2), and
complete active space second order perturbation theory139, 141-142 (CASPT2) deliver reliable
absorption energies in accordance with experimental results. However, these approaches are
computationally quite expensive for tackling a conjugated molecular system beyond the basic
PP. Other prominent approaches, such as symmetry adapted cluster-configuration
interaction143 (SAC-CI) and similarity transformed equation-of-motion coupled-cluster144
(STEOM-CC) are more accurate than CASPT2, but limited to molecular system up to 50 atoms
due to their high computational cost. To overcome the limits of CASPT2, second order N-
electron valence state perturbation theory145-146 (NEVPT2) has been introduced, which is more
efficient than CASPT2, size consistent and intruder-state-free, but like all multi-reference
approaches, the computational cost of NEVPT2 is still high for larger systems. Overall,
previously mentioned approaches yield reliable absorption energies for PPs, but suffer from a
high computational cost for increased molecular systems, making them practically unsuitable
for large systems.
To find an alternative for the prediction of excited state properties of large systems at a
moderate cost, time-dependent density functional theory (TD-DFT) appears to be a promising
candidate. TD-DFT is an extension of Kohn-Sham DFT and based on almost 35-years old
Runge-Gross theorem93 which has been thoroughly reviewed in the literature89, 92-93, 147-151.
Almost 25 years ago, Casida developed a constructive linear-response formalism for TD-DFT,
known as Casida equations92 but which we will refer to as the random-phase approximations
43
(RPA), allowing to efficiently determine the solution of the TD-DFT equations, which are
formulated in matrix equation involving the excitation and de-excitation matrices.
A popular approximation to the Casida equations is the Tamm-Dancoff approximation98
(TDA), which simplifies the algebra and associated algorithms to obtain the electronic
excitations, yet it typically yields electronic excitations close to those obtained by TD-DFT.152-
153 Unfortunately, TD-DFT on the basis of popular exchange correlation functionals suffers
accuracy limitations which are most evident in the failure to correctly describe Rydberg and
charge transfer (CT) states.103, 154 These drawbacks can usually be overcome by range-
separated hybrid (RSH) functionals, which employ a large amount of HF exchange at large
electron-electron distances and, therefore, reflect the correct asymptotic exchange potential.
TD-DFT in numerous variants has been applied to PPs, and in the following we are
summarizing the state of the art as found in the current literature:
In 1996, Bauernschmitt et al.155 employed TD-DFT to compute the first four electronic
excitations of PP to validate exchange correlation functionals, including the local density
approximation (LDA: S-VWN), the generalized gradient approximation (GGA: BP86) and
hybrid functional (B3LYP). Their results showed that TD-DFT excitation using the BP86
functional are in better accordance with experiment than CIS and TD-HF. Also, CASPT2
possesses an error of more than 0.3 eV for the Q-bands compared to experimental results.
However, the employed basis set was overall small for post-HF approaches.
In 2010, Tian et al.156 examined the performance of global hybrids (PBE0, B3LYP, M06, M06-
2X, M06HF) and long-range corrected (LC) hybrid functionals (ωB97X-D, ωB97X, ωB97,
LC-ωPBE and CAM-B3LYP) in TD-DFT calculations to predict the spectral properties of PP
analogues. Among the many functionals tested, the LC functional ωB97X-D results in an error
of 0.05 eV for Qy band. Moreover, they concluded that the results are robust with respect to
44
subtle geometry changes resulting from the functional choice for geometry optimization and
showed that diffuse functions have only a minor effect on calculated absorption spectra.
However, the quite general study included only two porphyrinoids.
Eriksson et al.157 (2011) investigated the ability of LC hybrid functionals ωB97, ωB97X and
ωB97X-D within the TD-DFT framework. They found that ωB97X reproduces the experiment
best with an error of up to 0.09 eV. Additionally, it was confirmed that the applied functional
for geometry optimization has only a small influence on the calculated spectra.
Lee et al.158 (2012) benchmarked five DFT functionals (B3LYP, LC-ωPBE, LC-BLYP, CAM-
B3LYP and ωB97X-D) using TD-DFT for PP derivative. It was found that ωB97X-D yields
the best agreement to the reference for the LC functionals (Qave bands: 0.055 eV). Overall,
better results were obtained for B3LYP for the Soret and Q-bands. However, it was not
recommended due to the susceptibility for charge transfer excitations.
A benchmark set of 66 medium-sized and large aromatic organic molecules, including five
porphyrinoids, has been studied by Winter et al.159 in 2013. B3LYP was outperformed by the
investigated post-HF approaches (ADC (2), CC2, SOS-CC2, SCS-CC2).
Fang et al.160 (2014) compiled a subset of 96 excitations of 79 different organic and inorganic
molecules, including basic PP.161 They have assessed diverse DFT functionals (BP86, B3LYP,
PBE0, M06-2X, M06-HF, CAM-B3LYP and ωB97XD) and two wave-function based
approaches (CIS and CC2). Overall, the lowest error was produced by CC2 with MAE of 0.19
eV. However, it was found that CC2 approach did not perform well for inorganic systems
(MAE: 0.31 eV) while the MAE of B3LYP is only 0.22 eV.
Theisen et al.162 (2015) validated the performance of diverse DFT functionals (B3LYP, PBE0,
CAM-B3LYP, M062X, M06, M11) for Zn-phthalocyanine (ZnPC). Interestingly, the extra
45
diffuse function in 6-31+g(d) caused convergence problems in the TD-DFT calculations.
Among the investigated functionals, M11 showed the best accordance with experiment with an
error of 0.13 eV for the Qx (0-0) band.
Despite the many successful applications of TD-DFT on a wide range of molecular systems, it
is often challenging in TD-DFT to calculate a sufficient number of excited states for a complete
spectrum or spectra of extended biological systems. To overcome this challenge, the Grimme
group presented two highly efficient approaches, the simplified Tamm–Dancoff-
Approximation106 (sTDA) and simplified Time-Dependent Density Functional Theory
approach107 (sTD-DFT). In both approaches, the computational resources needed to tackle a
targeted system is solely determined by the ground state DFT calculation. This is achieved by
approximating Coulomb and exchange interactions of the electrons by monopole interactions.
Additionally, the CI space is truncated with a screening based on second-order perturbation
theory. Note, the central concepts of the sTDA approach to increase the computational
efficiency can be also employed in tight-binding approaches and, thus, allows fast access to
excited state properties of systems with an amazing size.163 Computational studies validating
sTDA or sTD-DFT for PPs are missing in the literature so far.
With the goal to identify a computational feasible approach to investigate the absorption
properties of PP-containing materials and extended biological systems, we compare the semi-
empirical sTDA, sTD-DFT and canonical TD-DFT (RPA and TDA) for UV-Vis spectra
calculations of porphyrinoids. After a short summary of computational details, we assess
diverse DFT functionals regarding their performance for the calculations of absorption energies
of the Q- bands. This includes the (for sTDA unsuccessful and unnecessary) attempt to improve
the results by an empirical scaling of excitation energies can improve results significantly.
3.2 Computational Methodologies
46
All geometries have been fully optimized using the Turbomole-suite128, employing the BLYP
functional with Grimme’s D3 correction for London dispersion (BLYP-D3)164-166 in
combination with the resolution of identity (RI) approximation,167-169 and the TZVP170 split-
valence basis set of triple-ζ quality with polarization functions. The convergence criterion for
the self-consistent field approach was increased to 10−8 Hartree. This approach is very fast for
the molecules studied here, but also easily affordable in periodic calculations that suffer severe
performance loss for hybrid functionals. As hybrid functionals are known to produce more
accurate structures, we assessed the influence of the geometry on the excited state properties.
For that purpose, we reoptimized all geometries using the B3LYP-D3 hybrid functional164-166,
171 , again employing the TZVP basis set and the RI.
For excited state properties we applied the ORCA code129 with a wide range of functionals,
basis sets and TD-DFT approaches. A summary of the calculation types is given in Table S3.1
in the SI. In detail, we calculated UV-Vis spectra using the following density-functionals:
GGA and mGGA functionals: BLYP,164-165 BP86,164, 172 PBE,173-174 TPSS,175 M06-L176
Global hybrid functionals: B3LYP,164-165, 171 PBE0,173-174, 177 B3P86,171-172 BHLYP,178
TPSS0,179 M06,180 M06-2X,180
Range separated functionals: ωB97,181 ωB97X,181 LC-BLYP,182 CAM-B3LYP183
Double hybrid functionals: B2PLYP,184 B2GP-PLYP,185 mPW2PLYP186
The motivation of this work is to quantitatively reproduce the Q-bands of porphyrinoids with
the possibly lowest computational cost which plays a vital role for the simulations in bio- and
material related chemistry. Hence, each method is validated with the relatively small basis set
def2-SVP187 which is of double-ζ quality. For basis set validation, we repeated the calculations
with the def2-TZVP basis set187 for the sTDA and sTD-DFT approaches, and we also
investigated the impact of diffusive functions for sTDA (def2-SVPD188 and def2-TZVPD).188
47
To speed up the calculations, we employed the RI approximation throughout, including its
variant for double hybrid functionals,189-190 and the RIJCOSX approximation191 was employed
for the global hybrid and range-separated hybrid functionals. For comparison, we have also
included the post-Hartree-Fock methods CIS192 and CIS(D).193-194
The performance of each approach was assessed by calculation of the mean error (ME), the
mean absolute error (MAE), and the absolute maximum error (MAXE) to the experimental
reference values.
Benchmark Set: We have included diverse variants of porphyrinoids starting from basic PP
to the extension of conjugated π-system of the central core followed by ring functionalization
and modification of metal atoms. The molecules included in our benchmark set are given in
Figure 3.1 while Table 3.1 list the experimental references.
Table 3.1 Experimental references of benchmark-set of investigated porphyrinoids
Porphyrinoids Benchmark-Set Abbrev. Ref.
[1] Porphyrin H2PP [195-197]a
[2] Octaethylporphyrin H2OEP [196-198]b
[3] Magnesium Octaethylporphyrin MgOEP [196-197, 199]a
[4] Zinc Octaethylporphyrin ZnOEP [196-197, 200]a
[5] Tetraphenylporphyrin H2TPP [196-197, 201]a
[6] Magnesium Tetraphenylporphyrin MgTPP [196-197, 202]a
[7] Zinc Tetraphenylporphyrin ZnTPP [196-197, 201]a
[8] Tetrakis(o-aminophenyl) porphyrin H2TAPP [196-197, 203]a
[9] Zinc tetrakis(4-carboxyphenyl) porphyrin ZnTCPP [204]c
[10] Zinc [5,15-dipyridyl-10,20-bis(pentafluorophenyl) porphyrin F-ZnP [205]d
[11] Zinc [5,15-di(4-pyridylacetyl)-10,20-diphenyl] porphyrin DA-ZnP [205]d
[12] Octabromotetraphenyl porphyrin H2OBP [206]e
Toluenea ; Benzeneb ; THFc ; DMFd ; CH2Cl2e
48
3.3 Results and Discussion
In this section, the performance of diverse functionals is presented. We will start the validation
with the computationally least costly DFT approach, the GGA functionals, and will finish with
the most expensive one, the double hybrid functionals. We would like to add here that the
present TD-DFT studies involve only transitions in the frozen ground state of the molecules.
Therefore, only the 0 → 0 transitions of the Q-bands can be obtained from the calculations. We
Figure 3.1 Molecular structures of porphyrinoids included in our benchmark set.
49
will focus on the Q-bands in the following because they absorb in the visible light range.
Furthermore, these transitions can be clearly distinguished from other transitions in the excited
state calculations.
3.3.1 GGA and meta-GGA Functionals
GGA and meta-GGA functionals do not require four-center integrals as the Coulomb
interaction can be calculated directly via the electron density, which is particularly beneficial
for periodic calculations and for codes employing different basis functions than Gaussian-type
orbitals. On the other hand, pure Kohn-Sham DFT is very prone to errors originating from the
self-interaction error. Thus, an overall poor general performance for excited state calculations
can be expected due to weakly bound electrons.
As can be seen in Table 3.2 and Figure 3.2a, the performance of TD-DFT for the GGA
functionals PBE, BP86 and BLYP is very similar. Compound 8 shows a large error resulting
in an outlier of about 0.5 eV. This can be attributed to a significant contribution of charge
transfer excitations to the Q-bands (see SI, Table S3.2 and Figure S3.2a, S3.2b for a detailed
description). Employing the meta-GGA functionals TPSS and M06-L reduces significantly the
MAXE. However, the MAE (denoted by ‘+’ sign in Figure 3.2a) is not improved and still
exceeds 0.12 eV. Furthermore, meta-GGAs tend stronger to over-estimate the absorption
energies compared to GGAs. Employing the RPA-approach does not result in significant
improvements in comparison to the TDA-approach (see Table 3.2 and Figure 3.2b). For
instance, the calculated MAE from both approaches in combination with the GGA-functionals
is nearly similar. Only for M06-L, the MAE is reduced by about 0.03 eV. Additionally, the
RPA-approach tends to lower absorption energies than the TDA-approach.
Table 3.2 Calculated original error values in eV for the GGA and meta-GGA functionals
50
GGA and meta-
GGA
Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
PBE
ME 0.02 -0.04 -0.08 -0.12 -0.18 -0.20
MAE 0.11 0.11 0.09 0.13 0.18 0.21
MAXE 0.48 0.48 0.52 0.53 0.49 0.50
BP86
ME 0.02 -0.04 -0.08 -0.12 -0.18 -0.20
MAE 0.11 0.11 0.09 0.13 0.18 0.21
MAXE 0.47 0.47 0.52 0.52 0.48 0.49
BLYP
ME 0.01 -0.05 -0.08 -0.13 -0.18 -0.21
MAE 0.10 0.10 0.09 0.14 0.19 0.21
MAXE 0.46 0.46 0.49 0.50 0.47 0.48
TPSS
ME 0.06 0.00 -0.02 -0.06 -0.12 -0.15
MAE 0.12 0.10 0.08 0.09 0.13 0.16
MAXE 0.38 0.38 0.41 0.42 0.39 0.41
M06-L
ME 0.11 0.05 0.05 0.01 -0.05 -0.08
MAE 0.14 0.11 0.10 0.08 0.09 0.11
MAXE 0.25 0.26 0.28 0.30 0.29 0.31
The computationally cheaper approaches, sTDA and sTD-DFT, show a comparable MAXE for
GGAs (see Table 3.2 and Figure 3.3a, 3.3b). However, the MAE of the GGA-functionals is
strongly affected by the selected approach and basis set. For example, the ME and MAE of
sTDA with the functional BLYP increases by about 0.1 eV when the larger def2-TZVP basis
set is employed (see Table 3.2 and Figure 3.4a). Changing from sTDA to sTD-DFT results also
in large MAE values. The ME and MAE of a given approach-basis-set-combination is overall
close to each other in all cases and thus, highlighting systematic deviations. Please note, that
the sTDA approach includes empirical parameters optimized for functionals with a Hartree-
Fock exchange contribution between 20% and 60% and not for pure DFT functionals.106 TPSS
51
shows an improvement to the GGAs but is still significantly affected by the selected basis-set.
The MAE of M06-L for sTDA and sTD-DFT is only slightly affected by the choice of basis
set which is in contrast to the GGAs. To sum up, the MAE of GGAs and meta-GGAs exceeds
0.08 eV while the MAXE is reduced to 0.30 eV only for the M06-L functional. Finally, a
systematic under-estimation of absorption energies, especially for the sTDA and sTD-DFT in
combination with a large basis set, is observed suggesting a global scaling of the obtained
energies to match better the experimental reference. This approach is rather semi empirical but
allows to access excited state calculations of extended system sizes due to the low cost of pure
Kohn-Sham density functional theory.
After scaling of energies, significant improvements of the MAE and MAXE are only obtained
for the sTDA and sTD-DFT approaches in combination with the large basis-set, (see Figure
3.4b for e.g. BLYP). All functionals with scaled error value are listed in Table S3.3 and a
graphical illustration can be seen in Figure S3.5. Nonetheless, the MAE is still above 0.05 eV
and high MAXE is obtained as well. Thus, GGAs and meta-GGAs cannot be recommended for
calculations of UV-Vis-spectra of porphyrinoids.
3.3.2 Hybrid Functionals
A hybrid functional is defined as an approximate KS density functional where a part or all the
semi-local DFT exchange expression 𝐸𝑋𝐷𝐹𝑇 is replaced by exact Hartree-Fock (HF) exchange
𝐸𝑋𝐻𝐹. The amount of HF exchange for typical hybrid functionals lies in the range of 10-25%
but can be as high as 50-55% like in the BHLYP and the M06-2X functional. Increasing the
amount of HF exchange also increases the likelihood of encountering triplet instabilities (i.e.,
imaginary triplet excitation energies which indicate that the ground state is unstable with
respect to symmetry breaking. Moreover, Incorporation of exact HF exchange reduce the self-
interaction error (SIE) which is a significant troublemaker in TD-DFT. However, it also
52
introduces a four-index integral into the Hamiltonian which leads to higher computational cost
in comparison to the GGA and meta-GGA functionals.
As shown in Table 3.2 and 3.3, similar trends are observed for global hybrids as for pure DFT
functionals, e.g. RPA tends to lower absorption energies than TDA. In contrast, the large error
which stem from the outliers are significantly reduced for the global hybrids with respect to
GGAs (see Table 3.3 and Figure 3.2a, 3.2b). TDA in combination with global hybrids tends
strongly to over-estimate absorption energies of Q-bands which can be reduced by employing
the RPA approach, especially in combination with the BHLYP and M06-2X functional.
Nonetheless, MAE is still above 0.10 eV and thus, this approach cannot be recommended.
