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Kristallchemie und Kristallstrukturdatenbanken
Pulverdiffraktometrie
Einkristall Strukturanalyse
Strukturanalyse mittels Pulverdaten
Kristallchemie in der StrukturanalyseModellbauSimulated annealingEvolutionäre AlgorithmenFOCUSCharge flipping
Simulated annealing und Zeolithe
M.W. Deem and J.M. Newsam, "Determination of 4-connected framework crystal structures by simulated annealing" Nature 342, 260-262 (1989)
M. Falcioni and M.W. Deem, "A biased Monte Carlo scheme for zeolite structure solution" J. Chem. Phys. 110, 1754-1766 (1999)
Simulated annealing und Zeolithe
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Simulated annealing und Zeolithe
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T-T Abstände
T-T-T Winkel
Anzahl nächste Nachbaren
Pulverdiagramm
figure of merit (χ2)
zufällige Verschiebung aller Atome
oder n < e-δ
δ = (χ2neu-χ2
alt )/T
χ2neu < χ2
alt
"Move" akzeptiert wenn
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Simulated annealing und Zeolithe
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χ2neu-χ2
alt klein und/oder T gross
δ klein
e-δ gross
"Move" eher akzeptiert
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Simulated annealing und Zeolithe
chemische ZusammensetzungVerknüpfung
MolekülstrukturenC10H16N6
S
Simulated annealing und Molekülstrukturen
Cimetidine
Bindungslängen, Bindungswinkel, Torsionswinkel
C - S 1.82 Å C - C - S 109.5˚ C - C - C - S 180˚
N
C - S 1.82 Å C - C - S 109.5˚
Cimetidine
Molekül kann mittels interne Koordinaten beschrieben werden
HN N
S
HN
HN
N
C - C 1.36 Å
C - C 1.49 Å C - C - C 120˚
Simulated annealing und Molekülstrukturen
ParameterPosition des Moleküls X,Y,Z
Orientierung des Moleküls Θ, Φ, Ψfreie Torsionswinkel τ1, τ2, τ3, τ4, τ5, τ6, τ7
Molekül kann mittels interne Koordinaten beschrieben werden
statt 17 x 3 = 51 Atomkoordinaten
Total: 13
Simulated annealing und Molekülstrukturen
N
Cimetidine
HN N
S
HN
HN
N
(6) Nachdem die vorgeschriebene Anzahl T reduziert"Moves" akzeptiert
Kann auch andere Kriterien berücksichtigenz.B. Coulomb Potentiale(3) Strukturparameter modifizieren φneu = φalt + m*Δφalt
(4) Neuer Figure-of-merit rechnen χ2neu
(2) Figure-of-merit (z.B. R-Wert) rechnen χ2 alt
(5) χWenn 2neu < χ2
alt oder φneu φalt
n < exp (-(χ2neu - χ2
alt) / T)
(7) Zurück zu Schritt (3)
optimierte Struktur
Struktur chemisch sinnvoll
m ist ein Zufallszahl zwischen 0 und 1
n ist ein Zufallszahl zwischen 0 und 1ermöglicht Herauskommen aus falsche Minima
Annealing Schemaweniger Strukturen mit χ2
neu > χ2alt akzeptiert
sonst φalt unverändert
Simulated annealing und Molekülstrukturen
(1) Start mit einem Satz Strukturparameter φalt
{X,Y,Z,Θ,Φ,Ψ,τ1-n}
Reduce temperature
yes
no yesPrescribed number of
moves reached?
no Back to previous model
Simulated Annealing
no
yes
Is the model chemically
reasonable?
Move acceptable?
