Perturbation Theory Treatment of Spin–Orbit Coupling II: A Coupled Perturbed Kohn–Sham Method

• Published in: Journal of chemical theory and computation Vol. 17; no. 8; pp. 4712 - 4732
• Main Authors: Desmarais, Jacques K, Erba, Alessandro, Flament, Jean-Pierre, Kirtman, Bernard
• Format: Journal Article
• Language: English
• Published: Washington American Chemical Society 10-08-2021
• Subjects: Chemical Physics; Chemical Sciences; Coupling (molecular); Density functional theory; Floating point arithmetic; Negative ions; or physical chemistry; Perturbation theory; Physics; Quantum Electronic Structure; Relativistic effects; Self consistent fields; Spin-orbit interactions; Theoretical and
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.1c00460

A noncanonical coupled perturbed Kohn–Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment of spin–orbit coupling (SOC) is provided. We take the scalar-relativistic KS-DFT/HF solution, obtained with a relativistic effective core potential, as the zeroth-order approximation. Explicit expressions are given for the total energy through the 4th order, which satisfy the 2n + 1 rule. Second-order expressions are provided for orbital energies and density variables of spin-current DFT. Test calculations are carried out on the halogen homonuclear diatomic and hydride molecules, including 6p and 7p elements, as well as open-shell negative ions. The computed properties through second or third order match well with those from reference two-component self-consistent field calculations for total and orbital energies as well as spin-current densities. In only one case (At2 –) did a significant deviation occur for the remaining density variables. Our coupled perturbation theory approach provides an efficient way of adding the effect of SOC to a scalar-relativistic single-reference KS-DFT/HF treatment, in particular because it does not require diagonalization in the two-component spinor basis, leading to saving factors on the number of required floating-point operations that may exceed one order of magnitude.