PREDICCIÓN DE ESTRUCTURAS DE CRISTALES CON MOLÉCULAS PREDICCIÓN DE ESTRUCTURAS DE CRISTALES CON MOLÉCULAS FLEXIBES EN SU CELDAFLEXIBES EN SU CELDA

V. Bazterra, M. B. Ferraro,

J. C. Facelli

Departamento de Física

Facultad de Ciencias Exactas y Naturales

Universidad de Buenos Aires

2007

Crystal engeneering

Pharmaceutical design

Polymorphism Application in materials.

AIM OF THE APPLICATIONAIM OF THE APPLICATION

Why GENETIC ALGORITHMS?

Useful to model atomic and molecular clusters.

Difficult crystal prediction from first principles.

Polymorphic forms in organic crystals

MGAC Crystal Structure Prediction CapabilitiesMGAC Crystal Structure Prediction CapabilitiesVictor E. Bazterra, Matthew Thorley, Marta B. Ferraro, Victor E. Bazterra, Matthew Thorley, Marta B. Ferraro,

and Julio C. Facelliand Julio C. FacelliJ. Chem. Theory Comput. J. Chem. Theory Comput. 2007, 2007, 3, 3, 201-209201-209

Search for crystal structures within Search for crystal structures within any symmetry groupany symmetry group and with an and with an arbitrary number of moleculesarbitrary number of molecules and molecular types per asymmetric and molecular types per asymmetric unit.unit.

Search structures using either the Search structures using either the rigid or flexiblerigid or flexible molecule models. molecule models.

Automatically Automatically generate the molecule’s generate the molecule’s force fieldforce field using existing force using existing force field libraries.field libraries.

Increase the sampling power and the complexity of molecules amenable Increase the sampling power and the complexity of molecules amenable

to CSP studies using the to CSP studies using the parallel and distributedparallel and distributed computing computing capabilities of the system.capabilities of the system.

Automatically compare, sort and archiveAutomatically compare, sort and archive the most relevant structures the most relevant structures in a user database.in a user database.

GENETIC CODING

Molecular center of mass {R1, R2,…Rn}

Its orientations {1 , 2 ,… \n }

Relevant dihedral angles {1 , 2 , …..n }

Space group and lattice parameters {a,b,c,,,}

(Rigid bodies)

Genetic Algorithms ApplicationGenetic Algorithms Application

SEMI-RIGID APPROXIMATIONSEMI-RIGID APPROXIMATION

DATA

-Crystallographic group

-Number of molecules in the cell

PARAMETERS

-Lattice angles, , ,

-Lattice axis a, b, c

APTITUDE FUNCTION-AMBER FORCE FIELD -CHARMm FORCE FIELD

in CHARMM code

MOLECULES:-center of mass positions-relative orientations

SEMIRIGID APPROXIMATIONSEMIRIGID APPROXIMATION

Rigid bodies with flexible chains

Parameters to be optimized

-crystallographic cell axes and angles.

-positions of the center of masss of each molecule.

-Euler angles respect to the unit cell.

-Ndihe molecular angles.

K=6+Z(6+Ndihed.)

Interface with CHARM Interface with CHARM ModuleModule

GA Module

File System

CHARMm

Interface

Benzene

-51-50-49-48-47-46-45-44-43-42-41-40

1 4 7

10

13

16

19

22

25

28

31

Generations

En

erg

y[k

J/m

ol]

Average EnergyMaximum EnergyMinimum Energy

Benzene

010203040

50607080

-50 -49 -48 -47 -46

Energy [kJ/mol]

Nu

m. i

nd

ivid

ual

s

Evolution of the population energy

Hystogram of the evolution

Population analysisPopulation analysis

Comparison between Comparison between crystalscrystals

Fragment matchingFragment matching

Local optimization using CHARMM 6, 7 with the GAFF 14 parameters. Local optimization using CHARMM 6, 7 with the GAFF 14 parameters. cutoff of 14 Å, and the electrostatic interactions were calculated using cutoff of 14 Å, and the electrostatic interactions were calculated using the Ewald technique. the Ewald technique.

Atomic charges, , using the restrained electrostatic potential approach Atomic charges, , using the restrained electrostatic potential approach implemented on the RESP program. Gaussian03 32 package at HF/6-implemented on the RESP program. Gaussian03 32 package at HF/6-31G* level.31G* level.

Restricted searches using 30 individuals in the population for up to 130 Restricted searches using 30 individuals in the population for up to 130 generations, for the 14 most common symmetry groups for organic generations, for the 14 most common symmetry groups for organic molecules, P1, P-1, P21, C2, Pc, Cc, P21/c, C2/c, P212121, Pca21, Pna21, molecules, P1, P-1, P21, C2, Pc, Cc, P21/c, C2/c, P212121, Pca21, Pna21, Pbcn, Pbca and Pnma. Pbcn, Pbca and Pnma.

For each molecule we performed between 150 and 200 runs leading to at For each molecule we performed between 150 and 200 runs leading to at least 100 complete runs with 130 generations. least 100 complete runs with 130 generations.

From these short lists we manually detected clearly unphysical From these short lists we manually detected clearly unphysical structures and duplicated ones that were not eliminated in the previous structures and duplicated ones that were not eliminated in the previous step that were identified by comparison of their XRPD spectra step that were identified by comparison of their XRPD spectra

CSP2007 MethodologyCSP2007 Methodology

Molecule IMolecule I

Molecule IMolecule I

Molecule IIIMolecule III

Molecule XIIMolecule XIIACRY02

Space group: Pbca

Molecule XIIMolecule XII

EXP.EXP.Acry02 (Pbca)Acry02 (Pbca)

PredictedPredictedCrystal_051_050 (Pbca)Crystal_051_050 (Pbca)

aa 6.764 (6.764 (6.9706.970)) 6.7646.764

bb 9.866 (9.866 (9.7529.752)) 9.8669.866

cc 9.536 (9.536 (9.5149.514)) 9.5369.536

9090 9090

9090 9090

9090 9090

RMS (RMS (Å)Å) 0.2458170.245817

ENERGY (kJ/mol)ENERGY (kJ/mol) -22.402-22.402 -22.402-22.402

Molecule XIVMolecule XIV

P21/c

Molecule XIVMolecule XIVExp.Exp.

Alphyph Alphyph (P21/c)(P21/c)

Predic.Predic.Crystal_06_006 Crystal_06_006

(P21, P21/c)(P21, P21/c)

aa 14.042 14.042 ((13.06013.060))

14.882, 14.046 14.882, 14.046

bb 9.613 9.613 (9.738(9.738))

9.612, 9.6129.612, 9.612

cc 8.264 8.264 ( ( 9.3359.335))

9.551, 8.2639.551, 8.263

9090 90, 9090, 90

100.9 100.9 ((105.8105.8))

1156.942, 100.9456.942, 100.94

9090 90, 9090, 90

RMS (RMS (Å)Å) 0.8301750.830175

ENERGY ENERGY (kJ/mol)(kJ/mol)

- 19.660 - 19.660 -19.675-19.675

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Test predictions of benchmark crystalsTest predictions of benchmark crystals

Prediction of experimental dataPrediction of experimental data

Incorporation of additional Incorporation of additional pseudopotentialspseudopotentials

Cosmetics and website.Cosmetics and website.

Departamento de FísicaUniversity of Buenos AiresArgentina

Marta Ferraro

Víctor Bazterra

Center for HighPerformance ComputingUniversity of Utah

Julio C. Facelli

Martin Cuma