  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 in
crystals, photochemistry and quantum sensing to name but a few. Over the years,
an amalgam of powerful quantum chemistry methods, simple intuitive models, and
phenomenological parameterizations have been developed, providing increasingly
complex and specialized methodologies. Even with increasing specialization, a
pervasive challenge remains that is surprisingly universal - the simultaneous
description of continuous symmetries (e.g. spin and orbital angular momenta)
and discrete symmetries (e.g. crystal field). Modeling behavior in these
complex systems is increasingly important for metal ions of unusual or
technologically relevant behavior. Additionally, development of broad-scope
models with physically-meaningful parameters carries the potential to
facilitate interdisciplinary collaboration and large-scale meta analysis. We
propose a generalized algorithmic approach, the molecular symmetry adapted spin
space (mSASS), to localized electronic structure. We derive the Hamiltonian in
symmetry-constrained matrix form with an exact account of free parameters and
examples. Although preliminary in its implementation, a fundamental benefit of
this approach is the treatment of spatial and spin-orbit symmetries without the
need for perturbative approximations. In general, the mSASS Hamiltonian is
large but finite and can be diagonalized numerically with high efficiency,
providing a basis for conceptual models of electronic structure that naturally
incorporates spin while leveraging the intuition and efficiency benefits of
crystallographic symmetry. For the generation of the mSASS Hamiltonian, we
provide an implementation into the Mathematica Software Package, GTPack.