Table 3.3 Calculated original error values in eV for the global hybrid functionals
Global Hybrid
Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
PBE0
ME 0.22 0.15 -0.09 -0.12 -0.22 -0.24
MAE 0.22 0.15 0.10 0.12 0.22 0.24
MAXE 0.31 0.25 0.23 0.27 0.40 0.42
B3P86
ME 0.19 0.13 -0.02 -0.06 -0.15 -0.17
MAE 0.19 0.13 0.06 0.08 0.16 0.18
MAXE 0.28 0.24 0.18 0.22 0.34 0.35
B3LYP
ME 0.18 0.12 -0.03 -0.07 -0.16 -0.18
MAE 0.18 0.12 0.06 0.08 0.17 0.19
MAXE 0.27 0.23 0.18 0.22 0.35 0.36
TPSS0
ME 0.24 0.16 -0.04 -0.08 -0.17 -0.20
MAE 0.24 0.16 0.07 0.09 0.18 0.20
MAXE 0.32 0.27 0.18 0.24 0.35 0.37
M06 ME 0.15 0.07 -0.16 -0.20 -0.31 -0.33
53
MAE 0.15 0.10 0.16 0.20 0.31 0.33
MAXE 0.24 0.17 0.30 0.34 0.48 0.51
BHLYP ME 0.28 0.14 -0.30 -0.36 -0.44 -0.53
MAE 0.28 0.14 0.30 0.36 0.44 0.53
MAXE 0.36 0.22 0.42 0.47 0.61 0.69
M06-2X ME 0.28 0.15 -0.40 -0.49 -0.54 -0.66
MAE 0.28 0.15 0.40 0.49 0.54 0.66
MAXE 0.35 0.23 0.54 0.61 0.73 0.83
The approximate sTDA and sTD-DFT approaches fail significantly for the global hybrids with
large amount of HF exchange like BHLYP and M06-2X. However, global hybrids with HF-
exchange contributions in the range of 20-25% show significant improvement compared to the
pure DFT functionals (see Table 3.3 and Figure 3.3a, 3.3b). For example, sTDA in combination
with the B3LYP functional and def2-SVP basis set possesses a MAE of 0.06 eV while the
MAXE is 0.18 eV. Increasing the basis set increases the deviation, similarly as for the GGA
functionals (see Figure 3.4a for e.g. B3LYP and Figure S3.5 for all the tested functionals).
The MAE and MAXE can be reduced by energy scaling due to systematic deviations. A global
hybrid with large HF-exchange contribution works best: sTDA/sTD-DFT in combination with
the functionals BHLYP or M06-2X and the def2-SVP basis set possess MAE’s of only 0.06
eV (see SI, Table S3.4 and Figure S3.5). Moreover, MAXE is reduced to 0.12 eV for M06-2X
functional in combination with the RPA-approach and def2-SVP basis set. Therefore,
employing global hybrids with large HF-exchange contribution and energy scaling might be a
suitable, albeit somewhat empirical approach to estimate the absorption energies of PPs.
3.3.3 Range Separated Hybrid Functionals
54
Range separated hybrid functionals (RSH) possess a different contribution of HF exchange in
short and long interelectronic distances. Short range corrected functionals, like HSE06, possess
a medium amount of HF exchange in the short range while it drops commonly to zero at long
interelectronic distances. This allows a faster calculation of solid-state properties compared to
global hybrid functionals but an improvement for excited states cannot be expected for this
type of functional. In contrast, long-range corrected (LC) RSH possess a large amount of HF
exchange at long interelectronic distances. This significantly reduces errors originating from
Rydberg states and charge transfer excitations in TD-DFT calculations.183, 207-209 Therefore, we
will focus solely on LC-RSH.
The performance of TDA for the investigated RSH functionals is overall comparable to that of
global hybrids, as visible in Table 3.3, 3.4 and Figure 3.2a. Additionally, TDA tends stronger
to over-estimate the absorption energies. The RPA approach for CAM-B3LYP results in
overestimated absorption energies, while other LC-RSH functionals tend to underestimate
these energies. Overall, RPA has a strong dependency on the type of functional and produce
lower absorption energies than TDA (see Table 3.4 and Figure 3.2b).
Table 3.4 Calculated original error values in eV for investigated RSH functionals
Range Separated
Hybrid Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
ωB97
ME 0.21 -0.16 -0.16 -0.45 -0.18 -0.45
MAE 0.21 0.16 0.16 0.45 0.18 0.45
MAXE 0.31 0.23 0.39 0.69 0.40 0.68
ωB97X
ME 0.22 -0.08 -0.18 -0.43 -0.20 -0.42
MAE 0.22 0.09 0.18 0.43 0.20 0.42
MAXE 0.30 0.17 0.41 0.67 0.42 0.65
55
LC-BLYP
ME 0.20 -0.09 -0.13 -0.35 -0.16 -0.35
MAE 0.20 0.10 0.15 0.35 0.16 0.35
MAXE 0.28 0.18 0.37 0.59 0.38 0.58
CAM-
B3LYP
ME 0.24 0.07 0.03 -0.02 -0.13 -0.17
MAE 0.24 0.08 0.05 0.05 0.13 0.17
MAXE 0.31 0.16 0.10 0.14 0.27 0.29
On the other hand, as can be seen in Table 3.4, Figure 3.3a and 3.3b, the performance of sTDA
and sTD-DFT is improved over global hybrids only for CAM-B3LYP which amounts up to
46% HF-exchange. In contrast to CAM-B3LYP, LC-RSH functionals incorporating up to 85-
100% HF-exchange result in remarkably large errors. This is in agreement with the original
work where sTDA was developed for long-range corrected hybrids where best results of
excitation energies were obtained with CAM-B3LYP for charge transfer free systems.210
Employing large basis sets does not improve the results based on simplified approaches. (see
Figure 3.2 Boxplot displaying original error values in eV for the variant of density-functionals in
combination with TD-DFT types (a) TDA, (b) RPA, and def2-SVP basis set. Here, MAE is
denoted by (+) while outliers (•) termed as extremes error values which are outside the range
given in bars. (scaled error values can be seen in SI, Figure S3.3)
56
Figure 3.4a for e.g. CAM-B3LYP case and Figure S3.5 for all the tested functionals). Thus,
results obtained with the def2-SVP in combination with simplified approaches are most reliable
and reasonable.
Figure 3.3 Boxplot displaying original error values in eV for the variant of density-functionals in
combination with TD-DFT types (a) sTDA, (b) sTD-DFT, and def2-SVP basis set. (scaled error
values can be seen in SI, in Figure S3.4).
Figure 3.4 Boxplot displaying error values in eV, where (a) original and (b) scaled for the selected
DFT functional in combination with different basis-set qualities (def2-SVP and def2-TZVP) and
simplified time dependent approaches (sTDA and sTD-DFT).
57
To sum up and as shown in Figure 3.5a, GGA functionals produce large errors in the form of
outliers e.g., BLYP in combination with def2-SVP basis set. Global hybrid functionals, e.g.
B3LYP, produces MAE of 0.06 eV in combination with sTDA and the def2-SVP basis set and
appears to produce overall reliable results. However, best results, and indeed excellent ones,
are obtained with the RSH, CAM-B3LYP in combination with sTDA and an overall small
def2-SVP basis set which yields a MAE of about 0.05 eV. This can be barely improved by
energy scaling (see Figure 3.5b and scaled error values are listed in Table S3.5).
3.3.4 Double Hybrid Functionals and post-Hartree Fock approaches
In addition to the exact HF exchange, double hybrid functionals include a second order
perturbation theory correction term (MP2) for the correlation part of the functional. This
improves mainly the consideration of dispersion forces. However, the computational time is
comparable to MP2. Therefore, we have also included some traditional post-HF approaches
with comparable computational cost such CIS and CIS(D), in our study.
Figure 3.5 Boxplot displaying error values in eV, where (a) original and (b) scaled for the selected
functionals from DFT-group in combination with TD-DFT types and def2-SVP basis set. A detailed
box-plot representation (original and scaled error values) of all the investigated density functional-
approaches-basis set combinations can be seen in SI, Figure S3.5 (in eV) and Figure S3.6 (in nm).
58
Table 5. Calculated original error values in eV for double hybrids and post HF methods
Approach def2-SVP
B2PLYP
ME 0.24
MAE 0.24
MAXE 0.31
B2GP-PLYP
ME 0.29
MAE 0.29
MAXE 0.37
mPW2PLYP
ME 0.25
MAE 0.25
MAXE 0.33
CIS
ME 0.26
MAE 0.26
MAXE 0.39
CIS (D) ME 0.51
MAE 0.51
MAXE 0.60
Figure 3.6 Boxplot displaying error distribution in eV, where (a) original value and (b) scaled values
for the double hybrid functional and post HF methods in combination with def2-SVP basis-set
59
As can be seen in Table 3.5 as well as in Figure 3.6a, double hybrid functionals produce large
errors comparable to CIS. Including perturbative double corrections results in even larger errors
of the CI approach. However, we would like to highlight that the employed basis set is only of
double-ζ quality due to the system size. The strong systematic overestimation of absorption
energies for the double hybrid functionals and post HF methods suggests a scaling of the
obtained absorption energies. Indeed, the results are significantly improved and an accuracy
comparable to CAM-B3LYP can be reached (see Figure 3.6b and Table S3.6). Thus, CIS(D)
with scaled absorption energies might be a suitable approach to verify results obtained with
sTDA, def2-SVP and CAM-B3LYP.
3.3.5 Influence of diffuse basis set functions and ground state structure
Commonly, diffuse basis sets are recommended for weakly bound electrons found in anions or
in excited states. Therefore, we have selected three functionals, BLYP, B3LYP and CAM-
B3LYP, and extended the employed Ahlrichs basis set by diffuse functions. Independent of the
employed functional type, including diffuse basis set functions provides poorer results
compared to the def2-SVP double-ζ basis set, (see SI, Figure S3.7a and Table S3.7). The worse
performance cannot explained by the ϵ (HOMO) criterion211 (see SI, Table S3.8). Also scaling
of energy does not improve results since including diffuse basis sets increases the scattering of
the calculated absorption energies in most cases (see SI, Figure S3.8a). Thus, unintuitively, the
smallest basis set provides the most accurate results.
Finally, we investigated the influence of the electronic structure method during structure
optimization. Instead of the GGA BLYP, the more expensive hybrid functional B3LYP was
selected for structure optimization. The influence is overall negligible for absorption energies
obtained by BLYP and B3LYP, compare Table S3.7 and S3.9 in SI. In case of the RSH CAM-
60
B3LYP, the errors without energy scaling are even increased pointing to some error
compensation for the most reliable approach (see SI, Figure S3.7b). Nonetheless, global scaling
of energy provides nearly identical results. Thus, as long as the correct combination of scaling
factor, structure optimization setup and absorption energies calculation approach are selected,
results can be barely improved.
3.4 Conclusions
We have presented a detailed validation of the simplified time dependent density functional
theory method developed by Grimme et al. for the calculation of UV-Vis-spectra of
porphyrinoids including free base and metal containing PPs. The original RPA-approach tends
to smaller absorption energies than TDA, which is also visible for the simplified versions.
Local GGA functionals produce large errors and therefore cannot be recommended. In contrast
to local DFT functionals, global hybrids yield significantly improved results only after energy
scaling, especially BHLYP and M06-2X. We can recommend as global hybrid B3LYP which
produces MAE of 0.06 eV in combination with sTDA and the def2-SVP basis set which can
be barely improved by energy scaling. Best results without energy scaling are obtained with
the RSH CAM-B3LYP in combination with sTDA and the def2-SVP basis set yielding a MAE
of about 0.05 eV. Significantly more expensive perturbative corrected double hybrid
functionals tend to yield results comparable to CAM-B3LYP solely when energies are scaled.
Apart from that, employing a hybrid instead of a GGA functional for geometry optimization
has less-significant effect on the calculated absorption bands whereas increasing the basis set
does not improve the calculated absorption bands. Most notable, including diffuse basis
functions even leads to worse results. Thus, employing a cheap GGA like BLYP for structure
optimization, selecting an overall small basis set of double-ζ quality in combination with a
CAM-B3LYP and the sTDA approach provides a cost-efficient approach to estimate the
61
absorption spectra of porphyrinoids which can be barely improved by more expensive
approaches. Unfortunately, none of the local functionals has sufficient predictive power, which
is an obstacle in particular for periodic calculations.
62
63
Chapter 4
Computational Screening of Surface Mounted Metal-
Organic Frameworks Assembled from Porphyrins
"No amount of experimentation can ever prove me right;
a single experiment can prove me wrong." – Albert Einstein
The studies summarized in this Chapter have been published as:
Bridging the Green Gap: Metal-Organic Framework Heteromultilayers Assembled from
Porphyrinic Linkers Identified Using Computational Screening
Ritesh Haldar+, Kamal Batra+, Stefan Michael Marschner, Agnieszka B. Kuc, Stefan Zahn,
Roland A. Fischer, Stefan Bräse, Thomas Heine, and Christof Wöll
Chem. Eur. J. 2019, 25, 7847-7851 © Wiley-VCH Verlag GmbH & Co. KgaA
64
This Chapter investigates the potential of computational screening methods for tailoring the
photophysical properties of porphyrin-based surface-mounted metal-organic framework (PP-
SURMOF) thin films. This study involves a close collaboration between experiment and theory.
First, we briefly mention their contributions followed by the Chapter’s outline:
Experimental contributions: (i) Synthesis and characterization of multi-functionalized PP-
linkers are led by S. Marschner and S. Bräse; (ii) Thin film depositions and photophysical
characterization of PP-based SURMOFs are led by R. Haldar, C. Wöll, and R. Fischer.
Theoretical contributions: (i) Electronic structure and properties calculations of multi-
functionalized PP-linkers are led by me, S. Zahn, and T. Heine (ii) Computational screening
and band structure calculations of PP-based SURMOFs are led by me, A.B. Kuc, and T. Heine.
In Section 4.1, after a brief outline of organic photovoltaics followed by their shortcomings,
we introduce the benefits of crystalline systems and an approach based on the regular assembly
of PP-linkers into thin-films of MOFs. Then we summarize the shortcomings of other PP-
based thin-film approaches and the scope of PP-linkers to assemble in SURMOFs. Finally, we
investigate the tuning of characteristic Q-bands of the multi-functionalized PPs by using a
validated computational protocol (see Chapter 3) for improving their absorption efficiency.
Section 4.2 lays out a summary of the computational methodologies utilized in this study.
Besides, we highlight the three interesting strategies for tuning the structure and absorption
efficiency of PPs on behalf of computational screening. Finally, we select three promising PPs
exhibiting important differences in their characteristic Q-bands and utilize them for
assembling into SURMOF structures.
In Section 4.3, first, we compare the predicted absorption spectra with experimental results for
the promising PPs. Next, to rationalize the experimental absorption spectra of the PP-
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SURMOFs, we investigate the impact of the arrangement, also known as stacking, of the PP-
linkers in the framework structures by calculating the respective electronic band structures.
Furthermore, we estimate an indirect band gap having band dispersion for one of the
promising structures, that is substantially larger (≈200meV) than the previously reported
(≈5meV) value for a different PP‐SURMOF.
Finally, in Section 4.4, we present an attractive route to prepare chromophoric assemblies by
the SURMOF-based approach and demonstrate the power of computational screening methods
to identify the most promising PP linkers for the construction of layered PP-SURMOFs with
the desired photophysical properties.
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4.1 Introduction
While presently the highest conversion efficiencies are achieved with inorganic (Si, Ge)212-213
and hybrid (Grätzel-cell, perovskites)214-217 semi-conductor based photovoltaic (PV) devices,
organic materials are an interesting alternative with advantages in more specific
applications.218-219 Main obstacles in this area are efficiency and stability issues. Progress in
this field is only gradual, and the search for organic molecules suited as an active PV material
is to a large extent still dominated by empirical approaches.218-221 Use of computer-based
screening methods is hampered by the fact that the characteristics of most organic PV (OPV)
materials are strongly impacted by intermolecular interactions.222 and, for disordered systems,
many configurations have to be samples to make reliable predictions.223
Major progress has thus to be expected when employing crystalline systems with exactly
known structures.224 In such cases, periodic boundary conditions (PBCs) can be applied, which
allows for a thorough theoretical analysis utilizing the solid state analysis toolbox.223 The OPV
device characteristics can then be predicted on the basis of first-principles electronic structure
calculations carried out both for single molecules as well as for the condensed phases of these
organic semiconductors. In the latter case, the precise arrangement of the functional molecules
in the crystalline state is taken fully in account. In addition to a reliable theoretical analysis
with high predictive power, for crystalline systems additional effects may be employed, for
example the emergence of band dispersion favoring large charge carrier mobilities and the
formation of indirect band gaps.225-227 Indirect band gaps are beneficial in photovoltaics since
they favor a fast and highly efficient charge separation and thus charge carrier recombination
is strongly suppressed.
Herein, we demonstrate an approach based on assembly of multi-functionalized PP linkers into
thin films of MOFs.228-229 PPs are a particular promising class of organic compounds for
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investigating the beneficial effect of a regular arrangement of photoactive molecules with
regard to light harvesting.71, 230-233 PPs form a very rich class (>100,000 compounds known)131,
234-240 which are also common in nature. In plants, PPs like chlorophyll transform solar energy
into chemical energy. Since PPs are among the best-performing organic compounds regarding
photon absorption, charge separation, and stability,131, 235-240 numerous previous works have
been carried out with the aim to prepare well-defined, thin films of PP aggregates deposited on
conducting and transparent substrates.241-243 The approaches employed previously include
vapor-phase deposition of PP molecules, a rather sophisticated method, or self-assembly from
appropriate solutions. The latter strategy has been rather successful, but the resulting systems
do not exhibit a high degree of ordering, thus largely excluding the formation of band-structure
effects. In addition, the different types of molecular packing in the amorphous films make more
precise predictions of absorption properties difficult.
The typical absorption spectrum of a PP chromophore consists of a sharp, high-intensity Soret
band, which is typically located in the UV region, and four Q bands located in the visible range
(Figure 4.1a). In principle all transitions of the frontier orbitals are symmetry-allowed.
However, as the frontier orbitals are nearly degenerate, the electronic structure can be
approximated by a 18π cyclic polyene model, as suggested by Gouterman,13 in which two
Figure 4.1. a) Typical spectrum of a porphyrin. Blue lines in the Lewis structure highlight the π-
electrons on which a 18π cyclic polyene model is reasonable; b) Comparison of the frontier orbitals
obtained from DFT calculations of porphyrin and the 18π cyclic polyene model.
