Coordination chemistry in molecular symmetry adapted spin space (mSASS)

TL;DR

The paper introduces mSASS, a novel algorithmic framework for modeling localized electronic structures in complex systems, integrating continuous and discrete symmetries without perturbation, and implemented in Mathematica.

Contribution

It presents the mSASS approach, a generalized, symmetry-adapted method for electronic structure modeling that treats spin and spatial symmetries exactly, improving upon existing models.

Findings

Hamiltonian derived in symmetry-constrained matrix form

Exact treatment of spin-orbit and spatial symmetries

Implemented in Mathematica's GTPack package

Abstract

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.