<br/>The effect of a dielectric environment on a molecule can be profound, causing changes in nuclear configuration and electronic structure. For electronically excited molecules, solvent can shift the absorption bands and affect molecular dynamics on the excited state potential energy surfaces. Unfortunately, quantum chemical simulation of a solute-solvent system can be prohibitively expensive due to the large number of degrees of freedom attributed to the solvent. To remedy this, two scales can be used; A quantum mechanical (QM) treatment of the solute and a continuum or molecular mechanical model of the solvent. When calculating excited states properties of an embedded system at the QM level, the time dependent self-consistent field (TD-SCF) family of methods (e,g, TD-HF, TD-DFT) are widely used low cost alternatives to higher accuracy methods. When the QM system is isolated, i.e. not embedded, the excitation energies calculated in these ways are variational quantities. This, along with the well known Z-vector equation, creates a variational excited state energy which is used to explore the excited state potential energy surface with analytical gradients. This treatment fails in a correct application of solvent models for calculation of the excited state potential energy surface. In a correct application of solvent models, the mutual polarization of the solute and solvent must be considered. This is also referred to as a state-specific solvent model. Modification of the standard TD-SCF eigensystem to accomodate a state-specific solvent model creates a nonlinear TD-SCF eigenequation. In current implementations the excitation energies then become non-variational. This prevents analytical gradients from being formulated so that excited state potential energy surfaces cannot be explored. In this talk, it is shown how a variational formulation of existing state specific solvent models can be derived from a Lagrangian formalism and give numerical results for the variability of calculated quantities. Model dynamics using state-specific solvent models are showcased.

Variational state specific solvent models for excited states from time dependent self-consistent field methods

249th National Meeting (2015)

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