68
transitions are allowed between the degenerated frontier orbitals (Δk=1), whereas two are
forbidden (Δk=9) (Figure 4.1b). Detailed quantum chemical studies confirm Gouterman’s
conclusions and explain the typical absorption spectra of PPs in detail.14-15 Tuning the energy
levels of HOMO-1, HOMO, LUMO and LUMO+1 strongly affects the absorption intensity of
the characteristic absorption bands of porphyrins. The higher the energy gap between HOMO-
1 and HOMO as well as LUMO and LUMO+1, the stronger will be the absorption intensity of
the Q-bands. While this allows the rational design of PP molecules, the prognostication of
absorption spectra for PP-based SURMOFs remains difficult. This is mainly due to the fact
that the bulk structure is not known a priori, and changes of absorption intensity and band
positions resulting from intermolecular interactions are thus difficult to predict.
Herein, we circumvent the problem of structure prediction for the condensed phase by focusing
on porphyrinic dicarboxylic acids that can be used as ditopic linkers to assemble PP-MOFs. In
order to identify a small set of chromophoric MOF linkers to cover the green gap we first
carried out a computational screening of a library containing 14 PP structures, see Supporting
Information (SI), Figure S4.1 in appendix B.2). This library was generated by functionalization
of two of the phenyl rings at the meso-positions with carboxylate groups to produce ditopic
MOF linkers. In the first group of PP derivatives, the H atoms at the β-positions are substituted
by halides and methyl groups (1-X group, X = F, Cl, Br, CH3), and in the second group the two
phenyl rings that do not serve as linking groups are substituted. The library contains
substitution groups which can modulate PP ring planarity (e.g. substitution at β-position by
bulky Br atoms), and electron density (electron donating /pulling).
To obtain theoretical predictions with sufficient reliability, simplified time-dependent
functional approach was applied (see section 3.2, computational methodologies). As expected,
functionalization is found to be a suitable means for both Q-band intensity enhancement and
69
tuning of absorption band positions. For example, β-substitution by Br as well as meso-
positioned phenyl group substitution creates a large red shifts of Q bands by >50 nm in
comparison to 1-H (see Table S4.2). Additionally, the absorption of the Q bands is significantly
enhanced (Figure S4.3).
3.2 Computational Methodologies
For molecular systems: The CAM-B3LYP functional183 in combination with the TZVP basis
set170 was employed in all calculations. The energy convergence criterion of the self-consistent
field cycle was set to 10−8 Hartree and dispersion forces were considered by the 3rd version of
Grimme’s empirical dispersion correction D3 in combination with the improved Becke–
Johnson damping.166, 244 To speed up the density functional theory calculations, the resolution
of identity approximation167-168, 245 (RI) was employed for the Coulomb integrals while
exchange contributions were accelerated by the “chain of spheres” approximation191 (COSX).
After structural optimizations, excited states were calculated by the simplified time-dependent
functional theory.107 We have employed the CAM-B3LYP functional, since this long-range
corrected hybrid functional keeps the accuracy of B3LYP for excited states, but nearly
eliminates errors from charge transfer excitations.183 All calculations were carried out
employing the ORCA 4.1.1 program package.129
For solid-state systems: The structure models have been created using AuToGraFS125. The
frameworks structure and lattice parameters of porphyrin based SURMOFs were pre-optimized
using Universal Force Field (UFF)126 employing UFF4MOF parameters.246 The bond order
specified between paddlewheel Zn atoms was set to 0.25, paddlewheel Zn-O bonds were set to
0.50, all other bond orders were specified according to the standard chemical notation.
Frameworks geometry optimizations have been carried out using the self-consistent charge,
density functional based tight-binding (SCC-DFTB) method including UFF-dispersion along
70
with DFTB.org/3ob-3-1 parameters. The optimized lattice constants (a, b, and c) calculated for
the periodic frameworks are given in Table S4.5. Single-point calculations for band gaps and
band structures were performed using CRYSTAL17130 program along with DFT PBE173-174
functional, pob-TZVP247 basis type and 100 k-points in the Monkhorst-Pack mesh. Calculated
band-gaps for 1-Br ', 5 ' and 10 ' are given in the SI, Table S4.6. Also, stacking information of
PP-SURMOFs are given in the SI, Table S4.7.
3.3 Results and Discussion
On the basis of this computational screening, three PPs (Figure 4.2a) have been selected for
synthesis (see experimental section in the SI) and validation of the theoretical predictions.
Selection criteria were the enhancement of Q-band intensity and the tuning of band position.
These selected three PPs exhibit important differences: i) the presence of electron withdrawing
functional groups (fluorinated phenyl), ii) π-conjugation of the substituent (phenyl group or
acetylene group), and iii) planarity of the porphyrin core (twisted octabromo porphyrin). The
Figure 4.2. a) Three selected PP linkers; (b) TD-DFT predicted (left) and experimental (right) UV-
Vis spectra of the linkers. Experimental spectra were recorded for 20 M ethanolic solution of the
linkers at RT.
71
experimental methods developed for organic synthesis of the multi-substituted porphyrins were
successful. The required A2B2-type porphyrins were assembled in a modular fashion starting
from dipyrromethene building blocks and functional aldehydes. Subsequent cross-coupling
reactions led to the designed porphyrins (see Experimental Section in appendix B.2). Figure
4.2b, shows the predicted (left) and experimental (right) UV-Vis spectra of 1-Br, 5 and 10.
Generally, a good agreement is seen between the TD-DFT gas-phase predictions and the
experimental results (solvated). Note, that the agreement is not expected to be quantitative since
solvatochromic shift affect the experimental absorption spectra.248-249 In these synthesized PPs,
apart from the Q-bands in near-IR region, also the Soret band shifts to visible range, in
comparison to the 1-H.
For applications, the assembly of PP dyes into thin films of high optical quality is crucial.
Therefore, in a final step, the selected PP linkers were assembled into SURMOF-2 thin films
containing optically silent Zn2 paddle wheel units, following the spin-coated variant of the
layer-by-layer (LbL) liquid phase epitaxy method.68, 250-253 The SURMOF-2 structure consists
of Zn2-paddle-wheel type secondary building units (SBUs) tethered with ditopic linkers to yield
two-dimensional planes stacked along the (010) crystallographic direction (Figure 4.3).60 Note
that the framework of SURMOF-2 has P4 symmetry, and the lattice constant only depends on
Figure 4.3. a) Simulated XRD pattern of 1-Br', and experimental out-of-plane XRD patterns of 1-
Br', 5' and 10'; calculated atomistic PP-based Zn-SURMOF structures of b) 1-Br', c) 5', and d) 10',
view along [010] direction
72
the length of the PP linkers (i.e. distance between the two carboxylic acid groups), while the
addition of side groups to the PPs are not expected to create changes of the SURMOF unit cell.
In all three cases, SURMOF-2 structures, labelled as 1-Br ', 5 ' and 10 ', exhibit well-defined
out-of-plane XRD patterns (Figure 4.3a). The position of the diffraction peaks is almost
identical, yielding unit cell dimensions with a = b = 2.3 nm, in excellent agreement with the
prediction. These observations confirm the expectation that irrespective of the type of group
attached at meso or β-position to the PPs, the unit cell parameters of the resulting MOF
structures remain unchanged. (Figure 4.3, for details, see SI). Figures 3b-d show the DFTB
optimized atomistic structures of 1-Br ', 5 ' and 10 '. In 10, fluorination of the linkers creates
significant electrostatic repulsion, so the inter-linker distance is maximized when the PPs are
untwisted. This maintains the overall P4 symmetry in 10 with a distance between the PP units
of 6.3 Å. In contrast, the longer linkers in 5′ interact strongly, causing a tilting of 32° and
reducing the distance between the PP planes to 3.3 Å.
Figure 4.4 compares the UV-Vis spectra of 1-Br ', 5 ' and 10 ' with those of the solvated linker
molecules 1-Br, 5 and 10. In 1-Br ', the distorted basal planes of the linker (1-Br) prevent
periodicity along the PP stacks (along (010)). Consequently, the bands are not shifted compared
to those of the solvated 1-Br, but significantly broadened (Figure 4.4a). However, the
Figure 4.4 Experimental UV-Vis comparison spectra of the synthesized PP linkers (solid line) and
their corresponding fabricated SURMOF-2 structures (broken line); a) 1-Br, b) 5 and c) 10. Note
that the molecular spectra are recorded in ethanol at RT.
73
experimental data reveal that crystallization of 5 in the SURMOF-2 structure causes a
significant redshift of all bands in 5 ' (Figure 4.4b). Notably, this redshift affects both the Soret
and the Q-bands. In addition, all bands are substantially broadened. The spectra of 10 and 10 '
are very similar, indicating negligible interaction between the PP linkers (also in line with the
predicted structure) (Figure 4.4c).
To rationalize the experimental UV-Vis spectra recorded for the PP-SURMOFs, we have
calculated the band structures of 1-Br ', 5 ' and 10 ' (for details, see SI), which are shown in
Figure 4.5(a-c). The band structure of 1-Br ' reflects the idealized structure and therefore is not
directly suitable to interpret the UV-Vis spectrum (Figure 4.5a). For 5 ', we observe significant
band dispersion along the Z direction of the Brillouin zone (see Figure 4.5b, 4.5d), which is
responsible, both for the redshift of the absorption bands, as well as for the charge carrier
mobility along the PP stacks (along (010)). We observe an indirect band gap of ~200 meV,
Figure 4.5. (a-c) Band structure of 1-Br, 5′ and 10′; (d) brillouin zone; (e) a schematic illustration
of trilayer SURMOF (left) and corresponding UV-Vis spectrum (right). (The gray filled box = SBU,
filled diamond shape = PP).
74
which is substantially larger than that (5 meV) reported in previous work for a different PP-
SURMOF-2 structure.72 For 10 ', no band dispersion is observed, confirming the hypothesis
that the linker molecules 10 do not interact in the SURMOF-2 structure (Figure 4.5c). As a
result, the UV-Vis data for the corresponding SURMOF-2 film mainly show the molecular
features. Due to the lack of band dispersion, no ballistic transport is possible for such structure.
While for the 1-Br′ and 10′ no substantial aggregation-induced shifts of the absorption band
positions were observed, a broadening of the absorption bands is evident. This is a beneficial
effect, and together the three PP-linkers allow covering the full visible spectrum ranging from
violet to near-IR. Inspired by such broad absorption, we have fabricated a multilayer
SURMOF-2 structure by employing heteroepitaxy.59, 254 Layers of 1-Br ', 5 ' and 10 ' were
sequentially deposited on top of each other to make a crystalline thin film with a broad
absorption ranging UV-to-NIR, as shown in Figure 4.5e. Such straightforward fabrication
method, combining all the potential photon absorbing dyes as a thin film is a promising strategy
towards further improvement of OPV materials.
4.4 Conclusions
In conclusion, we present here an attractive route to create OPV absorber layers in the visible
regime, covering the entire range from the violet to the near infrared, including the green gap.
Starting point is a set of candidate structures, in this case, tetraphenyl porphyrin derivatives
with different substitution patterns. Instead of scheduling a vast amount of structures for
synthesis, we used a computational approach to first select promising chromophoric MOF
linkers from an in-silico library. Indeed, after synthesis, the three candidates, showed excellent
performance. 1-Br exhibits distorted basal plane that imposes a significant red shift of both
Soret and Q-bands in the free molecule. The second one (5) has a large aromatic ligand
(extended conjugation), which enhances the Q-band intensity, but does not affect the position
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of the Soret band. The third one (10) is functionalized with strong electrostatically active
groups. Arranging these dyes into a SURMOF-2 structure yields three different pictures: In 1-
Br′, distorted basal planes of the linkers avoid regular stacking, and while the positions of the
absorption bands of the free linkers are maintained, they are significantly broadened in the
SURMOF structure. In 5′, the strong intermolecular interactions lead to a red shift and
broadening of all bands. Finally, in 10′, electrostatic repulsion reduces intermolecular
interactions and thus the absorption spectrum of the corresponding SURMOF is dominated by
the molecular properties of 10.
Altogether our results reveal that the strategy to prepare chromophoric assemblies via a
SURMOF-based approach carries a huge potential. Depending on the stacking within the MOF,
one can realize systems with small inter-chromophore coupling, which are essentially
dominated by features of the individual molecules. By adjusting the MOF topology together
with chromophore substitution patterns, intermolecular couplings can be introduced, which
allow to invoke band structure effects, thus increasing charge carrier mobility and allowing of
indirect band gap formation. Finally, the SURMOF approach then provides the prospect to
realize energy funneling via fabrication of hetero-multilayers or gradient structures.
76
77
Chapter 5
The Proximity Effect in Porphyrin-based Surface-
Mounted Metal-Organic Frameworks
"The important thing in science is not so much to obtain new facts
as to discover new ways of thinking about them." – Sir William Bragg
The studies summarized in this Chapter have been published as a part of the
Progress Report:
Proximity Effect in Crystalline Framework Materials: Stacking-Induced Functionality in
MOFs and COFs
Agnieszka B. Kuc, Maximilian A. Springer, Kamal Batra, Rosalba Juarez-Mosqueda,
Christof Wöll, and Thomas Heine
Adv. Funct. Mater. 2020, 30, 1908004 © Wiley-VCH Verlag GmbH & Co. KGaA
78
This Chapter discusses the tuning of stack interactions in layered porphyrin-based surface-
mounted metal-organic frameworks (PP-SURMOFs) with a future goal for identifying the most
promising molecular framework structures by proper selection of functional groups in the PP-
linkers. The exact stacking in PP-SURMOF layers is of paramount importance for their
photophysical properties.
In Section 5.1, after an introduction of molecular framework materials followed by discussing
the proximity effect, which is caused by van der Waals interactions between stacked aromatic
molecules, we present the impact of proximity effect that results in the first reported indirect
band gap formation in a PP-SURMOF. Then we briefly summarize the shortcomings of the
reported PP-SURMOF and the scope of functionalizing the PP-linkers. Finally, we present
three most promising PP-linkers and incorporate them into SURMOF to examine their effects.
Section 5.2 lays out a short summary of the computational methodologies utilized in this study
to predict and analyze the proximity effect.
In Section 5.3, we discuss the impact of the proximity effect by analyzing the stack interactions
within three most promising PP-SURMOFs. For one of these PP-SURMOFs, we investigate
the band dispersion as a function of the rotation of the functionalized PP-linker in a bulk
framework. Furthermore, we present that different degrees of structural rotations lead to
different structures in the electronic bands. i.e. dispersion in the valence and conduction bands.
Finally, in Section 5.4, we observe substantial dispersion of both band edges for a structure
with out-of-plane rotated (by 110) substituents and this shows that the proximity effect can
render strong electronic effects if the aromatic molecules are arranged in exact or well-
controlled stacks.
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5.1 Introduction
Molecular framework materials, including metal-organic frameworks (MOFs),26, 255-256
coordination polymers,257 and covalent organic frameworks (COFs),258-259 provide an
intriguing bridge between chemistry and solid-state physics. They are composed of molecular
units that may carry the whole range of functional groups known to chemistry. These molecular
building blocks are stitched together by strong bonds. This setup provides much higher
chemical, thermal, and mechanical stability as compared to molecular crystals and, thus, allows
the formation of large pores which can reach up to 10 nm in diameter,60, 260-262 as well as
extremely large internal surface areas.261 These unique properties have motivated intense MOF
research during the past years: they allow high gas uptake capacities and, thus, application in
methane and hydrogen storage.263-264 Coupling these properties, intrinsic to porous materials,
with molecular functionalities integrated into nodes and linkers can yield to multifunctionality:
selective uptake, CO2 capture265-266, hydrogen isotope separation,267-268 as well as switching
permeance and selectivity via optical269 or electrical270 switching. Even though the IUPAC
recommendations for nomenclature explicitly specifies that these materials are not necessarily
crystalline,271 high crystal order is observed for many of them.
Crystallinity allows high-quality structural analysis by experimental methods, e.g., via X-ray
diffraction (XRD). Consequently, theoretical work can be carried out in a straightforward
fashion and can then be compared directly to experimental results, thus, allowing for a direct
validation of computational approaches. The well-defined structure also makes a proper
physicochemical characterization of these materials possible and provides, thus, the basis for
the high level of understanding of their structure and electronic structure. At the same time,
crystal order is the reason for solid-state effects that are caused by the translational symmetry,
such as indirect band gaps and ballistic charge transport.272 As in other crystalline solids,
80
defects play a critical role for certain properties, including electronic and optical properties,
thus, a proper characterization of defect types and their density is crucial.58, 273 This point is
particularly important, as the properties discussed below are a direct consequence of the
crystallinity of the framework materials.
Ballistic transport is typically hindered either by the large effective masses of the typically
dispersion less bands or by the chemical composition of the frameworks, where non-carbon
centers (for example oxygen, boron, or nitrogen) can effectively block electron conjugation.
Only recently, ballistic transport, facilitated by electron conjugation, has been demonstrated in
layers of two-dimensional (2D) crystalline frameworks.274-277 There is, however, a more subtle
way to implement strong band dispersion in crystalline molecular framework materials:
Controlled stacking of aromatic molecules, incorporated into the materials as linkers or as
pillars with suitable intermolecular distance, is subject to the proximity effect, more precisely,
the molecules interact via π-stacking, which causes strong alterations of the electronic structure
of the framework materials. While this type of stacking is rather obvious for the class of layered
crystalline frameworks278 with atomically thin layers and with aromatic connectors or linkers,
it can also be achieved in MOF thin films with suitable crystal structure.72, 135 A further option
of MOFs is to grow superstructures by applying layer-by-layer (LbL) procedures (MOF-on-
MOF) and to fabricate structurally well-defined organic/organic heterointerfaces.251, 279
Several groups have introduced LbL methods to deposit MOF thin films on substrate, first, in
2007, Wöll and Fischer reported on the LbL route to MOF synthesis,50, 68, 280 and later H.
Kitagawa and coworkers.69 Such surface-mounted MOFs are referred to as SURMOFs. They
exhibit high crystallinity and can be investigated using virtually all surface science techniques,
see also Section on SURMOFs synthesis in the SI. SURMOF-2, being an iso-reticular series
based on MOF-2,281-282 is one of the simplest MOF architectures suited for LbL growth.60 They
81
are derived from MOF-2, a bulk framework material based on paddle-wheel units with four
dicarboxylate groups and typically Cu2+ or Zn2+-dimers connected to ditopic organic linkers of
different length, the shortest one being 1,4-benzene dicarboxylate. The length of the linkers
determines the lattice constant and, thus, the pore size of the resulting SURMOFs, where up to
4 nm in diagonal have been reached up thus far.60 Layers of such SURMOFs form square
lattices and, theoretically, could be stacked together in three different arrangements i.e.
eclipsed, slipped, and inclined. The most symmetric P4 variant is the eclipsed stacking with
linkers and connectors in one layer directly on top of linkers and connectors in another layer.
