# Crystal Structure Prediction

The goal of crystal structure prediction is to predict crystal structures from the molecular geometry alone as a starting point. The state of the art prior to the development of GRACE has been assessed in a series of blind tests^{1}‘^{2}‘^{3}.

GRACE uses dispersion-corrected DFT calculations^{4} (d-DFT) to first generate reference data to which a detailed tailor-made force field^{5} is fitted for every molecule under consideration. The DFT calculations are carried out by means of the VASP program^{6}‘^{7}‘^{8}‘^{9}.

Crystal structures are generated with a Monte Carlo parallel tempering algorithm that uses the tailor-made force field for the calculation of lattice energies and energy derivatives. Only the most stable crystal structures according to the tailor-made force field are then re-optimized and re-ranked using d-DFT. Assessing the completeness of the crystal structure generation and the re-ranking is of major importance. The completeness of the crystal structure generation procedure is monitored by counting the number of times that each crystal structure is generated independently. Typically, the structure generation is stopped when the 50 most stable crystal structures according to the tailor-made force field have been found each at least twice. The re-ranking proceeds from stable to less stable structures. From the lattice energies calculated with the tailor-made force field and the hybrid method, the standard deviation and the offset for both types of energy calculations can be worked out^{4}. In turn, the standard deviation and the offset are used to compute the probability that none of the structures not yet re-optimized with d-DFT ends up after re-optimization below a certain energy threshold, for instance the energy of the most stable structure found so far. We always make sure that the re-ranking has reached the most stable crystal structure according to d-DFT with a probability of at least 99%.

As the first program ever GRACE produced a 4 in 4 success rate in the 4th blind test of crystal structure prediction.^{10}‘^{11}

Next page: Fourth blind test

### References

^{1} Lommerse, J. P. et al. A test of crystal structure prediction of small organic molecules, Acta Cryst. B 56, 697-714 (2000)

^{2} Motherwell, W. D. S. et al. Crystal structure prediction of small organic molecules: a second blind test, Acta Cryst. B 58, 647-661 (2002)

^{3} Day, G. M. et al. A third blind test of crystal structure prediction, Acta Cryst. B 61, 511-527 (2005)

^{4} Neumann, M. A. & Perrin, M.-A. Energy ranking of molecular crystals using density functional theory calculations and an empirical van der Waals correction , J. Phys. Chem. B 109, 15531-15541 (2005)

^{5} Neumann, M. A. Tailor-made force fields for crystal-structure prediction , J. Phys. Chem. B 112, 9810-9829 (2008)

^{6} Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558-561 (1993)

^{7} Kresse, G. & Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6, 15-50 (1996)

^{8} Kresse, G. & Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B. 54, 11169-11186 (1996)

^{9} Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method Phys. Rev. B 59, 1758-1775 (1999)

^{10} Neumann, M. A., Leusen, F. J. J. & Kendrick, J. A major advance in crystal structure prediction , Angew. Chem. Int. Ed. 47, 2427-2430 (2008)

^{11} Sanderson, K. Model predicts structure of crystals , Nature 450, 771 (2007)