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

Most of the density-to-potential inversion methods developed over the years follow a general algorithm $ v_{xc}^{i+1}( $r$ ) = v_{xc}^{i}( $r$ )

\Delta v_{xc}( $r$ ) $, w h e r e$ \Delta v_{xc}( $r$ ) = \frac{\delta S[\rho]}{\delta \rho( $r$ )} \Big |{ \rho_i( $r$ )} - \frac{\delta S[\rho]}{\delta \rho( $r$ )}\Big|{ \rho_0( $r$ )} $a n d$ 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 $S [ρ]$ in each iterative step. The method is demonstrated by calculating exchange-correlation potential of atoms, clusters and the Hookium.

Most of the density-to-potential inversion methods developed over the years follow a general algorithm $ v_{xc}^{i+1}( $r$ ) = v_{xc}^{i}( $r$ )

\Delta v_{xc}( $r$ ) $, w h e r e$ \Delta v_{xc}( $r$ ) = \frac{\delta S[\rho]}{\delta \rho( $r$ )} \Big |{ \rho_i( $r$ )} - \frac{\delta S[\rho]}{\delta \rho( $r$ )}\Big|{ \rho_0( $r$ )} $a n d$ 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 $S [ρ]$ in each iterative step. The method is demonstrated by calculating exchange-correlation potential of atoms, clusters and the Hookium.

文献摘要