This stacking is found in all SURMOF-2 derivatives discussed in this Chapter and leads to a
less stable system due to unfavorable non-covalent interactions. Computational investigations
showed60 that two other stackings are energetically more favorable. These are slipped and
inclined stackings, with P2 and C2 symmetries, respectively, which emerge in bulk
synthesis.281, 283-284 However, in the SURMOF approach, the metastable P4 symmetry with
eclipsed stacking is enforced by the anchoring of the first MOF layers to the nucleating surface.
The first report on indirect band gap formation in MOFs was published in 2015.72 Thin films
of epitaxial MOFs have been studied, and photoinduced charge-carrier generation was
observed. The investigated Zn-paddle wheel SURMOF-2 derivative utilized Pd-porphyrinoid
linkers (Pd-PP-Zn-SURMOF, see Figure 5.1a). As parent SURMOF-2, this structure is also a
square lattice in-plane and layers are stacked in the AAAA fashion. Such a system results in
fairly dispersion less bands of the electronic structure (see Figure 5.1b), however, zoom-in to
the conduction and valence bands reveals a small but distinct dispersion in an order of 5meV.
This value corresponds to a mobility of about 0.003 cm2 V-1 s-1, which at that time was larger
than for any other MOF. This MOF exhibits an indirect band gap, which should result in
suppressed electron-hole recombination and improved photovoltaic properties in such organic-
semiconductor based devices.
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The photovoltaic efficiency of the reported PP-SURMOF amounts to only 0.2%,72 and is thus
far too low for realizing a competitive device. Another issue is the absorbance of the PP itself:
the strongly absorbing Soret band is in the ultraviolet, while the Q-bands, which are located in
the visible spectrum, are only weakly absorbing. PP functionalization can strongly enhance the
absorbance of the Q-bands. Among the large number of possibilities, three particularly
interesting ones have been identified by combining rational design with computational
screening.135 (i) 1-Br, distorting the planarity alters the selection rules and, thus, enhances the
intensity of the Q bands. This can be achieved by bromination of the PP core (twisted
octabromo porphyrin). (ii) 5, the π-conjugation of the PP can be extended by adding a phenyl-
acetylene (PhA) group. (iii) 10, the π-system can be affected by the presence of electron-
withdrawing fluorinated phenyl substituents.135 All three strategies show an effect on the
Figure 5.1 (a) Building block (Pd-porphyrinoid, Pd-PP) together with the top and side views of Pd-
PP-based Zn-SURMOF, and (b) the corresponding band structure with zoom-in to the top of valence
and bottom of conduction bands adapted from Ref. [72]. Bands are fairly flat, however, small out-
of-plane dispersion occurs in the direction perpendicular to the layers. The dispersion is in the limit
of a couple of meV. Pictures of structures made with VESTA.
83
isolated PP linker molecules, in particular, the Q-band intensity increases. Incorporated to a
SURMOF, these three linkers, however, show very different absorbance (see Chapter 4). This
can, again, be attributed to the proximity effect and will be discussed in section 5.3 after a short
summary of the computational methodologies used in this Chapter to further exploit this effect
by probing different degree of structural rotation for one of the promising PP-based SURMOFs.
5.2 Computational Methodologies
This section gives an overview of methods that are useful for computationally tackling layered
SURMOFs, from constructing the atomistic structures to obtain high-level electronic structure
data. It includes the methods that have been used (as in Chapter 4) to obtain the results.
The structure models have been created using AuToGraFS125. The frameworks structure and
lattice parameters of PP-based SURMOFs were pre-optimized using Universal Force Field
(UFF)126 employing UFF4MOF parameters. 246 The bond order specified between paddlewheel
Zn atoms was set to 0.25, paddlewheel Zn-O bonds were set to 0.50, all other bond orders were
specified according to the standard chemical notation. Frameworks geometry optimizations
have been carried out using the self-consistent charge, density functional based tight-binding
(SCC-DFTB) method including UFF-dispersion along with DFTB.org/3ob-3-1 parameters.
Single-point calculations for band gaps and band structures were performed using
CRYSTAL17130 program along with DFT PBE173-174 functional, pob-TZVP247 basis type and
100 k-points in the Monkhorst-Pack mesh. The optimized lattice constants (a, b, and c) and the
calculated band-gaps for 1-Br ', 5 ' and 10 ' are given below in Table S4.1 and S4.6 respectively
Also, the stacking information of above mentioned PP-SURMOFs are given in Table S4.7. (see
SI of Chapter 4). Besides, the calculated band gap values for rotations angles, αi and βi, of the
functional groups with respect to the PP plane of SURMOF (5’) are given in Table S5.1.
84
5.3 Results and Discussion
For the brominated linker, the geometrically distorted building blocks fail to arrange
themselves into well-ordered stacks. As a result, loosely packed linker stacks with distances of
≈6.1 Å, too far to cause a significant proximity effect, are obtained. Hence, the incorporation
of the brominated PP (1-Br) into the MOF lattice does not affect the absorber properties
significantly. For the fluorinated species (10), also the formation of a well-ordered lattice is
Figure 5.2 (Top panel) Building blocks together with the top and side views of three Zn-SURMOFs
assembled from multi-functionalized PP linkers: (a) 1-Br ', (b) 5 ' and (c) 10 ' (Bottom panel) The
corresponding band structures. Adapted from the Chapter 4 or Ref. [135]. Strong band dispersion
observed for the PP-Zn-SURMOF (5 ') in the stacking direction, due to enhanced London dispersion
interactions between the PP linkers. Pictures of structures made with VESTA.
85
reported. However, Coulomb repulsion keeps the linkers at the widest possible distance (≈6.3
Å) and the resulting absorption spectrum is very similar to that of the individual molecules. If
large and aromatic linkers are used (as in case of PA, (5)), the attractive London dispersion
interaction fosters linker rotation to the extent that the PP molecules form well-ordered stacks
Figure 5.3 (a) Top and side view of the 5 '. The interlayer distance (d = 3.3 Å) corresponds to the
distance between PP units in adjacent layers; (b) Cluster structure of the linker with possible
rotations angles, i and i, of the functional groups with respect to the PP plane; (c) Band structures
corresponding to different values of i and i. The strongest band dispersion was obtained for both
angles of about ±110°. The band structure from the Chapter 4 or Ref. 135 corresponds to the case
of i = 0° and i = 110°. Pictures of structures made with VESTA.
86
with intermolecular distance of ≈3.3 Å, very close to that in graphite. Consequently, the band
structure shows strong dispersion, which results in a red shift of the Soret band and enhances
and broadens the Q-bands. These results are summarized in Figure 5.3 and reported in Ref.135.
To what degree is the spatial extension of the aromatic system of the individual porphyrinic
linkers relevant to the properties, which are mainly caused by the proximity effect in the linker
stack? To answer this question, we analyzed the band dispersion as function of the rotation
angle between the PP moiety and the PhA substituent (see Figure 5.3). This is achieved by
rotating parts of the linker (PhA and the benzene rings connected to the paddle wheel). Indeed,
such a rotation results in a strong manipulation of the electronic bands, from almost flat
conduction band in a hypothetical structure with all likers at 0 with respect to the PP to very
strong dispersion in both band edges for rotations of both parts by 110. We believe that such
rotations can be achieved by proper selection of functional groups (steric control units, SCUs,
see below) in the PP linkers.
5.4 Conclusions
This Chapter shows that, in addition to molecular functional groups, undercoordinated metal
sites, porosity, and large surface areas, a further possibility of property control can be
incorporated into crystalline framework materials, e.g. SURMOFs: If aromatic molecules are
placed in well-controlled stacks, the proximity effect gives raise to strong electronic effects. If
the intermolecular distance between the basal planes of the aromatic molecules is in the range
of the interlayer distance of graphene (≈3-3.5 Å), disperse electronic bands emerge, resulting
in a ballistic charge carrier transport with appreciable mobilities. Thus, while the electronic
properties of most framework materials are merely the superposition of the electronic
properties of the constituting molecular building blocks, a suitable stacking of aromatic
87
building blocks can turn them into semiconducting materials with particular electronic and
optoelectronic properties.
Without steric control and sufficient flexibility, van-der-Waals interactions result in self-
assembly of PP stacks with strong proximity effect. Mutual shift and twist between the basal
planes of the aromatic PP linkers and intermolecular distance have a strong impact on the
resulting electronic structure change, due to the proximity effect. It is possible to control the
stacking by strong interlayer interactions, functional groups (or SCUs), and the introduction of
SCUs at the proper positions in the PP linkers. These control mechanisms are still beyond the
state-of-the-art and subject of the author’s ongoing research efforts.
88
89
Chapter 6
Computational Screening of Phthalocyanine-based
Surface Mounted Metal-Organic Framework
"Somewhere, something incredible is waiting to be known."
– Carl Sagan
This Chapter contains work that has not been published yet
90
This Chapter investigates the photophysical properties of phthalocyanine-based surface-
mounted metal organic framework (PC-SURMOF) thin films. We are interested in exploring
PCs as alternative SURMOF building blocks, because they are not only more stable, but also
possess enhanced absorption in the visible and the near IR spectral regions in comparison to
PPs. Hence, the exploitation of PCs could enrich the library of building blocks for crystalline
materials with controlled optical properties.
In Section 6.1, after a brief introduction to PCs followed by their pros and cons over PPs, we
introduce the benefits of crystalline systems and an approach based on the regular assembly
of PC-linkers into thin-films of MOFs. Then we briefly summarize the state-of-the-art
concerning PCs integration into MOFs and the scope of layered PC-SURMOF. Finally, we
estimate the absorption spectra for a series of multi-functionalized PCs by using the efficient
computational protocol as identified in Chapter 3.
Section 6.2 lays out a summary of the computational methodologies utilized in this study.
Besides, we briefly present the series of PC-derivatives having a diverse extent of π-
conjugation, ring functionalization, as well as inclusion of a central metal atom.
In Section 6.3, first, we discuss the predicted absorption spectra for a series of PCs. Next, we
select exemplary PCs exhibiting improvement in the characteristic Q-bands and thus utilize
them for assembling in a SURMOF structure. Finally, we investigate the impact of the
arrangement of PC-linkers in the theoretically modelled PC-SURMOF by calculating its
electronic band structure.
Finally, in Section 6.4, we summarize our preliminary findings while demonstrating the power
of computational screening protocols to identify the promising PC-linkers for the construction
of layered PC-SURMOFs with the desired photophysical properties.
91
6.1 Introduction
Phthalocyanines (PCs) and their derivatives are a group of heterocyclic macrocycles, best-
known as synthetic porphyrin (PP) analogues,285-286 consisting of four iso-indole units linked
together through nitrogen atoms. PCs possess an 18π-electron aromatic cloud delocalized over
an arrangement of alternating carbon and nitrogen atoms as shown in Figure 6.1. In a free base
PC, the two hydrogen atoms can be replaced by different central metal atoms and a variety of
substituents can be incorporated, both at the periphery of macrocycle and the axial positions,
thus allowing fine-tuning of the physical responses. PCs and their derivatives are chemically
and thermally stable, which makes them promising candidates to be integrated into devices
such as solar cells,287 sensors,288 transistors289 etc. Moreover, they have recently attracted an
increasing interest as a building blocks for the construction of new molecular materials that
give rise to promising photoelectric and photophysical properties.290-291
Like in porphyrinoids, the light harvesting properties of PCs and their derivatives constitute
one of their most fascinating attributes, which can be probed by UV-Vis spectroscopy. Also,
in this case, we can follow the 18-π cyclic polyene model, as suggested by Gouterman13 to
explain their UV-Vis spectrum. In PCs, the formal introduction of heteroatoms (nitrogen) at
Figure 6.1 The unsubstituted phthalocyanine macrocycle
92
the four meso positions, combined with four fused benzo rings significantly breaks the
degeneracy of the frontier orbitals, causes a progressive red-shift of the Q-band to the region
of 670 nm, and a blue-shift of the Soret-band, appearing at around 300 nm. Furthermore, the
strong mixing between the Soret and Q-band transitions is reduced. As a result, the weakly
intense Q-bands acquire significant intensity. To sum up, PCs are not only owing structural
robustness and stability, but also possess red-shifted Q-bands with a significantly enhanced
absorption intensity in the visible and near IR spectral regions as compared to PPs (Figure 6.2).
In contrast to above-mentioned advantages of PCs over PPs, it is worth to highlight that the
synthesis of PCs is more exhausting and challenging as compared to PPs. This is reflected by
the rough numbers of successful PCs syntheses, which amounts to over 100,000 for PPs
(according to Sci-Finder), but only to 20,000 for PCs (both including metalation reactions).
Given all the facts and figures, PCs are among the best-performing organic molecules regarding
light harvesting properties and perfectly suitable for their integration in solar energy conversion
devices e.g. organic photovoltaics (OPVs). Thin films of PCs have been playing an important
role in incorporating them into devices. Generally, in the field of molecular electronics, ordered
(crystalline) PC materials are preferred over disordered (amorphous) PC materials, which not
Figure 6.2 Comparison of calculated UV-Vis spectrum of PP-1H and PC-1H molecules
93
only facilitates their characterization and theoretical analysis, but also anticipate to
significantly enhance the device performance. Several previous investigations with different
approaches292-296 (e.g. sublimation, Langmuir-Blodgett [LB] etc.) have been performed with
the goal to develop well-defined, thin PC-layers on various substrates. The LB approach has
proved to be particularly useful for the fabrication of organized thin films of PCs.297 However,
the resulting systems do not exhibit a highest degree of ordering and orientation in the thin
films. In the recent work (see Chapter 4), we have demonstrated that PP-based SURMOFs
outperform the other type of PP-based thin films17-19 (made, e.g., using vapor phase deposition,
self-assembly etc.) as regards structural order and optical quality. The SURMOF approach is
well suited to grow crystalline, highly oriented, monolithic thin films which greatly simplify
the integration of chromophoric MOF materials into devices. Therefore, in this Chapter, we
propose to extend the successful fabrication of PP-SURMOFs to PC-SURMOFs. This will
enable the extension of MOF application areas to photo-electrochemistry, where the conditions
are much harsher.
As per state of the art, only very few articles reporting the integration of PCs into MOFs have
been published to date.54-56 Basically, all of these studies are linked to tetra-topic PCs
functionalized with -NH2/-OH groups. Reducing the connectivity to ditopic PCs can give more
structural flexibility, and variation. However, studies where ditopic PC-linkers were employed
for assembly of MOFs are not known as per our knowledge. The same is applicable for thin
films of PC-MOF, no prior literature was found on this area. The fact that works on PC-related
MOFs is limited results from the rather extensive synthesis effort need to synthesize PCs, and
in particular functionalized PCs. To circumvent the huge synthesis efforts and resources, we
estimate the absorption spectra for a series of multi-functionalized PCs by using the efficient
computational protocol as identified in Chapter 3. Only the most promising PC candidates will
then be synthesized and used to fabricate SURMOFs. Depending on the PC substitution pattern
94
and/or the choice of PC metal reaction, different intermolecular interactions can be supported,
reduced, or even blocked, thus affecting their electrical and optical properties.
6.2 Computational Methodologies
For molecular systems: All the geometries have been fully optimized by using BLYP
functional164 in combination with the TZVP basis set.170 The energy convergence criterion of
the self-consistent field cycle was set to 10−8 Hartree and dispersion forces were considered by
the 3rd version of Grimme’s empirical dispersion correction D3 in combination with the
improved Becke–Johnson damping.166, 244 To speed up the DFT calculations, the resolution of
identity approximation167-168, 245(RI) was employed for the Coulomb integrals, while exchange
contributions were accelerated by the “chain of spheres” approximation191 (COSX). After
structural optimizations, excited states were calculated by the simplified Tamm-Dancoff
approximation (sTDA).106 in combination with CAM-B3LYP functional183 and the def2-SVP
basis set.188 All calculations were carried out employing the ORCA 4.1.1 program package.129
For solid-state system: The structure models have been created using AuToGraFS.125 The
frameworks structure and lattice parameters of phthalocyanine based SURMOFs were pre-
optimized using Universal Force Field (UFF)126 employing UFF4MOF parameters.246 The
bond order specified between paddlewheel Zn atoms was set to 0.25, paddlewheel Zn-O bonds
were set to 0.50, all other bond orders were specified according to the standard chemical
notation. Frameworks geometry optimizations have been carried out using the self-consistent
charge, density functional based tight-binding (SCC-DFTB) method including UFF-dispersion
along with DFTB.org/3ob-3-1 parameters. Single-point calculations for band gaps and band
structures were performed using CRYSTAL17130 program along with DFT PBE173-174
functional, pob-TZVP247 basis type and 100 k-points in the Monkhorst-Pack mesh.
95
PC-derivatives set: We have included a series of PC-derivatives having a variety of
substituents, both at the periphery and the axial positions of the PC macrocycle: (i) ring
functionalization with electron donating and electron withdrawing groups; (ii) extension of π-
conjugation by including phenyl and phenylacetylene groups (iii) inclusion of a central metal
atom. The molecules include in our PC-derivative set are given in Figure 6.3
6.3 Results and Discussions
In this section, the UV-Vis spectrum of multi-functionalized PC-derivatives 1-10 is presented.
We will mainly discuss the positions and intensities of the characteristic Q-bands of PC-
derivatives in the following because they absorb light in the visible to near IR region of solar
spectrum. We would like to add here that the simplified time-dependent studies involve only
transitions in the frozen ground state of molecules. Furthermore, these transitions can be clearly
Figure 6.3 Molecular structures of diverse phthalocyanine derivatives [1-10]
96
distinguished from other transitions in the excited state calculations. Next, we investigate the
impact of the arrangement of PC-linkers in the theoretically optimized PC-SURMOF structure
by calculating and analyzing its electronic band structure diagram.
