The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical ͑MQC͒ simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ͑"surface hops"͒ and for calculating the loss of quantum-mechanical phase information ͑e.g., the decay of the off-diagonal elements of the density matrix͒. In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics ͑MD͒ algorithm, which we call mean-field dynamics with stochastic decoherence ͑MF-SD͒. MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrödinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.

In polar fluids such as water and methanol, the peak of the solvated electron's absorption spectrum in the red has been assigned as a sum of transitions between an s-like ground state and three nearly degenerate p-like excited states bound in a quasispherical cavity. In contrast, in weakly polar solvents such as tetrahydrofuran ͑THF͒, the solvated electron has an absorption spectrum that peaks in the mid-infrared, but no definitive assignment has been offered about the origins of the spectrum or the underlying structure. In this paper, we present the results of adiabatic mixed quantum/classical molecular dynamic simulations of the solvated electron in THF, and provide a detailed explanation of the THF-solvated electron's absorption spectrum and electronic structure. Using a classical solvent model and a fully quantum mechanical excess electron, our simulations show that although the ground and first excited states are bound in a quasispherical cavity, a multitude of other, nearby solvent cavities support numerous, nearly degenerate, bound excited states that have little FranckCondon overlap with the ground state. We show that these solvent cavities, which are partially polarized so that they act as electron trapping sites, are an inherent property of the way THF molecules pack in the liquid. The absorption spectrum is thus assigned to a sum of bound-to-bound transitions between a localized ground state and multiple disjoint excited states scattered throughout the fluid. Furthermore, we find that the usual spherical harmonic labels ͑e.g., s-like, p-like͒ are not good descriptors of the excited-state wave functions of the solvated electron in THF. Our observation of multiple disjoint excited states is consistent with femtosecond pump-probe experiments in the literature that suggest that photoexcitation of solvated electrons in THF causes them to relocalize into solvent cavities far from where they originated.

The linear response (LR) approximation forms the cornerstone of nonequilibrium statistical mechanics and has found special utility in studies of solvation dynamics, in which LR implies that nonequilibrium relaxation dynamics is governed by the same molecular motions responsible for fluctuations at equilibrium. When the motions at and away from equilibrium fall in the LR regime, the equilibrium and nonequilibrium response functions are identical. However, similarity of the equilibrium and nonequilibrium solvent response functions does not guarantee that LR holds and that the underlying molecular motions are the same. In this paper, we present computer simulation studies of the removal of charge from an atomic solute in liquid tetrahydrofuran, a system for which the equilibrium and nonequilibrium solvation responses appear quite similar. We then introduce a method for projecting nonequilibrium response functions onto specific molecular motions. We find that the equilibrium relaxation is dominated by solvent rotations, whereas the nonequilibrium relaxation is much more complex, having translations dominating at early times and a delayed onset of rotations. The results imply that LR may not hold as often as is widely believed and that care should be taken when using equilibrium response functions to understand nonequilibrium solvation dynamics.

Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensed-phase systems. There are many MQC algorithms available, however, and in cases where nonadiabatic coupling is important, different algorithms may lead to different results. Thus, it has been difficult to reach definitive conclusions about relaxation dynamics using nonadiabatic MQC methods because one is never certain whether any given algorithm includes enough of the necessary physics. In this paper, we explore the physics underlying different nonadiabatic MQC algorithms by comparing and contrasting the excited-state relaxation dynamics of the prototypical condensed-phase MQC system, the hydrated electron, calculated using different algorithms, including: fewest-switches surface hopping, stationary-phase surface hopping, and mean-field dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, mean-field dynamics with stochastic decoherence (MF-SD), is to be implemented for condensed-phase problems, and we apply MF-SD to the excited-state relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydrated-electron relaxation dynamics. We find that for three MQC methods that use Tully's fewest-switches criterion to determine surface hopping probabilities, the excited-state lifetime of the electron is the same. Moreover, the nonequilibrium solvent response function of the excited hydrated electron is the same with all of the nonadiabatic MQC algorithms discussed here, so that all of the algorithms would produce similar agreement with experiment. Despite the identical solvent response predicted by each MQC algorithm, we find that MF-SD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an excited-state lifetime that is longer with MF-SD than with any method that incorporates nonadiabatic effects with the fewest-switches surface hopping criterion.

We present simulations of exciton dissociation and charge separation processes in the prototypical conjugated polymer, poly-p-phenylenevinylene. Our mixed quantum/classical simulations focus on the nonadiabatic excited state dynamics of single and pi-stacked oligomers of varying length. By applying a constant external electric field, our simulations reveal the details and time scale for exciton dissociation and fluorescence quenching and suggest how those processes relate to charge carrier (polaron) formation in polymer systems. We find that, in such a polarizing environment, sufficiently long chromophores (either single or interacting chains) can form polaron pairs via a delayed exciton dissociation mechanism or nearly instantaneously following photoexcitation. However, we find that these processes are mechanically essentially the same, being highly nonadiabatic in character and requiring transitions through "gateway" states to reach the completely charge separated electronic states. Finally, we observe thermally driven polaron hopping dynamics between chains, similar to the energy transfer dynamics we had described previously (J. Phys. Chem. A 2009, 113 (15), 3427). Our results are consistent with a range of apparently conflicting experiments, resolving some controversies regarding the molecular mechanism for charge carrier photogeneration in conjugated polymers.