Errors in Hellmann-Feynman Forces due to occupation number broadening, and how they can be corrected

TL;DR

This paper investigates errors in Hellmann-Feynman forces caused by occupation number broadening in ab initio calculations and proposes correction methods, including a simple exact approach for small MD steps and a linear-response scheme, improving force accuracy.

Contribution

It introduces two correction schemes for occupation broadening errors in force calculations, enhancing the accuracy of ab initio molecular dynamics and geometry optimizations.

Findings

Simple correction method is exact for small MD steps.

Linear-response correction enables extrapolation to true forces.

Comparison shows proposed methods outperform smearing scheme.

Abstract

In ab initio calculations of electronic structures, total energies, and forces, it is convenient and often even necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a boardening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics (MD) calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the (111)-surfaces of aluminium and platinum. The second, more general, scheme employs linear-response theory and is applied to the calculation of the surface relaxation of Al(111). We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton.