This study describes variational energy expressions and analytical excited state energy
gradients for time-dependent self-consistent field methods with polarizable solvent effects.
Linear response, vertical excitation, and state-specific solvent models are examined.
Enforcing a variational ground state energy expression in the state-specific model is found to
reduce it to the vertical excitation model. Variational excited state energy expressions are
then provided for the linear response and vertical excitation models and analytical gradients …