The precursors for the synthesis of the PC can be modified through different substitution
pattern at the periphery of macrocycle and the axial positions in silico. Numerous possible
modifications of the molecular structure permit the fine-tuning of physical, electronic, and
optical responses. The peripheral substitution of PC-derivatives plays a significant role not only
in the fine-tuning of their characteristic absorption bands, but also improves their solubility and
permits the depositions onto substrates. The attached peripheral substituents can be divided
into electron donating or electronic withdrawing groups. The incorporation of metal at the
central cavity affects the electronic structure in a way that as thermodynamically stable
delocalized dianion with higher symmetry is obtained. The extension of π-conjugated system
Figure 6.4 Comparison of calculated UV-Vis-spectrum for phthalocyanine-derivatives [1-10]
97
(e.g. phenyl or phenylacetylene unit) offers another possibility to influence the absorption
properties which is present in the all the structures included in our set as shown in Figure 6.3.
Table 6.1 Calculated absorption wavelengths of PC-derivatives with employed abbreviations.
To examine the influence of attached substituents with respect to light absorbing properties of
PCs, we first investigate the simple free base and metal-containing PC-derivatives abbreviated
as 1 and 2, respectively. It can be deduced from Table 6.1 and Figure 6.4, the calculated Q-
bands values appears in the visible and near IR region. Moreover, an incremental red-shift in
the Qy-band through Zn-metal implementation is observed in the visible region (2 in Figure
6.4). Next, we examine the effect of four large bromine groups (replace the hydrogen-atoms in
1) at the β-positions of free base PC-derivatives abbreviated as 3. It can be deduced from Table
6.1, structure 3 exhibits a Qx-band ~30 nm at longer wavelength with respect to the structure
1 in the near IR region while there is no improvement of Qy-band in the visible region.
Likewise, 1 and 3, the similar trend is observed for Q-bands in the Zn-metal containing
Structures Abbrev.
Qx Band (nm)
Qy Band (nm)
1 722 665
2 703 671
3 750 667
4 732 668
5 723 668
6 751 686
7 728 694
8 722 670
9 750 685
10 727 695
98
structures 2 and 4, while a somewhat pronounced variation in their band width (see Table 6.1
and Figure 6.4).
Apart from ring functionalization effect at β-positions, we examine the impact of introduced
functionality (propyl groups) at the extent of π-conjugated structure in the form of cis and trans
conformers, abbreviated as 5 and 6 respectively. It can be deduced from Table 6.1, the
estimated Qx-band in near IR region for structures 5 and 6 are quite similar to structures 1 and
3 respectively, while the structure 6 outperforms 1 and 3 exhibiting a Qy-band ~20 nm at longer
wavelength in the visible region (see Table 6.1). To compare 5 and 6 conformers, 6 displays
progressive red shift in the Q-bands. Moreover, in the structure 6, an increased absorption and
incremental red-shift in Qy-band through Zn-metal implementation is observed in the visible
region (7 in Figure 6.4). Likewise 5-7, the similar trend is observed for the structures 8, 9 and
10 as well by extending the π- conjugated system with acetylene group forming cis/trans and
employing the Zn-metal to the central cavity of trans conformer (see Table 6.1 and Figure 6.4).
On the basis of computational screening of series of PC-derivatives, we have initially started
with an exemplary and simplest PC-derivative abbreviated as 1, exhibiting improvement in the
characteristic Q-bands as compared to PP/PC-derivatives and thus utilized for assembling in a
SURMOF structure. Based on our previous experience of PP-based SURMOF, we have
successfully optimized the geometry and lattice constants for the theoretically modeled PC-
SURMOF (see Figure 6.5a). The optimized lattice constants (a, b, and c) calculated for the
periodic framework are given in Table 6.2. Next, we have investigated the impact of the
arrangement of PC-linkers by calculating its band structure and observed significant band
dispersion along the Z direction of the Brillouin zone (see Figure 6.5b-c) which is responsible,
both for the bathochromic shift (red-shift) of the absorption band, as well as for the charge
carrier mobility along the PC-stacks. We have observed a formation of direct band gap with
99
significant band dispersion ≈280 meV (in the conduction and the valence band), which is larger
than that for (≈200 meV) reported in previous study (see Chapter 4) for PP-based SURMOFs
Table 6.2 Calculated lattice parameters for the exemplary PC-based SURMOF structure
Structures a (in Å) b (in Å) c (in Å)
PC-SURMOF 34.26 34.26 5.14
6.4 Conclusion
In conclusion, we present here an attractive route to model chromophoric assemblies by
SURMOF-based approach and demonstrate the power of computational screening methods to
identify the promising PC-linker for the construction of layered PC-SURMOFs with the desired
photophysical properties. The starting point is to set a candidate structure, in the case ditopic
PC-derivative with variant substitution pattern are optimized in silico. Based on the predictive
absorption properties, we select an exemplary PC-derivative exhibiting enhanced Q-bands
Figure 6.5 a) Top and side view of calculated atomistic PC-SURMOF structure; d) Brillouin Zone;
c) Electronic band structure diagram of PC-SURMOF structure.
100
absorption in the visible/near-IR region and thus utilized for modeling the SURMOF structure.
Based on successfully optimized geometry, we have calculated its electronic band structure
and observed a direct band gap with significant dispersion ≈280 meV, which larger than that
(≈200 meV) reported in previous work (see Chapter 4) for PP-SURMOF / (5´) structure.
Altogether, our preliminary findings demonstrate that photophysical properties of PC-based
SURMOF offers a huge potential for opto-electronic devices with covering the entire solar
spectrum, ranging from ultraviolet to infrared.
101
Chapter 7
Summary
"Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we
ourselves are a part of the mystery that we are trying to solve." – Max Planck
For inorganic semiconductors such as
silicon, crystalline order leads to bands
in the electronic structure which give
rise to drastic differences with respect to
disordered materials. Distinct band
features lead to photo-effect, and the
band structure can be tuned to optimize
the performance of the photovoltaic
(PV) device. An example is the presence of an indirect band gap. For organic semiconductors,
such effects are typically precluded, since most organic materials employed are disordered,
which hampers their characterization and theoretical analysis. The inspiration for this thesis
came from the very first evidence of an indirect band gap exhibited by highly ordered and
crystalline porphyrin-based surface-mounted metal-organic framework (Pd-PP-based
SURMOF) material.72 The presence of an indirect band gap should in principle result in
suppressed charge recombination and efficient charge separations which would significantly
enhance the PV device performance. However, the energy gain from the electronic band
dispersion in the reported Pd-PP-based SURMOF is far too low (≈5 meV) and results in a very
102
low photocurrent generation (efficiency 0.2%), which is certainly not sufficient for the
application. Another noticeable shortcoming is the weakly absorbing Q-bands of the employed
PP chromophore (Pd-metal containing porphyrinoid, Pd-PP) in the visible region of the solar
spectrum. Nevertheless, this novel research has highlighted the potential to improve the
photophysical properties of PP-SURMOFs by (i) introducing various functional groups or
metal ions to the PP-core and (ii) controlling the PP-stacking behavior in layered materials.
To overcome the posed shortcomings of the PP-MOF prototype PV material and to exploit the
potential of PP-SURMOFs, we have employed the following approach to increase the light
absorption and the electronic band dispersion.
Firstly, we proposed a computationally feasible protocol to investigate the light
absorption properties of PP derivatives or related PP-containing materials.
Secondly, we predicted the light absorption properties of multi-functionalized PPs (i.e.
tuning the weakly absorbing Q-bands) by using a validated computational protocol,
thus allowing us to identify different PP linkers with different light absorption
properties, allowing to bridge the so-called green gap.
Finally, we incorporated the most promising PP linkers for the construction of layered
SURMOF materials and optimized the PP-stacking behavior to achieve the desired
photophysical properties.
Besides PPs, we have extended our investigations to phthalocyanines (PCs) as alternative
individual SURMOF building blocks, because they do not only exhibit structural robustness
and stability but also possess enhanced absorption in the visible and the near IR spectral regions
in comparison to PPs. Hence, the exploitation of PCs could enrich the library of SURMOF
materials with the desired optical quality.
103
In line with these considerations, the objective of this thesis is two-fold. We first develop a
computationally feasible protocol to investigate the absorption properties of chromophores or
extended biological systems. Our second aim is to assemble the most promising chromophores
for the construction of layered SURMOF materials with the desired photophysical properties
such as increased electronic band dispersion or photocurrent.
Chapter 1 introduced the research topic and systems of interest. In Chapter 2, we discussed
theory and methods, as well as the computational protocols that have been applied to
investigate the posed problems and achieve the respective goals are briefly summarized.
In Chapter 3, we presented a detailed
validation of various variants of time-
dependent density-functional theory
(TD-DFT) for predicting the UV-Vis
spectra of PP derivatives with diverse extent of π-conjugation, ring functionalization, as well
as inclusion or modification of a central metal atom. With the aim to provide an approach that
is computationally feasible for large-scale applications such as molecular framework materials,
we have assessed the performance of the simplified Tamm-Dancoff approximation (sTDA),
sTD-DFT, and canonical TD-DFT (including TDA). We have compared the results given by
various computational protocols by exploiting various basis sets and density-functionals
(gradient corrected local functionals, hybrids, range separated, and double hybrids) with
respect to the experimental references. An excellent choice for these calculations is the range-
separated functional CAM-B3LYP in combination with sTDA and a basis set of double-ζ
quality (Mean Absolute Error [MAE] ≈0.05 eV). This is not surpassed by more expensive
approaches, not even by double hybrid functionals, and solely systematic excitation energy
scaling slightly improves the results (MAE ≈0.04 eV). Unfortunately, none of the gradient
104
corrected local functionals have sufficient predictive power (for a detailed discussion see
Chapter 3), which is an obstacle especially for periodic calculations.
In Chapter 4, by using the simplified
time-dependent approach identified
in Chapter 3 as the most cost-efficient
yet reliable method for accurate
prediction of the absorption spectra
of PPs, we have examined how the molecular and electronic structure of variously substituted
PPs can be tuned for increasing their absorption efficiency. Based on this computational
screening, three interesting strategies for tuning the structure and light-absorbing properties of
PPs have been identified:
(i) Distortion of the planarity of the PP core,
(ii) Extension of π-conjugation by adding a phenyl-acetylene substituent, and
(iii) Introduction of electron‐withdrawing functional groups.
These structural modifications cause pronounced changes in the positions and intensities of the
Q-bands of the respective PP molecules. For applications, the assembly of PP linkers into thin
films of high optical quality is crucial. In a final step, the identified PP linkers were assembled
into SURMOFs. To rationalize the experimental UV-Vis spectra of the synthesized PP‐based
SURMOFs, we have estimated the impact of the arrangement, also known as stacking, of the
PP linkers in the framework structures by calculating the respective electronic band structures
(for a detailed discussion see Chapter 4). We have calculated an indirect band gap dispersion
of ≈200 meV that is 40 times larger than the previously reported value of ≈5 meV for a Pd-PP‐
SURMOF.72 In conclusion, our study has demonstrated the power of computational screening
105
methods to identify the most promising PP derivatives for the construction of layered PP-
SURMOF materials with the desired photophysical properties.
In Chapter 5, we have provided in-
depth analysis of the proximity effect
and stacking control in the PP-
containing SURMOFs modeled in
Chapter 4. For one of the most
promising PP-based SURMOFs i.e. 5´, we have studied the band dispersion as a function of
the rotation of the introduced functional groups, such as phenyl and phenyl-acetylene, with
respect to the PP-core in a bulk framework (for a detailed discussion see Chapter 5). The
different degree of structural rotation causes different structure of the electronic bands - from
an almost flat conduction band in a hypothetical structure with all functional groups in-plane
with the PP core, to a pronounced dispersion of both band edges for a structure with out-of-
plane rotated (by 110) substituents. We believe that the desired molecular and electronic
structure of the PP-based SURMOFs can be achieved by a careful selection of the functional
groups and their introduction at the proper positions in the PP-linkers.
In Chapter 6, we presented theoretical
findings based on the screening of a
series of PC linker molecules and an
exemplary PC-based SURMOF. By
utilizing the simplified time-dependent
approach identified in Chapter 3, we
predicted the UV-Vis spectra of various
PC derivatives having diverse extent of π-conjugation, ring functionalization, inclusion of a
106
central metal atom, as well as conformer variants. The structural modifications cause
pronounced changes in the positions and intensities of the absorption bands of PC molecules,
covering the entire range from violet to the near infrared, including the green gap (for a detailed
discussion see Chapter 6). Based on the estimated light absorption properties of PC derivatives,
an exemplary PC derivative exhibiting enhanced Q-band absorption is thus utilized for
modeling the SURMOF structure. Next based on fully optimized geometry and lattice
parameters, we have calculated the electronic band structure and observed a direct band gap
with substantial electronic band dispersion of ≈280 meV. Altogether, our results demonstrate
that the photophysical properties of PC-based SURMOFs present a huge prospective for the
construction of optical devices.
By leveraging the light-harvesting properties of the chromophores, one can rationally design
novel chromophore-based SURMOFs. On one end, we have demonstrated from the electronic
structure and properties calculations (validated with experiments), that tuned and well-
controlled arrays of PP chromophores in layered SURMOFs display enhanced photophysical
properties compared to the previously reported Pd-PP-SURMOF. The substantial indirect band
dispersion of the PP-SURMOF i.e. (5´) reported in our work is ≈200 meV, which is 40 times
higher than the previously reported72 value of ≈5 meV (see illustrating Figure 7.1). On the other
end, our screening of an exemplary PC-based SURMOF results in a direct bandgap displaying
substantial band dispersion of ≈280 meV. Altogether, our results demonstrate that the solid-
state properties of chromophoric MOFs offer a huge potential for optoelectronic devices.
107
Figure 7.1. Left (a) Building block (Pd-porphyrinoid, Pd-PP) together with the top and side views
of Pd-PP-based Zn-SURMOF, and the corresponding band structure adapted from Ref. [72]. Bands
are fairly flat, and the dispersion is in the limit of ≈5 meV; Center (b) Building blocks together with
the top and side views of three Zn-SURMOFs assembled from multi-functionalized PP linkers: (i)
1-Br ', (ii) 5 ' and (iii) 10 '; Right (c) Strong band dispersion (≈200 meV) observed for the 5 ' in the
stacking direction, due to enhanced London dispersion interactions between the PP linkers.
108
109
A. Acronyms
2D Two Dimensional
3D Three Dimensional
ADC2 Second Order Algebraic Diagrammatic Construction
ADF Amsterdam Density Functional
ALDA Adiabatic Local Density Approximation
AMS Amsterdam Modeling Suite
AuToGraFS Automatic Topological Generator for Framework Structure
BO Born-Oppenheimer
BS Band Structure
CASPT2 Complete Active Space Second Order Perturbation Theory
CB Conduction Band
CC Coupled Cluster
CD Circular Dichroism
CI Configuration Interaction
COF Covalent-Organic Framework
COSX Chain of Spheres Approximation
CT Charge Transfer
DA-ZnP Zinc [5,15-di(4-pyridylacetyl)-10,20-diphenyl] porphyrin
DFT Density Functional Theory
DFTB Density Functional Tight Binding
DPA Diphenylamine
F-ZnP Zinc [5,15-dipyridyl-10,20-bis(pentafluorophenyl) porphyrin
GGA Generalized Gradient Approximation
GH Global Hybrid
H2OBP Octabromotetraphenyl porphyrin
H2OEP Octaethylporphyrin
H2TAPP Tetrakis(o-aminophenyl) porphyrin
H2TPP Tetraphenylporphyrin
HEG Homogeneous Electron Gas
HF Hartree-Fock
HK Hohenberg-Kohn
HOMO Highest Occupied Molecular Orbital
KS Kohn-Sham
LB Langmuir Blodgett
LbL Layer-by-layer
LC Long-range Corrected
LCAO Linear Combination of Atomic Orbitals
LDA Local Density Approximation
LPE Liquid Phase Epitaxial
LR Linear Response
LUMO Lowest Unoccupied Molecular Orbital
110
MAE Mean Absolute Error
MAXE Absolute Maximum Error
ME Mean Error
mGGA meta Generalized Gradient Approximation
MgOEP Magnesium Octaethylporphyrin
MgTPP Magnesium Tetraphenylporphyrin
MOF Metal-Organic Framework
MP2 Second Order Møller–Plesset Perturbation Theory
M-PP Metal-Porphyrin
NAFS-1 Nanofilm of MOFs on Surface-No.1
NAFS-2 Nanofilm of MOFs on Surface-No.2
NEVPT2 Second Order N-electron Valence State Perturbation Theory
OPV Organic Photovoltaic
PBC Periodic Boundary Condition
PC Phthalocyanine
PCP Porous Coordination Polymer
Ph Phenyl
PhA Phenyl Acetylene
PP Porphyrin
PV Photovoltaic
RG Runge-Gross
RI Resolution of Identity
RPA Random Phase Approximation
RSH Range Separated Hybrid
SAC-CI Symmetry Adapted Cluster Configuration Interaction
SBU Secondary Binding Unit
SCC-DFTB Self Consistent Charge Density Functional Tight Binding
SCU Steric Control Unit
SE Schrödinger Equation
SI Supporting Information
SIE Self Interaction Error
sTDA simplified Tamm-Dancoff Approximation
sTD-DFT simplified Time-Dependent Density Functional Theory
STEOM-CC Similarity Transformed Equation of Motion Coupled Cluster
SURMOF Surface-mounted Metal-Organic Framework
TDA Tamm-Dancoff Approximation
TD-DFT Time Dependent Density Functional Theory
UFF Universal Force Field
UV-Vis Ultraviolet-Visible
VB Valence Band
XC Exchange-Correlation
XRD X-Ray Diffraction
ZnOEP Zinc Octaethylporphyrin
ZnTCPP Zinc tetrakis(4-carboxyphenyl) porphyrin
ZnTPP Zinc Tetraphenylporphyrin
111
B. Appendices
B1. Supporting Information (SI) of Chapter 3 (S3)
Benchmarking the Performance of Time-Dependent Density
Functional Theory for Predicting the UV-Vis Spectral Properties of
Porphyrinoids
Table of Contents
I. UV-Vis Representation of Tetra-Phenyl-Porphyrin (H2TPP)
II. Computational Summary
III. Charge Transfer Excitations in Tetrakis(o-aminophenyl) Porphyrin
IV. Scaled Error Dataset for Diverse DFT Functional Approaches
V. Boxplot – Absolute Mean Error Representations
VI. Influence of Diffuse Functions and Geometry
112
I. UV-Vis Representation of Tetraphenyl Porphyrin (H2TPP)
II. Computational Summary
Table S3.1 Summarize the computational protocols (including various functionals, approaches
and basis-sets) applied for the PP-benchmark study.
