Density Functional Tight-Binding Model for Lithium-Silicon Alloys.

The predictive power of molecular dynamic simulations is mainly restricted by the time scale and model accuracy. Many systems of current relevance are of such complexity that requires addressing both issues simultaneously. This is the case of silicon electrodes in Li-ion batteries, where different Li$_x$Si alloys are formed during charge/discharge cycles. While first-principles treatments for this system are seriously limited by the computational cost of exploring its large conformational space, classical force-fields are not transferable enough to represent it accurately. Density Functional Tight-Binding (DFTB) is an intermediate complexity approach capable of capturing the electronic nature of different environments with a relatively low computational cost. In this work, we present a new set of DFTB parameters suited to model amorphous Li$_x$Si alloys. The latter is the usual finding upon cycling the Si electrodes in the presence of Li-ions. The model parameters are constructed with a particular emphasis on their transferability for the entire Li$_x$Si composition range. This is achieved by introducing a new optimization procedure that weights stoichiometries differently to improve the prediction of their formation energies. The resulting model is shown to be robust for predicting crystal and amorphous structures for the different compositions, giving excellent agreement with DFT calculations and outperforming state-of-the-art ReaxFF potentials.