Relativistic fully self-consistent $GW$ for molecules: Total energies and ionization potentials

TL;DR

This paper develops a relativistic fully self-consistent GW method for molecules with heavy elements, demonstrating improved accuracy in ionization potentials, spectra, and total energies, validated against experimental data and benchmarks.

Contribution

Introduces a relativistic scGW approach using X2C for molecules with heavy elements, enhancing accuracy and removing starting point dependence.

Findings

scGW outperforms G0W0 with PBE reference in ionization potentials

Photoelectron spectra at X2C level agree well with experiments

Accurate total energies and bond properties for heavy-element molecules

Abstract

The fully self-consistent $GW$ (sc$GW$) method with the iterative solution of Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of sc$GW$ for molecules containing heavy element using the exact two-component (X2C) Coulomb approximation. We benchmark $\texttt{SOC-81}$ dataset containing closed shell heavy elements for the first ionization potential using the fully self-consistent $GW$ as well as one-shot $GW$. The self-consistent $GW$ provides superior result compared to $G_0W_0$ with PBE reference and comparable to $G_0W_0$ with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with experimental spectra. We also observe that sc$GW$ provides very good estimation of ionization potential for the inner $d$ shell orbitals. Additionally, using the well conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of few halogen dimers using sc$GW$. Overall, our findings demonstrate the applicability of the fully self-consistent $GW$ method for accurate ionization potential, photoelectron spectra and total energies in finite systems with heavy elements with a reasonable computational scaling.