A Simple Algorithm for Determining Orthogonal, Self-Consistent Excited-State Wave Functions for a State-Specific...

We recently introduced a mixed quantum/classical model for the hydrated electron that includes electron/water polarization in a self-consistent fashion, using a polarizable force field for the water molecules [ J. Chem. Phys. 2010 , 133 , 154506 ]. Calculation of the electronic absorption spectrum for this model is not straightforward, owing to the state-specific nature of the Hamiltonian, the high density of electronic states, and the large solvent polarization response upon electronic excitation. Together, these properties make it difficult or impossible to converge the polarizable solvent dipoles self-consistently for each excited-state wave function. Here, we overcome this problem by means of an extended Lagrangian procedure for performing constrained annealing in the space of electronic variables. By construction, this algorithm affords self-consistent, mutually orthogonal solutions for any state-specific Hamiltonian, and we illustrate this approach by computing the optical spectrum of our polarizable model for the aqueous electron. The spectrum thus obtained affords better agreement with experiment than previous, perturbative calculations of solvent dipole relaxation. Strengths, weaknesses, and possible generalizations of this procedure are discussed.