Detlef W. M. Hofmann

Crystal structure prediction by data mining

Abstract The ever increasing number of experimentally determined crystal structures allows for the use of data mining methods to address crystallographic questions. Here we study the application of data mining for predicting the arrangement of molecules in unit cells of unknown dimensions (crystal structure prediction) as well as in unit cells of predetermined dimensions (fractional coordinate prediction). In this work, data mining is used to derive an atom-pair potential, which is then compared to known force fields. It is shown that the potential is physically reasonable when the data are sufficient in quality and quantity. For validation the energy function is applied to the problems of crystal structure prediction and fractional coordinate prediction. In both cases a large number of structures was generated and the structures were ranked according to their energies. Structure prediction was considered successful if a structure similar to the experimentally observed one was ranked highest. For crystal structure prediction the energy function is tested on an independent set of crystal structures taken from the P1 and P 1 space groups. We show that approximately 76% of the 218 molecules tested in space group P1 are predicted correctly. For the more complex space group P 1 the success rate is 24%. If the powder diffraction can be indexed, the problem simplifies to fractional coordinate prediction. With the assumption of known cell parameters the structure has been resolved in 92% of the test cases for P1 and 29% for P 1 .

A Discrete Algorithm for Crystal Structure Prediction of Organic Molecules

A new algorithm, FlexCryst, is presented for fast crystal structure prediction. The algorithm differs from existing algorithms in that it performs the analysis on the basis of only a single molecule and uses potentials for scoring energy that are derived statistically from a set of data on molecular structures. In a first step, the algorithm creates various potential unit cells. In the second step, a set of candidates for translation vectors for corresponding crystals is generated. In the third step, the algorithm selects triples of candidate vectors to form potential crystal structures. The fourth step ranks the crystal structures with respect to their energy as estimated by a suitable scoring function. In the last step, the crystal structures are clustered according to a newly defined measure of similarity for crystal structures. At the moment, the program can handle only triclinic crystals with one molecule per asymmetric unit. The algorithm was tested on a set of 131 experimentally resolved crystals of space group P1 and 95 crystals of space group P{\overline 1} from the Cambridge Structural Database. For P1, in 129 cases (98%), the observed crystal structure is among the crystal structures generated by the algorithm. The run time of the algorithm is a few s per molecule on a standard workstation. For P{\overline 1}, the experimental structure has been found among the proposed structures in 81 cases (85%). Owing to the more complex unit cell for this space group, the run time increases to about 2 h per molecule.

Molecular dynamics simulation of hydrated Nafion with a reactive force field for water

AbstractWe apply a newly parameterized central force field to highlight the problem of proton transport in fuel cell membranes and show that central force fields are potential candidates to describe chemical reactions on a classical level. After a short sketch of the parameterization of the force field, we validate the obtained force field for several properties of water. The experimental and simulated radial distribution functions are reproduced very accurately as a consequence of the applied parameterization procedure. Further properties, geometry, coordination, diffusion coefficient and density, are simulated adequately for our purposes. Afterwards we use the new force field for the molecular dynamics simulation of a swollen polyelectrolyte membrane similar to the widespread Nafion 117. We investigate the equilibrated structures, proton transfer, lifetimes of hydronium ions, the diffusion coefficients, and the conductivity in dependence of water content. In a short movie we demonstrate the ability of the obtained force field to describe the bond breaking/formation, and conclude that this force field can be considered as a kind of a reactive force field. The investigations of the lifetimes of hydronium ions give us the information about the kinetics of the proton transfer in a membrane with low water content. We found the evidence for the second order reaction. Finally, we demonstrate that the model is simple enough to handle the large systems sufficient to calculate the conductivity from molecular dynamics simulations. The detailed analysis of the conductivity reveals the importance of the collective moving of hydronium ions in membrane, which might give an interesting encouragement for further development of membranes. Figure: The structure of water in one pore of the highly hydrated Nafion membranes. FigureThe structure of water in one of pore of the highly hydrated Nafion membrane

PREDICTION OF CRYSTAL STRUCTURES OF ORGANIC MOLECULES

Abstract We have developed a new algorithm for crystal structure prediction that takes a conformer of an organic molecule and produces a number of candidates of crystal structures for this molecule, together with a score that roughly approximates the energy of the respective crystal structure. The prediction method takes steric aspects (dense packing) as well as chemical interactions into account. The algorithm differs from existing methods in three aspects. First, we analyse a single molecule rather than a collection of identical molecules. The analysis yields candidates for symmetry operations that are suitable for making the crystal. Each of the candidates is generated by a chemical interaction between two versions of the molecule. Second, we model space discretely, currently as a mesh with size 1 A. Third, the scoring function representing energy is derived statistically from known crystal structures and tabulated. Our program FlexCryst computes a list of crystal structures ranked according to our scoring function. The new algorithm is currently implemented for the four space groups P1, P 1 , P2 1 , and P212121. The three latter space groups are widespread in nature. The algorithm computes structural models of acceptable quality and shows excellent time performance.