Third-order density-functional perturbation theory: a practical implementation with applications to anharmonic couplings in Si

TL;DR

This paper introduces a practical third-order density-functional perturbation theory formulation, enabling efficient calculation of anharmonic phonon couplings in silicon, with invariance properties and application to real materials.

Contribution

It develops a new third-order perturbation theory approach that is invariant under unitary transformations and suitable for practical computation of anharmonic effects.

Findings

Successfully computed third-order anharmonic couplings in silicon

Demonstrated invariance under unitary transformations within occupied states

Provided a practical implementation for complex anharmonic calculations

Abstract

We present a formulation of third-order density-functional perturbation theory which is manifestly invariant with respect to unitary transfomations within the occupied-states manifold and is particularly suitable for a practical implementation of the so called `2n+1' theorem. Our implementation is demonstrated with the calculation of the third-order anharmonic coupling coefficients for some high-simmetry phonons in Silicon.