Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult
due to
the presence of conical intersections and locally avoided crossings,
as well as the inherently multiconfigurational character of excited
states. As such, one needs a multistate method that incorporates state
interaction in order to accurately model the potential energy surface
at all nuclear coordinates. The recently developed linearized pair-density
functional theory (L-PDFT) is a multistate extension of multiconfiguration
PDFT, and it has been shown to be a cost-effective post-MCSCF method
(as compared to more traditional and expensive multireference many-body
perturbation methods or multireference configuration interaction methods)
that can accurately model potential energy surfaces in regions of
strong nuclear–electronic coupling in addition to accurately
predicting Franck–Condon vertical excitations. In this paper,
we report the derivation of analytic gradients for L-PDFT and their
implementation in the PySCF-forge software, and we illustrate the
utility of these gradients for predicting ground- and excited-state
equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.