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Kristallchemie und Kristallstrukturdatenbanken

Kristallchemie und Kristallstrukturdatenbanken. Pulverdiffraktometrie. Einkristall Strukturanalyse Strukturanalyse mittels Pulverdaten Kristallchemie in der Strukturanalyse Modellbau Simulated annealing Evolution äre Algorithmen FOCUS Charge flipping. Simulated annealing und Zeolithe.

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Kristallchemie und Kristallstrukturdatenbanken

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  1. Kristallchemie und Kristallstrukturdatenbanken Pulverdiffraktometrie • Einkristall Strukturanalyse • Strukturanalyse mittels Pulverdaten • Kristallchemie in der Strukturanalyse • Modellbau • Simulated annealing • Evolutionäre Algorithmen • FOCUS • Charge flipping

  2. Simulated annealing und Zeolithe M.W. Deem and J.M. Newsam, "Determination of 4-connected framework crystal structures by simulated annealing" Nature342, 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)

  3. T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T Simulated annealing und Zeolithe

  4. T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T Simulated annealing und Zeolithe T-T Abstände T-T-T Winkel Anzahl nächste Nachbaren Pulverdiagramm  figure of merit (χ2) zufällige Verschiebung aller Atome

  5. T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T Simulated annealing und Zeolithe "Move" akzeptiert wenn χ2neu < χ2alt oder n < e-δ δ = (χ2neu-χ2alt )/T χ2neu-χ2alt klein und/oder T gross δ klein e-δ gross "Move" eher akzeptiert

  6. T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T Simulated annealing und Zeolithe

  7. Simulated annealing und Molekülstrukturen Molekülstrukturen • chemische Zusammensetzung C10H16N6S • Verknüpfung • Bindungslängen, Bindungswinkel, Torsionswinkel Cimetidine

  8. HN Simulated annealing und Molekülstrukturen HN S HN N N Cimetidine N Molekül kann mittels interne Koordinaten beschrieben werden C - C 1.36 Å C - C 1.49 Å C - C - C 120˚ C - S 1.82 Å C - C - S 109.5˚ C - C - C - S 180˚ C - S 1.82 Å C - C - S 109.5˚

  9. HN Simulated annealing und Molekülstrukturen HN S HN N N Cimetidine N Molekül kann mittels interne Koordinaten beschrieben werden • Parameter • Position des Moleküls X,Y,Z • Orientierung des MolekülsΘ, Φ, Ψ • freie Torsionswinkel τ1, τ2, τ3, τ4,τ5, τ6, τ7 Total: 13 statt 17 x 3 = 51 Atomkoordinaten

  10. Simulated annealing und Molekülstrukturen (1) Start mit einem Satz Strukturparameter φalt {X,Y,Z,Θ,Φ,Ψ,τ1-n} Struktur chemisch sinnvoll (2) Figure-of-merit (z.B. R-Wert) rechnen χ2 alt Kann auch andere Kriterien berücksichtigen z.B. Coulomb Potentiale (3) Strukturparameter modifizierenφneu= φalt + m*Δφalt m ist ein Zufallszahl zwischen 0 und 1 (4) Neuer Figure-of-merit rechnen χ2neu (5) Wenn χ2neu < χ2alt oder φneu φalt n < exp (-(χ2neu - χ2alt) / T) sonst φaltunverändert n ist ein Zufallszahl zwischen 0 und 1 ermöglicht Herauskommen aus falsche Minima (6) Nachdem die vorgeschriebene Anzahl T reduziert "Moves" akzeptiert Annealing Schema weniger Strukturen mit χ2neu > χ2alt akzeptiert (7) Zurück zu Schritt (3)  optimierte Struktur

  11. Random variation of X, Y, Z, Θ, Φ, Ψ, τn Back to previous model Reduce temperature no Is the model chemically reasonable? yes Powder data yes Move acceptable? Prescribed number of moves reached? no yes no Simulated Annealing Initial model SA control parameters http://vincefn.net/Fox/FoxWiki Evaluate fitness

  12. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  13. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  14. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  15. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  16. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  17. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  18. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  19. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  20. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  21. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  22. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  23. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  24. 1.45 Å 1.50 Å 1.39 Å 1.33 Å 1.53 Å 1.23 Å 2 5 7 3 1 6 8 4 9 Polymer Clarifier (C) H C7H3 || | | (C) = C1 - C2 – C3 – N5 – C6 – C8H3 || | O4 C9H3

  25. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  26. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  27. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  28. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  29. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  30. 17 1.52 Å 7 9 2 11 16 1.81 Å 1.53 Å 1.47 Å 1.37 Å 1.36 Å 8 3 1 10 12 1.81 Å 1.51 Å 1.37 Å 1.47 Å 1.34 Å 15 1.32 Å 1.34 Å 4 13 14 1.35 Å 5 1.14 Å 1.31 Å 1.36 Å 6

  31. Evolutionäre Algorithmen alternativer "global optimization" Verfahren Strukturparameter sind die Gene X,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 ...

  32. 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 = 0.25 R = 0.31 R = 0.22 R = 0.22 R = 0.35 R = 0.42 R = 0.3

  33. Strukturlösung mittels Modelbau (Zufälliges) Modell vom Computer Modell optimieren Methode der Optimierung least-squares refinement simulated annealing evolutionary algorithm lokal Optimierung } global Optimierung

  34. Strukturlösung mittels Modelbau Least squares refinement 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

  35. Strukturlösung mittels Modelbau Simulated annealing Simulated Annealing is like doing the same, but getting the kangaroo very, very drunk first.

  36. Strukturlösung mittels Modelbau Genetic algorithms Genetic Algorithms are like taking a whole plane load of kangaroos and letting them reproduce freely (not pictured)...

  37. Strukturlösung mittels Modelbau Genetic algorithms Note: no kangaroos were harmed in the making of this presentation and regularly shooting those at lower altitudes.

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