Automated MultireferenceVertical Excitations forTransition-Metal Compounds

Excited states of transition metal complexes are generally strongly correlated due to the near-degeneracy of the metal d orbitals. Consequently, electronic structure calculations of such species often necessitate multireference approaches. However, widespread use of multireference methods is hindered due to the active space selection problem, which has historically required system-specific chemical knowledge and a trial-and-error approach. Here, we address this issue with an automated method combining the approximate pair coefficient (APC) scheme for estimating orbital entropies with the discrete variational selection (DVS) approach for evaluating active space quality. We apply DVS-APC to the calculation of 67 vertical excitations in transition metal diatomics as well as to two larger complexes. We show DVS-APC generated active spaces yield NEVPT2 mean absolute errors of 0.18 eV, in line with previous accuracies obtained for organic systems, but larger than errors achieved with hand-selected active spaces (0.14 eV). If instead of using DVS we identify the best results from our trial wave functions, we find improved performance (mean absolute error of 0.1 eV) over the manually selected results. We highlight this deviation between DVS and hand selected active spaces as a possible measure of bias introduced when hand selecting active spaces. However, we find that multiconfiguration pair-density functional theory (MC-PDFT) using the tPBE and tPBE0 functionals is roughly 0.15 eV less accurate than NEVPT2 across this class of diatomic systems, potentially accounting for the decreased performance of DVS-APC, which uses MC-PDFT energies to select between active spaces. We also showcase an ability to “down-sample” the DVS-APC wave functions using natural orbital occupancies to achieve smaller minimal active spaces which retain the accuracy of the larger starting active spaces. Finally, DVS-APC and tPBE0 are proven to be effective when applied to modeling excited states in two larger transition metal complexes, suggesting that the transition metal diatomics may be a particular outstanding challenge for DVS-APC and MC-PDFT approaches.