Quasirelativistic two-component core excitations and polarisabilities from a damped-response formulation of the Bethe–Salpeter equation

Abstract

A damped-response formalism in the GW approximation to the Bethe–Salpeter equation (BSE) is presented and implemented. It is based on a quasirelativistic two-component (2c) approach that includes scalar-relativistic and spin–orbit effects derived from the one-electron Dirac equation. A generalised solver, which also allows to calculate static, dynamic and damped-response polarisabilites, is discussed in detail. Throughout our implementation, the resolution-of-the-identity approximation is employed to reduce the computational effort. The performance of 2c GW-BSE is benchmarked against experimental and high-level ab initio data and compared to standard density-functional theory approaches, including modern local hybrid functionals for which a proper non-collinear kernel for Kramers-restricted systems is reported.

GRAPHICAL ABSTRACT

Keywords:

• Time-dependent density-functional theory
• GW method
• spin–orbit interactions
• Bethe–Salper equation

Acknowledgments

MK gratefully acknowledges financial support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Transregional Collaborative Research Centre 88 ‘Cooperative Effects in Homo- and Heterometallic Complexes’ (Project C1). YJF is grateful for financial support by Fonds der Chemischen Industrie (FCI, German Chemical Industry Fund) through a Kekulé Scholarship and to Deutscher Akademischer Austauschdienst (DAAD, German Academic Exchange Service) for for a fellowship (grant no. 57438025) and Filipp Furche for hosting. YJF furthermore acknowledges financial support by TURBOMOLE GmbH. CH gratefully acknowledges support by DFG through the Priority Programme SPP 1807 ‘Control of London Dispersion Interactions in Molecular Chemistry’ (Project No. KL 721/5-2). We further thank Michael E. Harding for fruitful discussions and supplying a tailored auxiliary basis (cbas) for Xe.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Max Kehry http://orcid.org/0000-0002-2093-7808

Yannick J. Franzke http://orcid.org/0000-0002-8344-113X

Christof Holzer http://orcid.org/0000-0001-8234-260X

Wim Klopper  http://orcid.org/0000-0002-5219-9328