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.

Figures (15)

• Figure 1: Perpendicular $g$-shift of ZnH in parts per thousand (ppt) relative to the free-electon $g$-value computed using BP1-CASSCF-K and BP1-QDNEVPT2-K, the ANO-RCC basis set, and the (3e, 5o) active space as a function of the number of states. For BP1-QDNEVPT2-K, results are computed with three level shifting techniques and different values of shift parameter ($\varepsilon$, $E_h$). The experimental $g$-value ($-$17.1 ppt) is indicated by the horizontal black line.weltnerMagneticAtomsMolecules1983
• Figure 2: (a) Magnitude of the smallest [$-1'$] correlation energy denominator ($E_\mathrm{h}$, \ref{['eq:intruder_amp']}) computed for 30 electronic states in ZnH using QDNEVPT2, the ANO-RCC basis set, and the (3e, 5o) active space. (b) Heat map indicating the magnitude of QDNEVPT2 effective Hamiltonian matrix elements for the calculation in (a).
• Figure 3: Correlation between experimental and computed $g$-shifts (in parts per thousand, ppt) for the full benchmark set, comparing the effective Hamiltonian (EH) and Kramers (K) $g$-tensor formalisms combined with SO-QDNEVPT2 (a) and SA-CASSCF (b). See the Supplementary Material for numerical values.
• Figure 4: Difference in $g$-shift predictions between the EH and K formalisms plotted as a function of K $g$-shift across the benchmark set (in parts per thousand, ppt).
• Figure 5: Correlation between experimental and computed $g$-shifts (in parts per thousand, ppt) for molecules with unpaired electrons localized on either the $p$- (a) or $d$-shell (b).