Excited state gradients for a state-specific continuum solvation approach: The vertical excitation model within a Lagrangian TDDFT formulation

The accurate modeling of the environment response is a fundamental challenge for accurately describing the photophysics and photochemistry of molecules both in solution and in more complex embeddings. When large rearrangements of the electron density occur after an electronic transition, state-specific formulations, such as the vertical excitation model, are necessary to achieve a proper modeling of the processes. Such a state-specific model is fundamental not only to obtain accurate energies, but also to follow the geometrical relaxation accompanying the evolution of the excited-states. This study presents the analytical expression of the gradients of the vertical excitation model approach by a Lagrangian formulation in the time dependent density functional theory framework. Representative organic chromophores in solution are used to test the reliability of the implementation and provide comparisons with the linear response description.