DFT
Group
DFT
Functionals
Computational Approaches (Basis Set Choices)
TDA
(SVP)
RPA
(SVP)
sTDA
(SVP)
sTD-DFT
(SVP)
sTDA
(TZVP)
sTD-DFT
(TZVP)
sTDA
(SVPD)
sTDA
(TZVPD)
GGA and
mGGA
PBE x x x x x x
BP86 x x x x x x
BLYP x x x x x x x x
*BLYP x x x
TPSS x x x x x x
M06-L x x x x x x
PBE0 x x x x x x
Figure S3.1 UV-Vis-spectra of H2TPP and the transitions based on the model of Gouterman’s
113
Global
Hybrids
B3P86 x x x x x x
B3LYP x x x x x x x x
*B3LYP x x x
TPSS0 x x x x x x
M06 x x x x x x
BHLYP x x x x x x
M06-2X x x x x x x
Range
Separate
Hybrids
ωB97 x x x x x x
ωB97X x x x x x x
LC-BLYP x x x x x x
CAM-B3LYP x x x x x x x x
*CAM-B3LYP x x x
Double
Hybrids
and post
HF
B2PLYP x
B2GP-PLYP x
mPW2PLYP x
CIS x
CIS(D) x
Note: All the ground state geometries are fully optimized using BLYP-D3/TZVP level
Here (*) indicates the re-optimization of all geometries using B3LYP-D3/TZVP level to examine the
influence of applied functional on calculated absorption bands.
III. Charge Transfer Excitations in Tetrakis(o-aminophenyl) Porphyrin
Table S3.2: Charge transfer (CT) properties shown by GGAs in TD-DFT type (TDA and RPA)
for 8 (H2TAPP) molecule. Charge coefficients c yield the weights of the individual excitation,
calculated as 100% 𝑐2.
114
BLYP/TDA
State 1
E= 1.83 eV
PBE /TDA
State 1
E= 1.81 eV
BP86 /TDA
State 1
E= 1.82 eV
172 177 18 % (c= 0.43) 172 177 15% (c= 0.38) 172 177 15 % (c= 0.39)
175 177 32 % (c= 0.57) 175 177 35% (c= 0.59) 175 177 34 % (c= 0.58)
176 177 43% (c= 0.66) 176 177 46% (c= 0.68) 176 177 55 % (c= 0.67)
BLYP/TDA
State 2
E= 1.86 eV
PBE /TDA
State 2
E= 1.83 eV
BP86 /TDA
State 2
E= 1.84 eV
174 177 99 % (c= 0.99) 174 177 98% (c= 0.99) 174 177 98 % (c= 0.99)
BLYP/RPA
State 1
E= 1.82 eV
PBE /RPA
State 1
E= 1.80 eV
BP86 /RPA
State 1
E= 1.81 eV
172 177 18 % (c= 0.43) 172 177 15 % (c= 0.39) 172 177 16 % (c= 0.40)
175 177 22 % (c= 0.47) 175 177 25 % (c= 0.50) 175 177 24 % (c= 0.49)
176 177 54 % (c= 0.73) 176 177 55 % (c= 0.74) 176 177 55 % (c= 0.74)
BLYP/RPA
State 2
E= 1.86 eV
PBE /RPA
State 2
E= 1.83 eV
BP86 /RPA
State 2
E= 1.84 eV
175 178 99 % (c= 0.99) 174 177 99 % (c= 0.99) 174 177 99 % (c= 0.99)
Figure S3.2 (a) Molecular orbitals of 8 (H2TAPP)
115
IV. Scaled Error Dataset for Diverse Density Functional Approaches
Table S3.3 Calculated errors in eV for the GGA functionals with scaled absorption energies
GGA and m-GGA
Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
PBE
ME 0.01 0.01 0.01 0.01 0.01 0.01
MAE 0.11 0.11 0.10 0.10 0.09 0.09
MAXE 0.49 0.44 0.45 0.41 0.31 0.30
Scaling Factor 0.99 1.02 1.04 1.07 1.09 1.11
BP86
ME 0.01 0.01 0.01 0.01 0.01 0.01
MAE 0.11 0.11 0.10 0.10 0.09 0.09
MAXE 0.48 0.43 0.44 0.40 0.30 0.29
Scaling Factor 0.99 1.02 1.04 1.06 1.09 1.11
BLYP
ME 0.01 0.01 0.01 0.01 0.01 0.01
MAE 0.10 0.11 0.09 0.10 0.09 0.09
MAXE 0.46 0.41 0.41 0.38 0.28 0.27
Figure S3.2 (b) Density difference comparison of H2TAPP with representative functionals
116
Scaling Factor 1.00 1.03 1.04 1.07 1.10 1.11
TPSS
ME 0.01 0.01 0.01 0.01 0.00 0.00
MAE 0.10 0.10 0.09 0.09 0.09 0.09
MAXE 0.43 0.38 0.39 0.36 0.27 0.26
Scaling Factor 0.97 1.00 1.01 1.03 1.06 1.08
M06-L
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.09 0.09 0.08 0.08 0.08 0.09
MAXE 0.35 0.30 0.33 0.30 0.24 0.23
Scaling Factor 0.95 0.98 0.98 1.00 1.03 1.04
Table S3.4 Calculated errors in eV for the hybrid functionals with scaled absorption energies.
Global Hybrid
Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
PBE0
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.07 0.08 0.07 0.07 0.08 0.08
MAXE 0.14 0.15 0.17 0.18 0.22 0.22
Scaling Factor 0.90 0.93 1.04 1.06 1.12 1.13
B3P86
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.07 0.08 0.06 0.07 0.08 0.08
MAXE 0.15 0.16 0.17 0.18 0.22 0.22
Scaling Factor 0.91 0.94 1.01 1.03 1.08 1.09
B3LYP
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.07 0.08 0.06 0.07 0.08 0.08
MAXE 0.15 0.15 0.17 0.18 0.21 0.22
Scaling Factor 0.92 0.95 1.01 1.03 1.08 1.10
TPSS0
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.07 0.08 0.06 0.07 0.08 0.08
117
MAXE 0.14 0.15 0.16 0.17 0.21 0.22
Scaling Factor 0.90 0.93 1.02 1.04 1.09 1.11
M06
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.07 0.08 0.06 0.07 0.08 0.08
MAXE 0.14 0.15 0.17 0.18 0.21 0.22
Scaling Factor 0.93 0.97 1.08 1.11 1.17 1.19
BHLYP ME 0.00 0.00 0.00 0.01 0.00 0.00
MAE 0.07 0.07 0.06 0.06 0.08 0.08
MAXE 0.14 0.14 0.14 0.14 0.18 0.16
Scaling Factor 0.88 0.94 1.17 1.21 1.27 1.34
M06-2X ME 0.00 0.00 0.00 0.01 0.00 0.00
MAE 0.07 0.06 0.06 0.06 0.08 0.08
MAXE 0.13 0.12 0.14 0.15 0.19 0.18
Scaling Factor 0.88 0.93 1.24 1.31 1.35 1.47
Table S3.5 Calculated errors in eV for the RSH functionals with scaled absorption energies.
Range Separated
Hybrid Functionals
TDA
(def2-
SVP)
RPA
(def2-
SVP)
sTDA
(def2-
SVP)
sTD-DFT
(def2-
SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
ωB97
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.06 0.05 0.12 0.12 0.11 0.11
MAXE 0.12 0.11 0.23 0.23 0.22 0.23
Scaling Factor 0.91 1.08 1.08 1.28 1.09 1.27
ωB97X
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.06 0.05 0.12 0.12 0.11 0.11
MAXE 0.12 0.10 0.23 0.24 0.21 0.22
Scaling Factor 0.90 1.04 1.09 1.26 1.10 1.25
LC-BLYP ME 0.00 0.00 0.00 0.00 0.00 0.00
118
MAE 0.06 0.05 0.12 0.12 0.11 0.11
MAXE 0.12 0.10 0.24 0.24 0.22 0.22
Scaling Factor 0.91 1.05 1.07 1.20 1.08 1.20
CAM-
B3LYP
ME 0.00 0.00 0.00 0.00 0.00 0.00
MAE 0.06 0.05 0.04 0.05 0.06 0.07
MAXE 0.13 0.12 0.08 0.12 0.13 0.13
Scaling Factor 0.90 0.96 0.99 1.01 1.07 1.09
Table S3.6 Calculated errors in eV for the double hybrids and post-Hartree Fock (HF) methods
with scaled absorption energies
Double Hybrids and
Post-HF Methods (def2-SVP)
B2PLYP
ME 0.00
MAE 0.04
MAXE 0.08
Scaling Factor 0.90
B2GP-PLYP
ME 0.00
MAE 0.04
MAXE 0.09
Scaling Factor 0.88
mPW2PLYP
ME 0.00
MAE 0.05
MAXE 0.09
Scaling Factor 0.89
CIS
ME 0.00
MAE 0.10
MAXE 0.17
119
Scaling Factor 0.89
CIS (D) ME 0.00
MAE 0.04
MAXE 0.08
Scaling Factor 0.80
V. Box-Plots Analysis - Absolute Mean Error Representations
Box-plot of variant DFT functionals displaying the error distribution of dataset based on the
following four number summary: (+) mean absolute error; (box) range between lower and
upper quartile; (dashed lines) minimum and maximum, excluding outliers; (black dots) outliers
termed as extremes error values which are outside the range given in bar. Variant color box
represents functional-approach-basis-set combination such as yellow: TDA (def2-SVP); cyan:
RPA (def2-SVP); orange: sTDA (def2-SVP); sky blue: sTD-DFT (def2-SVP); red: sTDA
(def2-TZVP); blue: sTD-DFT (def2-TZVP); white: TDA+MP2 (def2-SVP); grey: CIS and
CISD, (def2-SVP); light brown: sTDA (def2-SVPD) and dark brown: sTDA (def2-TZVPD)
120
Figure S3.3 Boxplot displaying scaled error values in eV for the variant of density-functionals in
combination with TD-DFT types (a) TDA, (b) RPA, and def2-SVP basis set.
Figure S3.4 Boxplot displaying scaled error values in eV for the variant of density-functionals in
combination with TD-DFT types (a) sTDA, (b) sTD-DFT, and def2-SVP basis set.
121
Figure S3.5 Full box-plot error distribution in eV for all approaches and basis set combinations.
Original error values are on the left while scaled error values are shown on the right.
122
Figure S3.6 Full box-plot error distribution in nm for all approaches and basis set combinations.
Original error values are on the left while scaled error values are shown on the right.
123
VI. Influence of Diffuse Functions and Geometry
Table S3.7 Calculated original and scaled error values in eV for the selected density functionals
BLYP-D3/TZVP
Optimized Geometry
Original Error Values Scaled Error Values
sTDA-
def2-
SVP
sTDA-
def2-
SVPD
sTDA-
def2-
TZVPD
sTDA-
def2-
SVP
sTDA-
def2-
SVPD
sTDA-
def2-
TZVPD
BLYP
ME -0.08 -0.23 -0.26 0.01 0.00 0.00
MAE 0.09 0.23 0.26 0.09 0.09 0.09
MAXE 0.49 0.50 0.51 0.41 0.27 0.27
Scaling Factor - - - 1.04 1.12 1.14
ME -0.03 -0.22 -0.25 0.00 0.00 0.00
B3LYP MAE 0.06 0.22 0.25 0.06 0.09 0.09
MAXE 0.18 0.42 0.45 0.17 0.27 0.24
Scaling Factor - - - 1.01 1.12 1.14
ME 0.03 -0.20 -0.23 0.00 0.00 0.00
CAM-
B3LYP
MAE 0.05 0.20 0.23 0.04 0.08 0.09
MAXE 0.10 0.35 0.14 0.08 0.15 0.15
Scaling Factor - - - 0.99 1.10 1.12
124
Figure S3.7 Boxplot displaying original error values in eV for the selected density functionals with
and without diffuse (‘D’) basis set functions where (a) is the BLYP-D3-TZVP based geometry
optimization while (b) is B3LYP-D3/-TZVP based geometry optimization for the benchmark-set
Figure S3.8 Box-plot displaying scaled error values in eV for the selected density functionals with
and without diffuse(‘D’) basis set functions, where (a) is the BLYP-D3-TZVP based geometry
optimization while (b) is B3LYP-D3-TZVP based geometry optimization for the benchmark-set.
125
Table S3.8: ϵ (HOMO) criterion based on BLYP-D3-TZVP geometries
BLYP-sTDA B3LYP-sTDA CAM-B3LYP-sTDA
Molecules ϵ
(eV)
def2-
SVP
def2-
SVPD
def2-
TZVPD
def2-
SVP
def2-
SVPD
def2-
TZVPD
def2-
SVP
def2-
SVPD
def2-
TZVPD
H2PP ϵH-L 1.90 1.92 1.92 2.87 2.88 2.88 4.68 4.68 4.68
- ϵH 2.74 2.91 2.91 2.43 2.58 2.57 1.69 1.85 1.84
H2OEP ϵH-L 1.94 1.96 1.96 2.91 2.88 2.86 4.60 4.56 4.53
- ϵH 2.42 2.57 2.55 2.11 2.24 2.21 1.39 1.51 1.49
MgOEP ϵH-L 2.02 2.01 2.00 2.89 2.86 2.85 4.58 4.55 4.52
- ϵH 2.37 2.50 2.48 2.06 2.17 2.14 1.33 1.44 1.41
ZnOEP ϵH-L 2.04 2.02 2.01 2.91 2.88 2.86 4.61 4.56 4.54
- ϵH 2.34 2.51 2.48 2.04 2.17 2.14 1.30 1.44 1.41
H2TPP ϵH-L 1.75 1.75 1.76 2.69 2.69 2.69 4.46 4.46 4.46
- ϵH 2.69 2.87 2.85 2.39 2.54 2.52 1.67 1.82 1.80
MgTPP ϵH-L 1.82 1.80 1.80 2.74 2.72 2.72 4.51 4.48 4.49
- ϵH 2.65 2.80 2.79 2.34 2.48 2.46 1.62 1.76 1.74
ZnTPP ϵH-L 1.88 1.87 1.87 2.81 2.80 2.80 4.59 4.57 4.58
- ϵH 2.63 2.80 2.79 2.32 2.47 2.46 1.59 1.75 1.73
H2TAPP ϵH-L 1.72 1.74 1.75 2.70 2.70 2.71 4.50 4.50 4.51
- ϵH 2.76 2.96 2.94 2.46 2.63 2.61 1.73 1.91 1.88
ZnTCPP ϵH-L 1.87 1.86 1.87 2.80 2.79 2.79 4.58 4.56 4.57
- ϵH 3.00 3.26 3.23 2.72 2.93 2.91 1.98 2.20 2.17
F-ZnP ϵH-L 1.89 1.88 1.88 2.82 2.81 2.82 4.59 4.55 4.53
- ϵH 3.29 3.56 3.51 3.06 3.27 3.21 2.36 2.58 2.52
DA-ZnP ϵH-L 1.42 1.41 1.41 2.25 2.23 2.24 3.91 3.89 3.90
- ϵH 3.33 3.50 3.49 3.09 3.24 3.22 2.43 2.58 2.56
H2OBP ϵH-L 1.36 1.37 1.37 2.21 2.22 2.23 3.90 3.90 3.92
- ϵH 3.31 3.55 3.51 3.12 3.31 3.26 2.47 2.65 2.60
126
Table S3.9 Calculated original and scaled error values in eV for the selected density functionals
B3LYP-D3/TZVP
Optimized Geometry
Original Error Values Scaled Error Values
sTDA-
def2-
SVP
sTDA-
def2-
SVPD
sTDA-
def2-
TZVPD
sTDA-
def2-
SVP
sTDA-
def2-
SVPD
sTDA-
def2-
TZVPD
BLYP
ME -0.04 -0.19 -0.22 0.00 0.00 0.00
MAE 0.08 0.19 0.22 0.09 0.09 0.10
MAXE 0.46 0.46 0.47 0.42 0.27 0.27
Scaling Factor - - - 1.02 1.10 1.12
ME 0.02 -0.17 -0.21 0.00 0.00 0.00
B3LYP MAE 0.07 0.18 0.21 0.07 0.09 0.10
MAXE 0.18 0.37 0.41 0.16 0.26 0.25
Scaling Factor - - - 0.99 1.09 1.11
ME 0.08 -0.14 -0.18 0.00 0.00 0.00
CAM-
B3LYP
MAE 0.08 0.14 0.18 0.04 0.08 0.09
MAXE 0.16 0.30 0.34 0.07 0.15 0.16
Scaling Factor 0.96 1.07 1.09
Table S3.10: Molar attenuation coefficient, ε (cm-1/M) with BLYP functional in combination
of variant applied approaches-basis sets for the given PP-Benchmark-set. The ε (cm-1/M) for
all the porphyrinoids (benchmark-set) are taken from the references [195-206].
BLYP Functional
Molecules Ref. ε
(cm-1/M)
TDA
(def2-SVP)
RPA
(def2-SVP)
sTDA
(def2-SVP)
sTD-DFT
(def2-SVP)
sTDA
(def2-TZVP)
sTD-DFT
(def2-TZVP)
H2PP (1300) 100 253 70 186 39 114
(3000) 2 87 41 32 1 61
H2OEP (9000) 56 12 223 118 376 253
127
(16000) 632 287 1315 664 820 430
MgOEP (23000) 600 517 843 645 660 480
ZnOEP (38000) 603 707 810 594 618 458
H2TPP (4500) 2369 3289 2492 3091 2265 2686
(8000) 2838 4221 3174 4508 3320 4248
MgTPP (11000) 2009 2873 2599 3447 2757 3330
ZnTPP (5000) 1454 2185 1730 2429 1935 2382
H2TAPP (14) 410 662 997 1131 1808 1949
(8) 4 4 2168 2428 2938 3399
ZnTCPP (NA) 3687 4342 4236 4951 3970 4413
F-ZnP (8400) 1711 2371 2249 2971 2456 2916
DA-ZnP (51000) 61 77166 26 79667 60 74145
H2OBP (7500) 7405 8432 8871 9137 8735 8712
(13200) 9495 10955 11839 12652 11342 11533
Table S3.11: Molar attenuation coefficient, ε (cm-1/M) with B3LYP functional in
combination of variant applied approaches-basis sets for the given PP-Benchmark-set.
