Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins
of open-shell transition-metal
complexes is critical to understanding catalytic and materials properties
but also challenging with approximate electronic structure methods.
As an alternative approach, we demonstrate how structure alone can
be used to guide assignment of ground-state spin from experimentally
determined crystal structures of transition-metal complexes. We first
identify the limits of distance-based heuristics from distributions
of metal–ligand bond lengths of over 2000 unique mononuclear
Fe­(II)/Fe­(III) transition-metal complexes. To overcome these limits,
we employ artificial neural networks (ANNs) to predict spin-state-dependent
metal–ligand bond lengths and classify experimental ground-state
spins based on agreement of experimental structures with the ANN predictions.
Although the ANN is trained on hybrid density functional theory data,
we exploit the method-insensitivity of geometric properties to enable
assignment of ground states for the majority (ca. 80–90%) of
structures. We demonstrate the utility of the ANN by data-mining the
literature for spin-crossover (SCO) complexes, which have experimentally
observed temperature-dependent geometric structure changes, by correctly
assigning almost all (>95%) spin states in the 46 Fe­(II) SCO complex
set. This approach represents a promising complement to more conventional
energy-based spin-state assignment from electronic structure theory
at the low cost of a machine learning model.