Molecular g-Tensors From Spin-Orbit Quasidegenerate N-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 framework. Two g-tensor approaches are implemented: a spin-free effective Hamiltonian (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 Kramers 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.