Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation

de Carvalho, Felipe Franco; Curchod, Basile F.E.; Penfold, Thomas J.; Tavernelli, Ivano

Abstract

Using an approach based upon a set of auxiliary many-electron wavefunctions we present a rigorous derivation of spin-orbit coupling (SOC) within the framework of linear-response time-dependent density functional theory (LR-TDDFT). Our method is based on a perturbative correction of the non-relativistic collinear TDDFT equations using a Breit-Pauli spin-orbit Hamiltonian. The derivation, which is performed within both the Casida and Sternheimer formulations of LR-TDDFT, is valid for any basis set. The requirement of spin noncollinearity for the treatment of spin-flip transitions is also discussed and a possible alternative solution for the description of these transitions in the collinear case is also proposed. Our results are validated by computing the SOC matrix elements between singlet and triplet states of two molecules, formaldehyde and acetone. In both cases, we find excellent agreement with benchmark calculations performed with a high level correlated wavefunction method.

Citation

de Carvalho, F. F., Curchod, B. F., Penfold, T. J., & Tavernelli, I. (2014). Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation. The Journal of Chemical Physics, 140(14), Article 144103. https://doi.org/10.1063/1.4870010

• Journal Article Type: Article
• Acceptance Date: Mar 19, 2014
• Online Publication Date: Apr 9, 2014
• Publication Date: Apr 9, 2014
• Deposit Date: Nov 6, 2017
• Publicly Available Date: Dec 8, 2017
• Journal: Journal of Chemical Physics
• Print ISSN: 0021-9606
• Electronic ISSN: 1089-7690
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 140
• Issue: 14
• Article Number: 144103
• DOI: https://doi.org/10.1063/1.4870010
• Public URL: https://durham-repository.worktribe.com/output/1340849