Crystal structure prediction supported by incomplete experimental data

Abstract

The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations [1][2][3][4][5][6][7][8], the prediction of crystal structures comprising more than several tens of atoms in the unit cell still remains difficult due to the many degrees of freedom, which increase exponentially with the number of atoms. Here we show that when some experimental data is available, even if it is totally insufficient for conventional structure analysis, it can be utilized to support and substantially accelerate structure simulation. In particular, we formulate a cost function based on a weighted sum of interatomic potential energies and a penalty function referred to as "crystallinity", which is defined using limited X-ray diffraction data. This method is applied to well-known polymorphs of SiO 2 with up to 96 atoms in the simulation cell to find that it reproduces the correct structures efficiently with a very limited number of diffraction peaks. The penalty function is confirmed to destabilize the local minima of the potential energy surface, which facilitates finding the correct structure. This method opens a new avenue for determining and predicting structures that are difficult to determine by conventional methods, such as surface, interface, glass, and amorphous structures.

Search for common minima in joint optimization of multiple cost functions

“…It should be noted, however, that other non-trivial global minima with D(x) = 1 may appear, since it does not take into account the intensity. Although this fact makes more difficult to determine the correct structure by using the crystallinity alone relative to the R-value, it has been shown that the crystal structure prediction becomes much more reliable by combining the crystallinity with the the theoretical potential calculation [28]. In what follows, we demonstrate the COM is able to accelerate further the structure determination by using the property that the theoretical potential energy and the crystallinity share the identical target structure as the their global optimum.…”

“…1). This means that the gradient descent still gets trapped by one of the remaining local minima, and thus one has to introduce some metaheuristics, such as the simulated annealing [12,13,28].…”

“…This R-value is, however, sensitive to the noise and/or the background of the experimental data, and thus it does not necessarily give the global minimum even at the correct crystal structure. In the present work, we adopt a cost function that does not use the intensity information of the X-ray diffraction peaks [28], which is defined by…”

“…Some real crystal structures have been reproduced by using this method [23,24] much more efficiently than the methods that utilize only the experimental data, such as the direct space method [25,26] and the maximum entropy method [27]. More recently, the present authors demonstrated that the crystal structure prediction with reliable potential energy can be made quite efficient and robust by combining with partial and incomplete experimental data [28].…”

“…Indeed, in the example of the crystal structure predictions discussed above, the correct crystal structure is (at least approximately) a global minimum of the theoretical potential energy as well as that of the difference from the experimental data. This special property makes the Pareto optimization more robust against the choice of the weights between the cost functions [28]. Furthermore, as demonstrated below, if the cost functions have such a property, the global minimum is obtained by searching for a common minimum, instead of the minimum of the combined cost function, with a much higher success rate.…”