Unphysical Discontinuities in GW Methods

TL;DR

This paper reveals unphysical discontinuities and irregularities in GW calculations of molecular systems, showing that solution branches depend on the algorithm and cause significant energy jumps, especially in small-gap molecules.

Contribution

It demonstrates the multibranch nature of GW solutions and the resulting discontinuities, highlighting issues in partially self-consistent GW methods for molecules.

Findings

Discontinuities occur at solution switches in GW calculations.

Multiple solution branches are associated with each self-energy.

Small HOMO-LUMO gaps increase multibranch behavior.

Abstract

We report unphysical irregularities and discontinuities in some key experimentally-measurable quantities computed within the GW approximation of many-body perturbation theory applied to molecular systems. In particular, we show that the solution obtained with partially self-consistent GW schemes depends on the algorithm one uses to solve self-consistently the quasi-particle (QP) equation. The main observation of the present study is that each branch of the self-energy is associated with a distinct QP solution, and that each switch between solutions implies a significant discontinuity in the quasiparticle energy as a function of the internuclear distance. Moreover, we clearly observe "ripple" effects, i.e., a discontinuity in one of the QP energies induces (smaller) discontinuities in the other QP energies. Going from one branch to another implies a transfer of weight between two solutions of the QP equation. The case of occupied, virtual and frontier orbitals are separately discussed on distinct diatomics. In particular, we show that multisolution behavior in frontier orbitals is more likely if the HOMO-LUMO gap is small.