Charge Transfer with a Spin. I: A Variational Constrained-CASSCF Framework for Investigating Charge Transfer in the Presence of Spin–Orbit Coupling

Charge transfer in open-shell molecular systems can involve a delicate interplay between charge localization, orbital relaxation, and spin–orbit coupling (SOC), particularly near ground-excited state crossings. Here, we introduce a very inexpensive variational framework for treating these effects in odd-electron systems by extending the electron/hole-transfer Dynamically weighted State-Averaged Constrained CASSCF (eDSC/hDSC) method to include SOC. Our method incorporates the SOC Hamiltonian directly into the variational orbital optimization through complex-valued spinor orbitals, allowing orbital and spin degrees of freedom to relax self-consistently while preserving the time-reversal symmetry of doublet states. The method achieves smooth potential energy surfaces and rapid self-consistent field (SCF) convergence; moreover, from physically small to artificially large SOC strengths, the calculation can be converged to very tight thresholds across the whole potential energy surface. While the results presented here are for systems with two charge centers, as shown in the appendix, the theory is quite general and can be adapted to either a system of N charge centers or a metal-molecule surface with a continuum of states, so that charge transport (and not just charge transfer) can also be studied. The approach therefore provides a route toward ab initio studies of spin-dependent charge transfer and charge transport in molecular systems with nontrivial spin degrees of freedom.