The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes

Iron–sulfur
clusters comprise an important functional motif
in the catalytic centers of biological systems, capable of enabling
important chemical transformations at ambient conditions. This remarkable
capability derives from a notoriously complex electronic structure
that is characterized by a high density of states that is sensitive
to geometric changes. The spectral sensitivity to subtle geometric
changes has received little attention from correlated, large active
space calculations, owing partly to the exceptional computational
complexity for treating these large and correlated systems accurately.
To provide insight into this aspect, we report the first Complete
Active Space Self Consistent Field (CASSCF) calculations for different
geometries of the [Fe­(II/III)4S4(SMe)4]−2 clusters using two complementary, correlated
solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI)
and Density Matrix Renormalization Group (DMRG). We find that the
previously established picture of a double-exchange driven magnetic
structure, with minute energy gaps (<1 mHa) between consecutive
spin states, has a weak dependence on the underlying geometry. However,
the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry
dependent, changing by a factor of 3 upon slight deformations that
are still within biologically relevant parameters. The CASSCF orbital
optimization procedure, using active spaces as large as 86 electrons
in 52 orbitals, was found to reduce this gap compared to typical mean-field
orbital approaches. Our results show the need for performing large
active space calculations to unveil the challenging electronic structure
of these complex catalytic centers and should serve as accurate starting
points for fully correlated treatments upon inclusion of dynamical
correlation outside the active space.