B3LYP Functional
Molecules Ref. ε
(cm-1/M)
TDA
(def2-SVP)
RPA
(def2-SVP)
sTDA
(def2-SVP)
sTD-DFT
(def2-SVP)
sTDA
(def2-TZVP)
sTD-DFT
(def2-TZVP)
H2PP (1300) 1 29 0 22 10 0
(3000) 71 0 104 1 33 2
H2OEP (9000) 442 566 680 560 873 728
(16000) 1284 1264 1631 1182 1127 793
MgOEP (23000) 1398 1472 1431 1327 1196 1018
ZnOEP (38000) 2002 2240 2264 2150 1767 1583
H2TPP (4500) 1730 2517 1833 2364 1433 1821
(8000) 2314 3656 2600 3900 2304 3233
MgTPP (11000) 1428 2172 1899 2658 1704 2248
ZnTPP (5000) 929 1516 1153 1710 1158 1582
128
H2TAPP (14) 1538 2223 1675 2075 1133 1414
(8) 1883 2686 2266 3108 1604 2259
ZnTCPP (NA) 1863 2505 2300 2948 2034 2549
F-ZnP (8400) 1076 1617 1476 2061 1407 1865
DA-ZnP (51000) 86077 77451 87082 76493 77904 69693
H2OBP (7500) 9855 11039 10808 10904 9556 9591
(13200) 11352 13415 12793 14121 11105 11807
Table S3.12: Molar attenuation coefficient, ε (cm-1/M) with CAM-B3LYP functional in
combination of variant applied approaches-basis sets for the given PP-Benchmark-set.
CAM-B3LYP Functional
Molecules Ref. ε
(cm-1/M)
TDA
(def2-SVP)
RPA
(def2-SVP)
sTDA
(def2-SVP)
sTD-DFT
(def2-SVP)
sTDA
(def2-
TZVP)
sTD-DFT
(def2-
TZVP)
H2PP (1300) 101 90 67 18 204 135
(3000) 252 112 702 231 329 137
H2OEP (9000) 1230 1920 1739 1595 2288 2106
(16000) 2120 2292 4807 4171 3035 2673
MgOEP (23000) 2503 2632 4285 4194 3513 3327
ZnOEP (38000) 3499 3674 6445 6334 5028 4830
H2TPP (4500) 948 1188 1472 1884 991 1210
(8000) 1679 2579 2083 2805 1880 2741
MgTPP (11000) 778 1169 1122 1818 1042 1423
ZnTPP (5000) 406 690 397 816 493 739
H2TAPP (14) 738 933 1076 1341 652 818
(8) 860 1477 738 1590 730 1225
ZnTCPP (NA) 716 1049 658 1071 702 985
F-ZnP (8400) 466 744 541 963 596 868
DA-ZnP (51000) 63927 57422 76664 69434 71986 66438
H2OBP (7500) 10087 9775 15068 14156 13147 12483
(13200) 11002 12109 18425 20654 14395 15424
129
B.2 Supporting Information (SI) of Chapter 4 (S4)
Computational Screening of Surface-mounted Metal-Organic
Frameworks Assembled from Porphyrins
COMPUTATIONAL SECTION
Figure S4.1 Library of all porphyrins (PPs) selected for computational investigations.
130
S4.2. Calculated and experimental (selected) absorption wavelengths of the investigated
porphyrins with employed abbreviations (in nm).
Porphyrin
Structures
Calculated
Experimental
1-H 641, 550 646, 546
1-F 624, 538 --
1-Cl 704, 603 --
1-Br 692, 614 740, 615
1-Me 692, 595 --
2 632, 551 --
3 637, 548 --
4 661, 576 --
5 692, 613 688, 595
6 662, 631 --
7 701, 663 --
8 788, 542 --
9 664, 583 --
10 638, 546 598, 512
131
Figure S4.3 Comparison of the calculated absorption spectra of all the porphyrin linkers (see
Figure S1) with 1-H.
132
S4.4 List of all investigated PPs molecules with employed abbreviation and IUPAC name.
Abbreviation IUPAC Name
1-H 5,15-diphenyl-10,20-bis(4-carboxyphenyl) porphyrin
1-F Octafluoro-5,15-diphenyl-10,20-bis(4-carboxyphenyl) porphyrin
1-Cl Octachloro-5,15-diphenyl-10,20-bis(4-carboxyphenyl) porphyrin
1-Br Octabromo-5,15-diphenyl-10,20-bis(4-carboxyphenyl) porphyrin
1-Me Octamethyl-5,15-diphenyl-10,20-bis(4-carboxyphenyl) porphyrin
2 5,15-bis(pyridyl)-10,20-bis(4-carboxyphenyl) porphyrin
3 5,15-bis(bipyridyl)-10,20-bis(4-carboxyphenyl) porphyrin
4 5,15-bis(ethynyl)-10,20-bis(4-carboxyphenyl)porphyrin
5 5,15-bis(phenylethynyl)-10,20-bis(4-carboxyphenyl) porphyrin
6 5,15-diphenyl-10,20-bis(4-carboxyphenyl) dibenzo[b,l]-porphyrin
7 5,15-diphenyl-10,20-bis(4-carboxyphenyl) tetrabenzo-porphyrin
8 5,15-diphenyl-10,20-bis(4-carboxyphenyl) bacteriochlorin
9 5,15-bis(tert-butyl)-10,20-bis(4-carboxyphenyl) porphyrin
10 5,15-bis(3,4,5-trifluorophenyl)-10,20-bis(4 carboxphenyl)porphyrin
S4.5 Calculated lattice parameters for the selected PP-based SURMOF structures.
Structures a (in Å) b (in Å) c (in Å)
1-Br ' 23.75 23.75 6.12
5 ' 23.85 23.85 6.22
10 ' 23.85 23.85 6.38
S4.6 Calculated band gap for the selected PP-based SURMOF structures.
Structures Band gap (in eV)
1-Br ' 1.15
5 ' 1.09
10 ' 1.72
133
S4.7 Structural analysis of the selected PP-based SURMOFs shown in Fig. S8
Structures Distance, d (in Å) Angle, α (in °) Shift, s (in Å)
1-Br' (x-direction) 6.023 79.8 1.087
1-Br' (y-direction) 6.069 82.6 0.785
5' (x-direction) 3.314 32.2 5.262
5' (y-direction) 3.305 32.1 5.268
10' (x-direction) 6.358 85.2 0.529
10' (y-direction) 6.335 83.2 0.755
Note: slight differences in stacking values are due to the numerical noise.
-(d) distance between the PPs
-(α) angle with respect to crystal plane
-(s) shift from eclipsed stacking
-(x), -(y) denotes the stacking directions
134
Figure S4.8 Stacking analysis of the selected tuned-PPs (a) 1-Br' (b) 5' and (c) 10'
Figure S4.9 Band structure of the 5' with zoom-in of the valence band and conduction band
at PBE-level of theory
135
EXPERIMENTAL SECTION
Materials:
Reactions which require dry solvents were prepared using standard Schlenk conditions. Liquid
reagents were added via plastic syringes with stainless steel cannulas. Non-dry solvents were
used in p.a. quality (pro analysi) purchased from Fisher Scientific and Sigma Aldrich without
further purification. Dry THF was freshly distilled over potassium prior to use, dry
triethylamine was bought from Sigma-Aldrich and used without further purification.
Chemicals were purchased from ABCR, Alfa Aesar, Carbolution, Chempur, Sigma-Aldrich
and TCI and used without further purification unless stated otherwise. Monitoring of reactions
was done by TLC using silica gel coated aluminium plates (TLC silica gel 60 F254) purchased
from Merck and a UV lamp emitting with λ = 254 nm. Column chromatographies were
performed using silica gel 60 (0.040–0.063 mm, 230–400 mesh ASTM) purchased from Merck
as stationary phase and solvents in p.a. quality.
Zinc acetate dihydrate was purchased from Merck Millipore. 16-mercaptohexadecanoic acid
(MHDA, 97%), was purchased from Sigma-Aldrich (Germany). Absolute ethanol was
purchased from VWR (Germany).
Figure S4.10 Band structure of the 5' with zoom-in of the valence band and conduction
band at PBE0-level of theory
136
Substrates:
The silicon substrates with a [100] orientation are from Silicon Sense (US). The quartz glasses
are from Alfa Aesar. These substrates were treated with plasma (Diener Plasma) under O2 (50
sccm) for 30 min to remove the impurities and generated a surface with hydroxyl groups.
X-ray diffraction (XRD)
The XRD measurements for out-of-plane (co-planar orientation) were carried out using a
Bruker D8-Advance diffractometer equipped with a position sensitive detector Lynxeye in
geometry, variable divergence slit and 2.3° Soller-slit was used on the secondary side. The Cu-
anodes which utilize the Cu Kα1,2-radiation (ʎ = 0.154018 nm) was used as source.
Characterizations of Porphyrin linkers by 1H-NMR, 13C NMR and HR MS
All NMR spectra were recorded on a BRUKER Avanche 400 (1H NMR: 400 MHz, 13C NMR:
100 MHz, 19F NMR: 377 MHz) at room temperature using deuterated chloroform purchased
from Eurisotop. Chemical shift δ were given in ppm, with the residual solvent peak as reference
(7.26 ppm for 1H and 77.16 ppm for 13C NMR). Coupling constants J were given in Hertz (Hz)
as absolute values. For examination of spectra the following abbreviations are used: s = singlet,
bs = broad singlet, d = doublet, t = triplet, q = quartet, dd = doublet of doublets, td = triplet of
doublets, m = multiplet. The spectra were analyzed according to first order. For multiplicities
in 13C spectra the following abbreviations were used: + = primary or tertiary C, – = secondary
C, Cq = quaternary C. For the assignment of signals the following indices were used: meso =
meso position of porphyrin, Pyr = pyrrolic positions of porphyrin, Ph = phenyl.
(High resolution) Mass spectra were recorded on a Finnigan MAT 95 instrument using either
FAB (fast atom bombardement), with 3-nitrobenzyl alcohol used as matrix or EI (electron
impact) with 70 eV as ionization method. Mass spectra were interpreted by listing the
mass/charge ratios (m/z) of molecule fragments together with their intensities relative to the
base peak (100%).
Syntheses of Porphyrin linkers:
Di(1H-pyrrol-2-yl)methane (11)298
137
To 340 mL of freshly distilled pyrrole (330 g, 4.92 mol, 92.7 equiv.) were added 1.59 g of
paraformaldehyde (53.1 mmol, 1.00 equiv.) and the resulting suspension was stirred for 10 min
at 55 °C. Then 1.16 g InCl3 (5.25 mmol, 0.10 equiv.) were added and the resulting mixture was
stirred for additional 3 h at 55 °C. After cooling down to rt, 7.02 g powdered NaOH (176 mmol,
3.31 equiv.) were added and the mixture was stirred for another hour, followed by filtration.
The filtrate was evaporated under reduced pressure and the remaining crude product was
purified by column chromatography (CH/EE 10:1 with gradient to 2:1) to yield 5.05 g of 11
(34.5 mmol, 65%) as a white solid.
Rf (CH/EE 2:1) = 0.57. – 1H-NMR (400 MHz, CDCl3): (ppm) = 3.94 (s, 2H, CH2), 6.03–
6.09 (m, 2H), 6.18 (q, J = 2.9 Hz, 2H), 6.62 (td, J = 2.7, 1.6 Hz, 2H), 7.67 (bs, 2H, NH). – 13C-
NMR (100 MHz, CDCl3): (ppm) = 26.4 (–, CH2), 106.6 (+), 108.4 (+), 117.5 (+), 129.2 (Cq).
– IR (ATR): = 3325 (m), 1561 (w), 1468 (w), 1439 (w), 1327 (w), 1244 (w), 1181 (w), 1119
(w), 1108 (w), 1095 (w), 1024 (m), 961 (w), 884 (w), 857 (vw), 797 (m), 720 (s), 667 (m), 600
(m), 586 (m) cm–1. – MS (EI, 70 eV): m/z (%) = 146.1 (100) [M]+, 147.1 (11), 145.1 (70), 80.1
(30) [C5H6N]+. – HRMS (C9H10N2): ber.: 146.0844, gef.: 146.0845.
Ethyl 4-formylbenzoate (12)299
To a solution of 4.87 g 4-formylbenzoic acid (32.4 mmol, 1.00 equiv.) in 125 mL of DMF were
added 8.68 g K2CO3 (62.8 mmol, 1.94 equiv.) and 6.60 mL iodoethane (12.8 g, 62.8 mmol,
2.54 equiv.). After stirring the reaction for 3 h at rt, water was added, the phases were separated
and the aqueous phase was extracted with diethyl ether two times. The combined organic
phases were washed with brine, dried over MgSO4 and filtered. After removal of the solvent
under reduced pressure, the crude product was purified by column chromatography (CH/EE
6:1) to yield 4.90 g of 12 (27.5 mmol, 85%) as a light yellowish liquid.
Rf (CH/EE 6:1) = 0.83. – 1H-NMR (400 MHz, CDCl3): (ppm) = 1.38 (t, J = 7.1 Hz, 3H,
CH3), 4.38 (q, J = 7.1 Hz, 2H, CH2), 7.91 (d, J = 8.5 Hz, 2H, HPh), 8.16 (d, J = 8.5 Hz, 2H,
HPh), 10.06 (s, 1H, OCH). – 13C-NMR (100 MHz, CDCl3): (ppm) = 14.3 (+, CH3), 61.6 (–,
CH2), 129.5 (+, CPhH), 130.2 (+, CPhH), 135.5 (Cq), 139.2 (Cq), 165.6 (Cq, COO), 191.7 (+,
OCH). – IR (ATR): = 2924 (w), 2854 (w), 1701 (s), 1577 (w), 1503 (vw), 1448 (w), 1367
(w), 1272 (m), 1200 (w), 1172 (w), 1103 (m), 1017 (m), 854 (w), 818 (w), 758 (m), 733 (w),
690 (w), 630 (vw), 461 (vw) cm–1. – MS (EI, 70 eV): m/z (%) = 178.1 (44) [M]+, 179.1 (5),
138
149.1 (24) [M – CO]+, 133.1 (100) [M – C2H5O]+. – HRMS (C10H10O3): ber.: 178.0630, gef.:
178.0630.
5,15-Bis(4-ethoxycarbonylphenyl)porphyrin (13)300
Through a solution of 1.10 g di(1H-pyrrol-2-yl)methane (11) (7.53 mmol, 2.00 equiv.) and
1.36 g ethyl 4-formylbenzoate (12) (7.62 mmol, 2.02 equiv.) in 1.50 L CHCl3 was passed Ar
gas for 30 min, followed by the dropwise addition of 580 µL TFA (858 mg, 7.53 mmol,
2.00 equiv.). The reaction was stirred for 17 h in the dark, after which time 3.21 mL NEt3
(2.35 g, 23.2 mmol, 6.16 equiv.) and 5.52 g p-chloranil (22.4 mmol, 5.96 equiv.) were added
in this order. The mixture was then refluxed for 90 min and the solvent removed under reduced
pressure. After a filtration through silica gel (DCM) to remove most of the oligomeric side
products, the crude product was purified by column chromatography (DCM/EE 1:0 with
gradient to 50:1). The obtained solid was thoroughly washed with MeOH, leaving 1.07 g of 13
(1.76 mmol, 47%) as a purple solid.
Rf (DCM) = 0.42. – 1H-NMR (400 MHz, CDCl3): (ppm) = –3.13 (bs, 2H, NH), 1.58 (t,
J = 7.1 Hz, 6H, CH3), 4.61 (q, J = 7.1 Hz, 4H, CH2), 8.36 (d, J = 8.2 Hz, 4H, HPh), 8.51 (d,
J = 8.2 Hz, 4H, HPh), 9.04 (d, J = 4.6 Hz, 4H, HPyr), 9.42 (d, J = 4.6 Hz, 4H, HPyr), 10.34 (s,
2H, Hmeso). – 13C-NMR (100 MHz, CDCl3): (ppm) = 14.7 (+, CH3), 61.5 (–, CH2), 105.8 (+),
118.3 (Cq), 128.3 (+), 130.1 (Cq), 130.9 (+), 132.2 (+), 135.0 (+), 145.5 (Cq), 146.2 (Cq), 146.8
(Cq), 167.0 (Cq, COO). – UV/VIS (CHCl3): max (log ) = 405 (5.27), 504 (4.22), 539 (3.85),
576 (3.74), 631 (3.33) nm. – IR (ATR): = 3484 (vw), 3276 (vw), 2976 (vw), 1703 (m), 1602
(w), 1437 (w), 1398 (w), 1363 (w), 1305 (vw), 1268 (m), 1239 (w), 1194 (w), 1173 (w), 1096
(m), 1051 (w), 1017 (w), 986 (w), 971 (w), 952 (w), 900 (w), 868 (m), 843 (w), 812 (w), 792
(m), 752 (w), 736 (m), 723 (m), 691 (m), 520 (vw), 489 (w), 435 (w), 411 (vw) cm–1. – HRMS
(C38H31O4N4): ber.: 607.2340, gef.: 607.2340.
Cross coupling reactions were performed according to a known procedure established by Senge
et al.301
5,15-Dibromo-10,20-bis(4-ethoxycarbonylphenyl)porphyrin (14)302-303
139
To a solution of 933 mg porphyrin 13 (1.54 mmol, 1.00 equiv.) in 385 mL of CHCl3 were
added 0.38 mL pyridine (377 mg, 4.77 mmol, 3.10 equiv.). The mixture was cooled to 0 °C
and 646 mg NBS were added, as well as 50 mg in intervals of 30 min respectively, until a
complete conversion was observed by TLC (∑ 746 mg, 4.19 mmol, 2.72 equiv.). After addition
of the last portion, the reaction was stirred for 30 min and the mixture was directly filtered
through silica gel eluting with DCM. The solvent of the filtrate was removed under reduced
pressure and the crude product was purified by column chromatography (DCM). The obtained
solid was recrystallized from DCM/MeOH yielding 1.00 g of porphyrin 14 (1.31 mmol, 85%)
as a purple solid.
