# Simple way to apply nonlocal van der Waals functionals within all-electron methods

## TL;DR

This paper introduces a simple, basis-set independent smoothing method to efficiently apply nonlocal van der Waals functionals within all-electron methods, enabling accurate solid-state property calculations without extensive plane-wave expansions.

## Contribution

The authors develop a straightforward smoothing procedure that extends the Román-Pérez and Soler method to all-electron densities, facilitating nonlocal vdW functional calculations in all-electron frameworks.

## Key findings

- The smoothing method yields lattice constants and binding energies in good agreement with existing literature.
- Results demonstrate the method's simplicity, efficiency, and compatibility with all-electron calculations.
- The approach is basis-set independent and easily implementable.

## Abstract

The method based on fast Fourier transforms proposed by G. Rom\'an-P\'erez and J. M. Soler [Phys. Rev. Lett. 103, 096102 (2009)], which allows for a computationally fast implementation of the nonlocal van der Waals (vdW) functionals, has significantly contributed to making the vdW functionals popular in solid-state physics. However, the Rom\'an-P\'erez-Soler method relies on a plane-wave expansion of the electron density; therefore it can not be applied readily to all-electron densities for which an unaffordable number of plane waves would be required for an accurate expansion. In this work, we present the results for the lattice constant and binding energy of solids that were obtained by applying a smoothing procedure to the all-electron density calculated with the linearized augmented plane-wave method. The smoothing procedure has the advantages of being very simple to implement, basis-set independent, and allowing the calculation of the potential. It is also shown that the results agree very well with those from the literature that were obtained with the projector augmented wave method.