SOiCI and iCISO: combining iterative configuration interaction with spin–orbit coupling in two ways

Abstract

The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory

“…The improved virtual orbital scheme ,, was used in this work. More advanced virtual space decomposition approaches , will be evaluated in a future work.…”

“…Another advantage of CASPT2-SO is that real-valued MCSCF methods ,,− can be used in conjunction with the perturbation treatment, giving rise to an additional reduction in computational cost. A very recent work by Zhang and co-workers has introduced a new approach to treat relativistic effects and electron correlations with the iterative configuration interaction and second-order perturbation theory (iCIPT2) method …”

“…A very recent work by Zhang and coworkers has introduced a new approach to treat relativistic effects and electron correlations with the iterative configuration interaction and second-order perturbation theory (iCIPT2) method. 24 T h i s c o n t e n t i s In this work, we develop a relativistic two-component multistate multi-configurational perturbation theory to introduce the dynamic correlation to the relativistic Kramersunrestricted two-component MCSCF wave function which variationally includes scalar relativistic effects and spin−orbit coupling. A fully uncontracted perturbative formulation is introduced within a determinant basis.…”

“Relativity + Correlation + QED = Experiment”

“…Here, the gain in efficiency stems from the use of real-valued orbitals and hence integrals, which allow for an easy incorporation of point group and full spin symmetries in constructing the spin-free Hamiltonian matrix and both double group and time reversal symmetries in constructing the SOC Hamiltonian matrix. 106,107 For this reason, such approaches are usually called one-component (1C). The interplay between SOC and electron correlation can be accounted for in two ways, 108,109 one-step (denoted as SOX for method X) or two-step (denoted as XSO).…”

“…The interplay between SOC and electron correlation can be accounted for in two ways, 108,109 one-step (denoted as SOX for method X) or two-step (denoted as XSO). The former type of approaches 69,106,107,[110][111][112][113][114][115][116][117][118][119][120] aims to treat spin-orbit and electron-electron interactions on an equal footing, whereas the latter type of approaches 107,[121][122][123][124][125][126][127][128][129][130][131][132][133][134][135][136][137][138][139][140] amounts to treating SOC after correlation, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix over a small number of close-lying correlated scalar states. While XSO's miss by construction spin-dependent orbital relaxations, SOX's can recover a large amount of such relaxations (which is particularly true for SOCC 69,110 ).…”