Molecular <i>g</i> -tensors from spin–orbit quasidegenerate <i>N</i> -electron valence perturbation theory: Benchmarks, intruder-state mitigation, and practical guidelines

Abstract

Accurate prediction of molecular g-tensors for open-shell systems requires a balanced treatment of multireference electron correlation and relativistic spin–orbit coupling. Here, we develop and benchmark spin–orbit quasidegenerate second-order N-electron valence perturbation theory (SO-QDNEVPT2) for g-tensor calculations, treating dynamical correlation and spin–orbit effects consistently within a multistate effective Hamiltonian (EH) framework. Two g-tensor approaches are implemented: a spin-free EH approach based on second-order response and a Kramers (K) approach that extracts g from spin-mixed SO-QDNEVPT2 states. We assess their performance on a benchmark set of 23 molecules spanning diatomics and small polyatomics, low- to high-spin species, and weak to strong spin–orbit coupling. Across the dataset, SO-QDNEVPT2 improves agreement with experiment relative to state-averaged complete active-space self-consistent field. The EH and K formalisms agree for modest g-shifts, but the K approach becomes essential when the shifts become large. We demonstrate that QDNEVPT2 results can be sensitive to intruder-state instabilities that can be effectively mitigated with level-shift or renormalization techniques. We then analyze the dependence of SO-QDNEVPT2 results on key computational parameters, including active space, number of states, state-averaging weights, gauge origin, and basis set. These results establish SO-QDNEVPT2 as a robust framework for computing g-tensors in correlated, relativistic open-shell molecules, offering practical guidelines for its applications.