Random variation of X, Y, Z, Θ, Φ, Ψ,
τn
Initial modelSA control parameters
Evaluate fitness
Powder data
http://vincefn.net/Fox/FoxWiki
No. Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2
3 C3
4 O4
5 N5
6 C6
7 C7
8 C8
9 C9
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
Polymer Clarifier
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3
4 O4
5 N5
6 C6
7 C7
8 C8
9 C9
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3 1.50 Å 120˚ 2
4 O4
5 N5
6 C6
7 C7
8 C8
9 C9
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3 1.50 Å 120˚ 2
4 O4 1.23 Å 120˚ 0˚ 3
5 N5
6 C6
7 C7
8 C8
9 C9
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3 1.50 Å 120˚ 2
4 O4 1.23 Å 120˚ 0˚ 3
5 N5 1.33 Å 120˚ 180˚ 3
6 C6
7 C7
8 C8
9 C9
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3 1.50 Å 120˚ 2
4 O4 1.23 Å 120˚ 0˚ 3
5 N5 1.33 Å 120˚ 180˚ 3
6 C6 1.45 Å 120˚ 180˚ 5
7 C7
8 C8
9 C9
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1
2 C2 1.39 Å 1
3 C3 1.50 Å 120˚ 2
4 O4 1.23 Å 120˚ 0˚ 3
5 N5 1.33 Å 120˚ 180˚ 3
6 C6 1.45 Å 120˚ 180˚ 5
7 C7 1.53 Å 109.5˚
60˚ 6
8 C8 1.53 Å 109.5˚
180˚ 6
9 C9 1.53 Å 109.5˚
300˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 3
5 N5 1.33 Å 120˚ 180˚ 3
6 C6 1.45 Å 120˚ 180˚ 5
7 C7 1.53 Å 109.5˚
60˚ 6
8 C8 1.53 Å 109.5˚
180˚ 6
9 C9 1.53 Å 109.5˚
300˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 3
5 N5 1.33 Å 120˚ 180˚ 1 3
6 C6 1.45 Å 120˚ 180˚ 5
7 C7 1.53 Å 109.5˚
60˚ 6
8 C8 1.53 Å 109.5˚
180˚ 6
9 C9 1.53 Å 109.5˚
300˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 3
5 N5 1.33 Å 120˚ 180˚ 1 3
6 C6 1.45 Å 120˚ 180˚ 2 5
7 C7 1.53 Å 109.5˚
60˚ 6
8 C8 1.53 Å 109.5˚
180˚ 6
9 C9 1.53 Å 109.5˚
300˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 3
5 N5 1.33 Å 120˚ 180˚ 1 3
6 C6 1.45 Å 120˚ 180˚ 2 5
7 C7 1.53 Å 109.5˚
60˚ 3 6
8 C8 1.53 Å 109.5˚
180˚ 3 6
9 C9 1.53 Å 109.5˚
300˚ 3 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 5˚ 3
5 N5 1.33 Å 120˚ 180˚ 1 5˚ 3
6 C6 1.45 Å 120˚ 180˚ 2 1˚ 5
7 C7 1.53 Å 109.5˚
60˚ 3 5˚ 6
8 C8 1.53 Å 109.5˚
180˚ 3 5˚ 6
9 C9 1.53 Å 109.5˚
300˚ 3 5˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftm
ax
τmin τmax B
1 C1 0
2 C2 1.39 Å 0 1
3 C3 1.50 Å 120˚ 0 2
4 O4 1.23 Å 120˚ 0˚ 1 5˚ 0˚ 360˚ 3
5 N5 1.33 Å 120˚ 180˚ 1 5˚ -180˚ 180˚ 3
6 C6 1.45 Å 120˚ 180˚ 2 1˚ 160˚ 200˚ 5
7 C7 1.53 Å 109.5˚
60˚ 3 5˚ 30˚ 150˚ 6
8 C8 1.53 Å 109.5˚
180˚ 3 5˚ 150˚ 270˚ 6
9 C9 1.53 Å 109.5˚
300˚ 3 5˚ -90˚ 30˚ 6
Polymer Clarifier
(C) H C7H3
|| | |(C) = C1 - C2 – C3 – N5 – C6 – C8H3
|| | O4 C9H3
1.39 Å
1.50 Å 1.45 Å
1.33 Å 1.53 Å
1.23 Å
12
35
67
894
No Atom Distance
Angle τ A shiftmax τmin τmax B
1 C1
2 N2
3 C3
4 N4
5 C5
6 N6
7 N7
8 C8
9 C9
10 S10
1
2
3
4
5
6
79
10
11
12
1314
15
17
16 81.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å
No Atom Distance
Angle τ A shiftmax τmin τmax B
1 C1
2 N2 1.47 1
3 C3 1.37 2
4 N4 1.32 3
5 C5 1.36 4
6 N6 1.14 5
7 N7 1.37 3
8 C8 1.47 7
9 C9 1.53 8
10 S10 1.81 9
1.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å 1
2
3
4
5
6
79
10
11
12
