Challenges with relativistic GW calculations in solids and molecules

Abstract

For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis-sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis-sets particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

13 pages, 5 figures, and 4 tables

References in corpus (13)

• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• A Benchmark of GW Methods for Azabenzenes: Is the GW Approximation Good Enough?
• Gaussian and plane-wave mixed density fitting for periodic systems
• Systematically improvable multi-scale solver for correlated electron systems
• Multitier self-consistent $GW$+EDMFT
• Finite temperature quantum embedding theories for correlated systems
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Fast periodic Gaussian density fitting by range separation
• Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions
• Testing self-energy embedding theory in combination with GW
• Relativistic fully self-consistent $GW$ for molecules: Total energies and ionization potentials
• Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

Cited by in corpus (4)

• Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides