SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-orbit Coupling

TL;DR

The paper introduces SOiCISCF, a method combining SOiCI and iCISCF to accurately treat electron correlation and spin-orbit coupling with self-consistent orbital optimization, improving the description of heavy element systems.

Contribution

It develops SOiCISCF, integrating SOiCI and iCISCF, to better account for orbital relaxations in spin-orbit coupled systems with large active spaces.

Findings

Accurate fine structures of p-block elements demonstrated

Efficient use of double group and time reversal symmetries

Enhanced treatment of orbital relaxations in SOC calculations

Abstract

It has recently been shown that the SOiCI approach [J. Phys.: Condens. Matter 34 (2022) 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for, due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [J. Chem. Phys. 138 (2013) 104113] but with the iCISCF algorithm [J. Chem. Theory Comput. 17 (2021) 7545] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and assignment of target states. The fine structures of $p$-block elements are taken as showcases to reveal the efficacy of SOiCISCF.