(358f) Ab Initio Crystal Structure Prediction of Flexible Molecules

In previous work, we developed an algorithm for crystal structure prediction that identifies most low-energy minima (including the experimentally determined polymorphs) for crystals of both rigid [1] and flexible [2] molecules. This algorithm has been used successfully by our group and others to identify polymorphs for a wide range of molecules (including those with crystal structures in ?unusual? space groups, and also more than one molecule in the asymmetric unit), as well as co-crystals and salts.

The main limitation of the above algorithm is the rapidly increasing computational cost as a function of molecular flexibility. This arises from the need to compute a priori a grid of intramolecular energies that can be used to construct restricted Hermite interpolants. Although the use of Hermite interpolants reduces the number of quantum mechanical calculations needed during the search, the dimension of the grid grows exponentially with the number of flexible degrees of freedom, practically limiting the applicability of the algorithm.

In this paper, we present substantial improvements of the algorithm that make the explicit consideration of a much larger number of flexible degrees of freedom tractable. The proposed approach is significantly more computationally efficient thanks to the use of local approximate models (LAMs) which are constructed based on a small number of quantum mechanical calculations performed ?on-the-fly? during the search. The LAMs are used to compute the intramolecular energies based on a quadratic Taylor expansion of intra-molecular energy expressed in terms of the flexible molecular degrees of freedom. The expansion is constructed around a base point derived from an isolated-molecule wavefunction calculation of the intramolecular energy and its first and second order derivatives. The local approximate model is valid within a certain distance of the base point. The LAMs are generated as and when required and are stored in a look-up table, which allows their re-use if and when the search procedure returns to sample the same region of the conformational space.

The proposed algorithm requires only the atomic connectivity of the molecule under consideration and performs an extensive search for local minima of the lattice enthalpy surface by using deterministic low-discrepancy sequences to ensure an optimal coverage of the search space. Candidate structures can be generated in the 59 most common space groups with one or more crystallographically independent entities. These are then used as starting points of local optimization calculations performed with a sequential quadratic programming algorithm, which makes use of analytical partial derivatives with respect to all inter and intra- molecular degrees of freedom. A parallelized implementation of the algorithm allows minimizations from several hundreds of thousands of initial guesses to be carried out in reasonable time.

The validity of the proposed methodology is tested by predicting a set of single-component crystals and co-crystals containing flexible molecules. The use of the LAM significantly reduces the number of quantum mechanical evaluations that have to be performed. In practice, we find that many local optimizations can be done using a single quantum mechanical calculation carried out at the initial point. As a result, the proposed methodology addresses the computational limitations associated with our previous work and allows us to handle molecules with many flexible degrees of freedom.

References

[1] Karamertzanis, P. G. and Pantelides, C. C. J. Comput. Chem. 2005, 26, 304-324.

[2] Karamertzanis, P. G. and Pantelides, C. C. Mol. Phys. 2007, 105, 273-291.