Using random numbers to obtain Kohn-Sham potential for a given density

Abstract

Most of the density-to-potential inversion methods developed over the years follow a general algorithm $v_{xc}^{i+1}(\text{r})=v_{xc}^i(\text{r})+\Delta v_{xc}(\text{r})$, where $\Delta v_{xc}(\text{r})=\frac{\delta S[\rho ]}{\delta \rho (\text{r})}{|}_{{\rho }_i(\text{r})}-\frac{\delta S[\rho ]}{\delta \rho (\text{r})}{|}_{{\rho }_0(\text{r})}$ and $S[\rho ]$ is an appropriately chosen density functional. In this work we show that this algorithm can be used with random numbers to obtain the exchange-correlation potential for a given density. This obviates the need to evaluate the functional $S[\rho ]$ in each iterative step. The method is demonstrated by calculating exchange-correlation potential of atoms, clusters and the Hookium.

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