MC-PDFT Nuclear Gradients and L-PDFT Energies with Meta and Hybrid Meta On-Top Functionals for Ground- and Excited-State Geometry Optimization and Vertical Excitation Energies

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-MCSCF multireference electronic-structure method that explicitly models strong electron correlation, and linearized pair-density functional theory (L-PDFT) is a recently developed multistate extension that can accurately model conical intersections and locally avoided crossings. Because MC-PDFT and L-PDFT rely on an on-top energy functional, their accuracy depends on the quality of the on-top functional used. Recent work has introduced translated meta-gradient-approximation (meta-GA) on-top functionals, and specifically the MC23 hybrid meta-GA on-top functional, which is the first on-top functional specifically optimized for MC-PDFT. Here we report the derivation and implementation of analytic nuclear gradients for MC-PDFT calculations using meta-GA and hybrid meta-GA on-top functionals. This development also enables analytic nuclear gradients for the widely successful tPBE0 hybrid on-top functional. Because MC-PDFT nuclear-gradient calculations involve the derivative of the on-top functional, this development also enables the use of meta-GA on-top functionals in L-PDFT single-point energy calculations. We use the new capabilities to test MC23 for ground-state geometries, excited-state geometries, and vertical excitation energies of <i>s</i>-<i>trans</i>-butadiene and benzophenone as well as to test MC23, another hybrid meta-GA, and seven other meta-GA on-top functionals for 441 vertical excitation energies. We find MC23 performs the best of all nine meta and hybrid meta functionals for vertical excitation energies and is comparable in accuracy to tPBE0 and to the NEVPT2 multireference wave function method. Additionally, we directly compare our MC-PDFT vertical excitation results to previously computed TD-DFT values and find that MC-PDFT outperforms even the best performing Kohn-Sham density functional.