Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory

Abstract

This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations to the two-electron SOC integrals are also proposed and carefully assessed. Based on benchmark calculations of the second-order SOC corrections to the energies and electrical properties for a set of diatomic molecules, we show that the SFX2C-1e+SOC [der] scheme performs very well in the computation of perturbative SOC corrections and that the "2eSL" scheme, which neglects the (SS|SS)-type two-electron SOC integrals, is both efficient and accurate. In contrast, the SFX2C-1e+SOC [fd] scheme turns out to be incompatible with a perturbative treatment of SOC effects. Finally, as a first chemical application, we report high-accuracy calculations of the (201)Hg quadrupole-coupling parameters of the recently characterized ethylmercury hydride (HHgCH2CH3) molecule based on SFX2C-1e coupled-cluster calculations augmented with second-order SOC corrections obtained at the Hartree-Fock level using the SFX2C-1e+SOC [der]/2eSL scheme.

Dioxygen Activation by Iron Complexes: The Catalytic Role of Intersystem Crossing Dynamics for a Heme-Related Model

“…The effective SOC values for singlet−triplet transitions are assigned to be 51.6 cm −1 , and they are 184.6 cm −1 for that between triplets and quintets, which together engender an indirect singlet/quintet mixing. 104,105 3. RESULTS AND DISCUSSIONS 3.1.…”

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…Perturbative treatment of spin-orbit effects can be obtained using either the SFDC or the SFX2C-1e scheme as the zeroth-order treatment. [287][288][289] For the latter, the corresponding spinorbit integrals are defined as first derivatives of SFX2C-1e Hamiltonian integrals, thereby treating spin-orbit integrals in the four-component formulation as the perturbation and using the analytic SFX2C-1e derivative technique. In this way, scalar-relativistic effects on spin-orbit integrals, which represent the coupling between scalar relativistic effects and spin-orbit coupling, have been taken into account.…”

“…Two-electron spin-orbit contributions can be taken into account using the molecular mean-field (MMF) or the atomic mean-field (AMF) spin-orbit approach. 288,290,291 The resulting effective one-electron spin-orbit integrals can be contracted with one-electron transition density matrices to obtain spin-orbit matrix elements between two electronic states. The EOM-CCSD transition densities (also needed for the quasidiabatic couplings in Section IV.…”

Tuning Nuclear Quadrupole Resonance: A Novel Approach for the Design of Frequency-Selective MRI Contrast Agents

“…effects and their coupling [52][53][54][55][56][57]. In addition to the scalar relativistic (SR) effects, the influence of relativistic spinorbit coupling (SO) needs to be taken into account in the heavy element magnetic resonance parameters [55,57,58]. While combining relativistic theory with more elaborate electron correlation treatment with hybrid functionals of the density functional theory (DFT) is currently not feasible for periodic solids, we follow closely the approach of Roukala et al for the nuclear shielding tensor of 195 Pt in molecular solids [59].…”