Extended Lagrangian Excited State Molecular Dynamics.

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

Nonequilibrium solvent effects in Born-Oppenheimer molecular dynamics for ground and excited electronic states.

The effects of solvent on molecular processes such as excited state relaxation and photochemical reaction often occurs in a nonequilibrium regime. Dynamic processes such as these can be simulated using excited statemolecular dynamics. In this work, we describe methods of simulating nonequilibrium solvent effects in excited statemolecular dynamics using linear-response time-dependent density functional theory and apparent surface charge methods. These developments include a propagation method for solvent degrees of freedom and analytical energy gradients for the calculation of forces. Molecular dynamics of acetaldehyde in water or acetonitrile are demonstrated where the solute-solvent system is out of equilibrium due to photoexcitation and emission.

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients.

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 are formulated. Using semiempirical model chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline.

Solvent effects in time-dependent self-consistent field methods. I. Optical response calculations.

We implement and examine three excited state solvent models in time-dependent self-consistent field methods using a consistent formalism which unambiguously shows their relationship. These are the linear response, state specific, and vertical excitation solvent models. Their effects on energies calculated with the equivalent of COSMO/CIS/AM1 are given for a set of test molecules with varying excited state charge transfer character. The resulting solvent effects are explained qualitatively using a dipole approximation. It is shown that the fundamental differences between these solvent models are reflected by the character of the calculated excitations.