Rf (DCM) = 0.60. – 1H-NMR (400 MHz, CDCl3): (ppm) = –2.77 (bs, 2H, NH), 1.57 (t,
J = 7.1 Hz, 6H, CH3), 4.60 (q, J = 7.1 Hz, 4H, CH2), 8.23 (d, J = 8.1 Hz, 4H, HPh), 8.47 (d,
J = 8.1 Hz, 4H, HPh), 8.78 (d, J = 4.8 Hz, 4H, HPyr), 9.62 (d, J = 4.9 Hz, 4H, HPyr). – 13C-
NMR (100 MHz, CDCl3): (ppm) = 14.7 (+, CH3), 61.6 (–, CH2), 104.3 (Cq), 120.4 (Cq),
128.2 (+), 130.5 (Cq), 134.6 (+), 146.1 (Cq), 166.8 (Cq, COO). – UV/VIS (CHCl3): max
(log ) = 423 (5.42), 522 (4.21), 557 (4.01), 601 (3.66), 659 (3.62) nm. – IR (ATR): =3314
(vw), 2921 (w), 1709 (m), 1605 (w), 1557 (w), 1465 (w), 1397 (w), 1366 (w), 1336 (w), 1302
(w), 1272 (m), 1193 (w), 1175 (w), 1122 (w), 1106 (m), 1018 (w), 997 (w), 979 (w), 961 (m),
869 (w), 848 (w), 795 (m), 785 (m), 755 (m), 729 (m), 706 (m), 630 (w), 555 (vw), 523 (w),
500 (w), 458 (w), 394 (vw) cm–1. – HRMS (C38H29O4N479Br81Br): ber.: 765.0530, gef.:
765.0528.
5,15-Bis(3,4,5-trifluorophenyl)-10,20-bis(4-ethoxycarbonylphenyl)porphyrin (15)
140
Under Ar atmosphere 95 mg of porphyrin 14 (124 µmol, 1.00 equiv.), 265 mg (3,4,5-
trifluorophenyl)boronic acid (1.51 mmol, 12.2 equiv.), 650 mg K3PO4 (3.06 mmol,
24.6 equiv.) and 15 mg Pd(PPh3)4 (13 µmol, 0.10 equiv.) were dissolved in 75 ml of dry THF
and the mixture was heated to 80 °C overnight under protection from light. After cooling of
the solution to rt the solvent was removed under reduced pressure. The residue was dissolved
in DCM, washed with a saturated solution of NaHCO3 and water and dried over Na2SO4. After
evaporation of the solvent under reduced pressure, the product was isolated by column
chromatography (DCM/CH 5:1) and a subsequent thorough wash with methanol, yielding
98 mg of porphyrin 15 (113 µmol, 91%) as a purple solid.
Rf (CH2Cl2) = 0.74. – 1H-NMR (400 MHz, CDCl3): (ppm) = –2.91 (bs, 2H, NH), 1.57 (t,
J = 7.1 Hz, 6H, CH3), 4.60 (q, J = 7.1 Hz, 4H, CH2), 7.80–7.91 (m, 4H, CHCF), 8.30 (d,
J = 8.2 Hz, 4H, HPh), 8.48 (d, J = 8.3 Hz, 4H, HPh), 8.79–8.93 (m, 8H, HPyr). – 13C-NMR
(100 MHz, CDCl3): (ppm) = 14.7 (+, CH3), 61.6 (–, CH2), 117.1 (Cq), 118.7, 118.8, 118.9,
118.9, 120.0 (Cq), 128.2 (+), 130.5 (Cq), 134.6 (+), 137.8, 137.8, 139.1, 141.6, 146.3 (Cq),
148.4, 148.5, 148.5, 148.6 , 150.9, 151.0, 151.0, 151.1, 166.8 (Cq, COO). 19F-NMR (377 MHz,
CDCl3): (ppm) = –140.0 (d, J = 20.6 Hz), –165.4 (t, J = 20.6 Hz). – UV/VIS (CHCl3): max
(log ) = 417 (5.41), 514 (4.26), 549 (3.76), 590 (3.73), 646 (3.30) nm. – IR (ATR): = 3302
(vw), 3070 (vw), 1707 (m), 1607 (w), 1525 (w), 1475 (w), 1423 (w), 1401 (w), 1365 (w), 1307
(vw), 1271 (m), 1237 (w), 1176 (w), 1108 (w), 1040 (m), 1022 (w), 973 (w), 928 (w), 869 (w),
849 (vw), 805 (m), 762 (w), 732 (w), 717 (w), 636 (vw), 561 (vw), 541 (w), 408 (vw) cm–1. –
HRMS (C50H33O4N4F6): ber.: 867.2401, gef.: 867.2403.
5,15-Bis(phenylethynyl)-10,20-bis(4-ethoxycarbonylphenyl)porphyrin (16)
141
Under Ar atmosphere 77 mg of porphyrin 14 (101 µmol, 1.00 equiv.), 4 mg CuI (20 µmol,
0.20 equiv.) and 7 mg Pd(PPh3)2Cl2 (10 µmol, 0.10 equiv.) were dissolved in 10 mL of dry
THF and 21 mL of dry NEt3. The solution was then purged with Ar gas for 15 min, followed
by the addition of 44 µL phenylacetylen (41 mg, 404 µmol, 4.00 equiv.). The reaction was
stirred overnight at rt and subsequently directly filtered through silica eluting with DCM. The
solvent of the filtrate was removed under reduced pressure and the crude product was purified
by column chromatography (CHCl3), yielding 62 mg of porphyrin 16 (76.8 µmol, 76%) as a
greenish-purple solid.
Rf (DCM) = 0.69. – 1H-NMR (400 MHz, CDCl3): (ppm) = –2.06 (bs, 2H, NH), 1.58 (t,
J = 7.2 Hz, 6H, CH3), 4.61 (q, J = 7.1 Hz, 4H, CH2), 7.47–7.63 (m, 6H, HPh), 7.98–8.07 (m,
4H, HPh), 8.27 (d, J = 8.2 Hz, 4H, HPh), 8.48 (d, J = 8.2 Hz, 4H, HPh), 8.77 (d, J = 4.7 Hz, 4H,
HPyr), 9.68 (d, J = 4.7 Hz, 4h, HPh). – 13C-NMR (100 MHz, CDCl3): (ppm) = 14.7 (+, CH3),
61.5 (–, CH2), 91.8 (Cq), 97.8 (Cq), 101.8 (Cq), 120.8 (Cq), 123.8 (Cq), 128.2 (+), 128.9 (+),
129.0 (+), 130.4 (Cq), 131.9 (+), 134.6 (+), 146.1 (Cq), 166.9 (Cq, COO). – UV/VIS (CHCl3):
max (log ) = 307 (4.45), 442 (5.36), 599 (4.70), 690 (4.32) nm. – IR (ATR): = 2972 (w),
1709 (m), 1604 (w), 1553 (w), 1487 (w), 1470 (w), 1399 (w), 1362 (w), 1264 (m), 1176 (m),
1159 (w), 1099 (m), 1065 (m), 1019 (m), 973 (m), 923 (w), 866 (w), 807 (m), 788 (m), 761
(w), 749 (m), 716 (m), 683 (m), 633 (w), 581 (w), 565 (w), 540 (w), 514 (w), 441 (w) cm–1. –
HRMS (C54H39O4N4): ber.: 807.2966, gef.: 807.2964.
5,15-Diphenyl-10,20-bis(4-ethoxycarbonylphenyl)porphyrin (17)
142
Under Ar atmosphere 152 mg of porphyrin 14 (198 µmol, 1.00 equiv.), 287 mg phenylboronic
acid (2.36 mmol, 11.9 equiv.), 1.04 g K3PO4 (4.91 mmol, 24.7 equiv.) and 27 mg Pd(PPh3)4
(23 µmol, 0.12 equiv.) were dissolved in 45 ml of dry THF and the mixture was heated to 80 °C
overnight under protection from light. After cooling of the solution the solvent was removed
under reduced pressure. The residue was dissolved in DCM, washed with a saturated solution
of NaHCO3 and water and dried over Na2SO4. After evaporation of the solvent under reduced
pressure, the product was isolated by column chromatography (DCM/CH 1:1 with gradient to
1:0), yielding 134 mg of porphyrin 17 (176 µmol, 89%) as a purple solid.
Rf (DCM) = 0.50. – 1H-NMR (400 MHz, CDCl3): (ppm) = –2.78 (bs, 2H, NH), 1.57 (t, J =
7.1 Hz, 6H, CH3), 4.59 (q, J = 7.2 Hz, 4H, CH2), 7.72–7.85 (m, 6H, HPh), 8.23 (dd, J = 7.6,
1.7 Hz, 2H, HPh), 8.32 (d, J = 8.2 Hz, 4H, HPh), 8.47 (d, J = 8.2 Hz, 4H, HPh), 8.82 (d,
J = 4.9 Hz, 4H, HPyr), 8.89 (d, J = 4.9 Hz, 4H, HPyr). – 13C-NMR (100 MHz, CDCl3): (ppm)
= 14.7 (+, CH3), 61.5 (–, CH2), 119.1 (Cq), 120.7 (Cq), 126.9 (+), 128.0 (+), 130.1 (Cq), 142.0
(Cq), 147.0 (Cq), 167.0 (Cq, COO). – UV/VIS (CHCl3): max (log ) = 419 (5.39), 516 (4.28),
551 (3.92), 591 (3.76), 646 (3.57) nm. – IR (ATR): = 3297 (vw), 3048 (vw), 3103 (vw), 2906
(w), 2978 (vw), 1713 (w), 1604 (vw), 1473 (vw), 1438 (vw), 1401 (vw), 1364 (vw), 1309 (vw),
1269 (w), 1177 (w), 1099 (w), 1023 (w), 980 (w), 964 (w), 863 (vw), 799 (w), 754 (w), 730
(w), 704 (w), 656 (vw), 635 (vw), 564 (vw), 455 (vw) cm–1. – HRMS (C50H39N4O4): ber.:
759.2971, gef.: 759.2969.
2,3,7,8,12,13,17,18-Octabromo-5,15-Diphenyl-10,20-bis(4-ethoxycarbonylphenyl)porphyrin
(18)
143
The reaction was performed similar to a literature known procedure.304
To a solution of 39 mg of porphyrin 17 (51.4 µmol, 1.00 equiv.) in 16 mL of CHCl3 were added
821 mg copper acetate monohydrate (411 µmol, 8.00 equiv.). The reaction mixture was stirred
at rt until complete conversion to copper porphyrin was detected by TLC (< 3 h). Then 430 µL
of molecular bromine (1.36 g, 8.48 mmol, 165 equiv.) were added to the reaction mixture
directly and the solution was stirred overnight at rt. An aqueous solution of sodium thiosulfate
was added to quench the reaction, followed by washing of the reaction mixture with H2O for
four times. After filtration 4.0 mL of perchloric acid (70% solution in water, 6.6 g, 46 mmol,
900 equiv.) were added to the solution. The reaction mixture was vigorously stirred at rt
overnight again for demetalization. After addition of 10 mL of water, the organic layer was
separated and washed with water, a solution of sodium bicarbonate and water again, and dried
over Na2SO4. After removing the solvent under reduced pressure, the crude product was
isolated by column chromatography (DCM/EE 1:0 with gradient to 50:1) yielding 66 mg of the
octabromo porphyrin 18 (47.7 µmol, 93%) as a greenish-purple solid.
Rf (DCM) = 0.80. – 1H-NMR (400 MHz, CDCl3): (ppm) = –1.56 (bs, 2H, NH), 1.55 (t,
J = 7.1 Hz, 6H, CH3), 4.55 (q, J = 7.1 Hz, 4H, CH2), 7.72–7.90 (m, 6H, HPh), 8.17–8.25 (m,
4H, HPh), 8.31 (d, J = 8.3 Hz, 4H, HPh), 8.45 (d, J = 8.3 Hz, 4H, HPh). – 13C-NMR (100 MHz,
CDCl3): (ppm) = 14.6 (+, CH3), 61.6 (–, CH2), 119.6 (Cq), 121.4 (Cq), 128.6 (+), 129.5 (+),
130.1 (+), 131.5 (Cq), 136.9 (+), 137.1 (Cq), 141.2 (Cq), 166.9 (Cq, COO). – UV/VIS (CHCl3):
max (log ) = 372 (4.45), 472 (5.30), 572 (3.99), 627 (4.13), 740 (3.90) nm. – IR (ATR): =
2973 (vw), 2924 (vw), 1716 (w), 1605 (vw), 1464 (vw), 1403 (vw), 1365 (vw), 1269 (w), 1175
(vw), 1101 (vw), 1019 (vw), 1004 (w), 914 (vw), 818 (vw), 749 (vw), 727 (vw), 693 (vw), 607
(vw), 401 (vw) cm–1. – MS (FAB, 3-NBA): m/z (%) = 1390.3 (100) [M(79Br481Br4) + H]+.
(Fitting isotope pattern for eight bromines)
General procedure for saponification of porphyrins305
144
To a solution of the corresponding ester porphyrin 15, 16 or 18 (1.00 equiv.) in THF/MeOH
(4:1, 9.95 M) was added a 40w% aqueous solution of NaOH (1000 equiv.) and the mixture was
stirred at 90 °C overnight. After cooling to rt, the organic solvents were removed under reduced
pressure and the resulting water suspension was acidified with hydrochloric and acetic acid to
pH = 3. The mixture was cooled to 4 °C and subsequently filtrated. The precipitate was washed
with hot water and DCM and the remaining solid was dissolved in MeOH/EtOH/DMF/NEt3.
The solvents were removed under reduced pressure and the residual solid was dried in vacuo.
In all saponification reactions the determination of the respective yield resulted in >100% due
to possible formation of carboxylate salts. The obtained solids 1-Br, 5 and 10 were further used
without additional purification.
Fabrication of multilayer heteroepitaxial SURMOF-2:
Figure: Out-of-plane XRD of the heteroepitaxial SURMOF structure 1-Br′/5′/10′ (green), and
simulated XRD of 1-Br′ (black).
3 6 9 12 15
(002)
2
(001)(003)
145
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Acknowledgements
Having concluded three and half years of research work, it comes with no surprise that there were many
helping hands and minds that steered me along this journey and a few words of appreciation are too less
but absolutely justified. I try my best to acknowledge people chronologically.
First and foremost, I would like to thank my parents Shri Yad Ram Badgujar and Shrimati Bimla Devi
back in India for every struggle they endured so that my path towards and along this journey remains
as smooth as possible. Also, I give my heartfelt thanks to my three beloved sisters (Sangeeta, Manjeeta,
and Kavita) for their endless love and support throughout my entire life.
No words suffice for my supervisor (Doktorvater in German) Prof. Dr. Thomas Heine. I am highly
grateful to you for offering me this lifetime opportunity. Before coming to your lab, I trained primarily
within the experimental periphery of chemistry and material science. Besides, a little basic textbook
knowledge, I had no hands-on experience in theoretical aspects of chemistry. It was, therefore, all very
overwhelming when I undertook my thesis in theoretical chemistry, this not only extended my research
periphery but also elevated my computational skill set. During these years, I have learned a lot from our
meetings, personal talks and by just observing how you conduct yourself in social and professional life.
Despite your busy schedule you always find time to resolve my silly questions and doubts. Also, special
thanks for trusting in and giving me a lot of freedom to collaborate with other groups which helped me
to navigate effectively through this journey and reach the finish line of my PhD. It was amazing to work
as I learnt the qualities of being humble and at the same time being a successful researcher.
Next, I am indebted to Dr. Stefan Zahn for introducing me to the density functional calculations and his
willingness to mentor a novice like me. I really admire his hard work and expertise. Also, I would like
to especially thank Dr. Agnieszka Kuc for giving me a hands-on experience in electronic band structure
calculations. For all the technical support and solving the computational bottlenecks, I am thankful to
Dr. Lyuben Zhechkov and Dipl. Knut Vietze. Further, Dr. Jan-Ole Joswig for having useful discussions
and introducing me to the interesting teaching assistant duties. Grateful acknowledgment is also made
162
to Dr. Nina Vankova, who gave me continuous guidance in my projects and considerable help in my
thesis corrections by means of suggestions, comments, and fruitful discussions. I would like to express
my sincere gratitude towards Ms. Antje Völkel for all the help related to my administrative works and
organizing the group retreats and events. Hung-Hsuan for being my longest-running office mate and
sharing your ideas and thoughts in understanding chemistry. Hope you succeed in automating the whole
task of PhD itself. A big thanks also to all the present and past members of the theoretical chemistry
group in Leipzig and Dresden for their valuable discussions and brainstorms. Thank you all, for the nice
cakes, beers, barbecues, parties, and all the fun-adventurous biking-hiking trips.
Finally, the main part of the work on this thesis was performed while being employed in a position
funded by the DFG within the COORNETs project (SPP 1928). So, I want to thank the DFG and all its
representatives, as well as our principal investigators: Prof. Dr. Thomas Heine, Prof. Dr. Christof Wöll,
Prof. Dr. Stefan Bräse and Prof. Dr. Roland Fischer for providing and securing these funds and therefore
making this thesis possible. Further, ZIH Dresden is thanked for providing high-performance computing
resources and a big thank also to all the collaborators that participated in this wonderful project.
163
Versicherung
Hiermit versichere ich, dass ich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und ohne
Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe; die aus fremden Quellen
direkt oder indirekt übernommen Gedanken sind als solche kenntlich gemacht. Die Arbeit
wurde bisher weder im Inland noch im Ausland in gleicher oder ähnlicher Form einer anderen
Prüfungsbehörde vorgelegt.
Datum Unterschrift
Erklärung
Die vorliegende Arbeit wurde in der Zeit von Mai 2017 bis Dezember 2020 an der Technischen
Universität Dresden im Rahmen des Projektes zum Thema: “ Theoretical Investigations of the
Photophysical Properties of Chromophoric Metal-Organic Frameworks” unter
wissenschaftlicher Betreuung von Herrn Prof. Dr. Thomas Heine durchgeführt.
Datum Unterschrift
