Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient

Following the formulation of cavity quantum electrodynamical time-dependent density functional theory (cQED-TDDFT) models [Flick et al., ACS Photonics 6, 2757-2778 (2019); Yang et al., J. Chem. Phys. 155, 064107 (2021)], here we report the derivation and implementation of the analytic energy gradient for the polaritonic states of a single photochrome within the cQED-TDDFT models. Such gradient evaluation is also applicable to a complex of explicitly-specified photochromes, or, with proper scaling, a set of parallel-oriented, identical-geometry, non-interacting molecules in the microcavity.