Calculation of molecular g-tensors by sampling spin orientations of generalised Hartree-Fock states

TL;DR

This paper introduces a new two-step method combining generalised Hartree-Fock solutions and superpositions to accurately compute molecular g-tensors, especially in systems with significant spin-orbit coupling and orbital degeneracy.

Contribution

It presents a novel GCM-inspired approach for calculating molecular g-tensors that overcomes limitations of traditional methods by incorporating superpositions of GHF states.

Findings

Accurately reproduces experimental g-tensors for small molecules.

Correctly describes spin-orbit splitting in degenerate states.

Provides qualitative results with spin rotations for weak spin-orbit effects.

Abstract

The variational inclusion of spin-orbit coupling in self-consistent field (SCF) calculations requires a generalised two-component framework, which permits the single-determinant wave function to completely break spin symmetry. The individual components of the molecular g-tensor are commonly obtained from separate SCF solutions that align the magnetic moment along one of the three principal tensor axes. However, this strategy raises the question if energy differences between solutions are relevant, or how convergence is achieved if the principal axis system is not determined by molecular symmetry. The present work resolves these issues by a simple two-step procedure akin to the generator coordinate method (GCM). First, a few generalised Hartree Fock (GHF) solutions are converged, applying, where needed, a constraint to the orientation of the magnetic-moment or spin vector. Then, superpositions of GHF determinants are formed through non-orthogonal configuration interaction. This procedure yields a Kramers doublet for the calculation of the complete g-tensor. Alternatively, for systems with weak spin-orbit effects, diagonalisation in a basis spanned by spin rotations of a single GHF determinant affords qualitatively correct g-tensors by eliminating errors related to spin contamination. For small first-row molecules, these approaches are evaluated against experimental data and full configuration interaction results. It is further demonstrated for two systems (a fictitious tetrahedral CH4+ species, and a CuF4(2-) complex) that a GCM strategy, in contrast to alternative mean-field methods, can correctly describe the spin-orbit splitting of orbitally-degenerate ground states, which causes large g-shifts and may lead to negative g-values.