Crystal structure prediction supported by incomplete experimental data

Abstract

We propose an efficient theoretical scheme for structure prediction on the basis of the idea of combining methods, which optimize theoretical calculation and experimental data simultaneously. In this scheme, we formulate a cost function based on a weighted sum of interatomic potential energies and a penalty function which is defined with partial experimental data totally insufficient for conventional structure analysis. In particular, we define the cost function using ``crystallinity'' formulated with only peak positions within the small range of the x-ray-diffraction pattern. We apply this method to well-known polymorphs of ${\mathrm{SiO}}_{2}$ and C with up to 108 atoms in the simulation cell and show that it reproduces the correct structures efficiently with very limited information of diffraction peaks. This scheme opens a new avenue for determining and predicting structures that are difficult to determine by conventional methods.