Charge Transfer with a Spin. II: A Framework for Diabatization which Localizes Charge and Spin

TL;DR

This paper introduces a diabatization framework that localizes charge and spin in open-shell systems with charge transfer and spin-orbit coupling, using a novel two-step optimization method.

Contribution

It develops a new diabatization procedure combining complex-unitary rotations with AJD-like updates to localize charge and spin simultaneously.

Findings

Method converges rapidly and produces smooth diabatic surfaces.

Preserves dipole and spin properties along reaction paths.

Maintains time-reversal symmetry in the diabatic states.

Abstract

We investigate a diabatization procedure that localizes charges (in real space) and localizes spins (in spin space) for open-shell systems that exhibit charge transfer in the presence of spin-orbit coupling. The procedure is applied to a two-state crossing between pairs of Kramers-restricted doublet states (which can also be considered effectively a four-state crossing). To generate the relevant electronic states, we employ the recently developed electron/hole-transfer Dynamically-weighted State-Averaged Constrained CASSCF (eDSC/hDSC) method that treats systems with an odd number of electrons. To generate the relevant diabatic states, we employ a two-step optimization over complex-unitary rotations that sequentially maximizes dipole and spin moments through iterative Jacobi sweeps; the resulting update rules are effectively equivalent to those of approximate joint diagonalization (AJD) applied to charge and spin. The method converges rapidly and yields smooth diabatic potential energy surfaces that preserve dipole and spin properties (e.g., a slowly varying pseudospin texture) along the reaction coordinate while maintaining time-reversal symmetry.