On the gradient for metallic systems with a local basis set

TL;DR

This paper derives an analytical energy gradient formula for metallic periodic systems using Gaussian basis sets, applicable at the Hartree-Fock or DFT level, and confirms its accuracy through numerical comparisons.

Contribution

It extends the analytical gradient methodology to metallic systems with Gaussian basis sets, including thermal broadening effects, aligning with free energy derivatives.

Findings

Analytical gradients are consistent with numerical derivatives.

The method achieves reasonable accuracy in practical examples.

Gradient expressions are similar to those for insulating systems without broadening.

Abstract

The analytical gradient for periodic systems is presented, for the case of metallic systems. The total energy and the free energy are computed on the Hartree-Fock or density functional level, with the wave function being expanded in terms of Gaussian type orbitals. The expression for the gradient is similar to the case of insulating systems, when no thermal broadening is applied. When the occupation of the states is according to the Fermi function, then the gradient is consistent with the gradient of the free energy. By comparing with numerical derivatives, examples demonstrate that a reasonable accuracy is achieved.