Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

Prediction of spin-state
ordering in transition metal complexes
is essential for understanding catalytic activity and designing functional
materials. Semilocal approximations in density functional theory,
such as the generalized-gradient approximation (GGA), suffer from
several errors including delocalization error that give rise to systematic
bias for more covalently bound low-spin electronic states. Incorporation
of exact exchange is known to counteract this bias, instead favoring
high-spin states, in a manner that has recently been identified to
be strongly ligand-field dependent. In this work, we introduce a tuning
strategy to identify the effect of incorporating the Laplacian of
the density (i.e., a meta-GGA) in exchange on spin-state ordering.
We employ a diverse test set of M­(II) and M­(III) first-row transition
metal ions from Ti to Cu as well as octahedral complexes of these
ions with ligands of increasing field strength (i.e., H2O, NH3, and CO). We show that the sensitivity of spin-state
ordering to meta-GGA exchange is highly ligand-field dependent, stabilizing
high-spin states in strong-field (i.e., CO) cases and stabilizing
low-spin states in weak-field (i.e., H2O, NH3, and isolated ions) cases. This diverging behavior leads to generally
improved treatment of isolated ions and strong field complexes over
a standard GGA but worsened treatment for the hexa-aqua or hexa-ammine
complexes. These observations highlight the sensitivity of functional
performance to subtle changes in chemical bonding.