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Many areas of chemistry are devoted to the challenge of understanding,predicting, and controlling the behavior of strongly localized electrons.Examples include molecular magnetism and luminescence, color centers incrystals, photochemistry and quantum sensing to name but a few. Over the years,an amalgam of powerful quantum chemistry methods, simple intuitive models, andphenomenological parameterizations have been developed, providing increasinglycomplex and specialized methodologies. Even with increasing specialization, apervasive challenge remains that is surprisingly universal - the simultaneousdescription of continuous symmetries (e.g. spin and orbital angular momenta)and discrete symmetries (e.g. crystal field). Modeling behavior in thesecomplex systems is increasingly important for metal ions of unusual ortechnologically relevant behavior. Additionally, development of broad-scopemodels with physically-meaningful parameters carries the potential tofacilitate interdisciplinary collaboration and large-scale meta analysis. Wepropose a generalized algorithmic approach, the molecular symmetry adapted spinspace (mSASS), to localized electronic structure. We derive the Hamiltonian insymmetry-constrained matrix form with an exact account of free parameters andexamples. Although preliminary in its implementation, a fundamental benefit ofthis approach is the treatment of spatial and spin-orbit symmetries without theneed for perturbative approximations. In general, the mSASS Hamiltonian islarge but finite and can be diagonalized numerically with high efficiency,providing a basis for conceptual models of electronic structure that naturallyincorporates spin while leveraging the intuition and efficiency benefits ofcrystallographic symmetry. For the generation of the mSASS Hamiltonian, weprovide an implementation into the Mathematica Software Package, GTPack.

Coordination chemistry in molecular symmetry adapted spin space (mSASS)