1314
15
17
16 8
No Atom Distance
Angle τ A shiftmax τmin τmax B
1 C1
2 N2 1.47 1
3 C3 1.37 120 2
4 N4 1.32 120 3
5 C5 1.36 120 4
6 N6 1.14 180 5
7 N7 1.37 120 3
8 C8 1.47 120 7
9 C9 1.53 109.5 8
10 S10 1.81 109.5 9
1.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å 1
2
3
4
5
6
79
10
11
12
1314
15
17
16 8
No Atom Distance
Angle τ A shiftmax τmin τmax B
1 C1
2 N2 1.47 1
3 C3 1.37 120 2
4 N4 1.32 120 0 1 3
5 C5 1.36 120 0 2 4
6 N6 1.14 180 5
7 N7 1.37 120 180 1 3
8 C8 1.47 120 180 3 7
9 C9 1.53 109.5 180 4 8
10 S10 1.81 109.5 180 5 9
1.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å 1
2
3
4
5
6
79
10
11
12
1314
15
17
16 8
No Atom Distance
Angle τ A shiftmax τmin τmax B
1 C1
2 N2 1.47 1
3 C3 1.37 120 2
4 N4 1.32 120 0 1 1˚ 0 360 3
5 C5 1.36 120 0 2 1˚ 0 360 4
6 N6 1.14 180 0 5
7 N7 1.37 120 180 1 1˚ 180 540 3
8 C8 1.47 120 180 3 1˚ 180 540 7
9 C9 1.53 109.5 180 4 5˚ 180 540 8
10 S10 1.81 109.5 180 5 5˚ 180 540 9
1.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å 1
2
3
4
5
6
79
10
11
12
1314
15
17
16 8
No Atom Distance
Angle τ A shiftmax τmin τmax B
11 C11 1.81 100 180 6 5˚ 180˚ 540˚ 10
12 C12 1.51 109.5 180 7 5˚ 180˚ 540˚ 11
13 N13 1.34 126 0 8 5˚ 0˚ 360˚ 12
14 C14 1.31 108 180 0 13
15 N15 1.35 108 0 0 14
16 C16 1.34 108 0 0 15
17 C17 1.52 126 180 0 16
1.36 Å
1.35 Å
1.51 Å
1.31 Å
1.34 Å
1.52 Å
1.81 Å
1.81 Å
1.53 Å
1.47 Å
1.37 Å
1.37 Å
1.32 Å
1.47 Å
1.36 Å
1.14 Å1.34 Å 1
2
3
4
5
6
79
10
11
12
1314
15
17
16 8
Strukturparameter sind die GeneX,Y,Z,Θ,Φ,Ψ,τ1-n
Satz von Strukturparameter ist ein Chromosom {X,Y,Z,Θ,Φ,Ψ,τ1-n}
Start mit einem Anzahl verschieden Individuen
Neue Generation erzeugt via Rekombination/Mutation
Nur die "fittest" überleben
Neue Generation erzeugt ...
Evolutionäre Algorithmenalternativer "global optimization" Verfahren
Evolutionäre Algorithmen - Prinzipien
Parameterisierung
Algorithmus zur Erzeugung eines "Phenotyps"
Erzeugung einer Population möglicher Lösungen
Rekombination/Mutation
Berechnung der individuellen Fitness
"Survival of the fittest"
R = 0.31 R = 0.22
R = 0.25
R = 0.35R = 0.22
R = 0.42
R = 0.3
Strukturlösung mittels Modelbau
(Zufälliges) Modell vom Computer
Modell optimieren
Methode der Optimierung
least-squares refinement
simulated annealing
evolutionary algorithm
lokal Optimierung
}global Optimierung
Least squares is like dropping a kangaroo somewhere on the surface of the earth, telling it to hop only uphill and hoping it will get to the top of mount Everest
Least squares refinement
Strukturlösung mittels Modelbau
Simulated Annealing is like doing the same, but getting the kangaroo very, verydrunk first.
Simulated annealing
Strukturlösung mittels Modelbau
Genetic Algorithms are like taking a whole plane load of kangaroos and letting them reproduce freely (not pictured)...
Genetic algorithms
Strukturlösung mittels Modelbau
Genetic algorithms
and regularly shooting those at lower altitudes.
Note: no kangaroos were harmed in the making of this presentation
Strukturlösung mittels Modelbau
