We introduce an efficient configuration interaction (CI) method for the calculation of mixed quantum and classical nonadiabatic molecular dynamics for multiple electrons. For any given realization of the classical degrees of freedom (e.g., a solvent), the method uses a novel real-space quadrature to efficiently compute the Coulomb and exchange interactions between electrons. We also introduce an approximation whereby the classical molecular dynamics is propagated for several time steps on electronic potential energy surfaces generated using only a particularly important subset of the CI basis states. By only updating the important-states subset periodically, we achieve significant reductions in the computational cost of solving the multielectron quantum problem. We test the real-space quadrature for the cases of two electrons confined in a cubic box with infinitely repulsive walls and two electrons dissolved in liquid water that occupy a single cavity, so-called hydrated dielectrons. We then demonstrate how to perform mixed quantum and classical nonadiabatic dynamics by combining these computational techniques with the mean-field with surface hopping algorithm of Prezhdo and Rossky [J. Chem. Phys. 107, 825 (1997)]. Finally, we illustrate the practicality of the approach to multielectron nonadiabatic dynamics by examining the nonadiabatic relaxation dynamics of both spin singlet and spin triplet hydrated dielectrons following excitation from the ground to the first excited state. (C) 2003 American Institute of Physics.

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## Scholarly Works (9 results)

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) 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 matrix). 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 (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger 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. (c) 2005 American Institute of Physics.

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy fluctuations and nonequilibrium energy relaxation of a quantum-mechanical solute. As a first application of our formalism, we investigate the motions of classical water underlying the equilibrium and nonequilibrium excited-state solvent response functions of the hydrated electron; the results allow us to explain why the linear response approximation fails for this system.

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 (THF), 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 Franck-Condon 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-like) 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. (C) 2005 American Institute of Physics.

In the preceding paper, we presented an analytic reformulation of the Phillips-Kleinman (PK) pseudopotential theory. In the PK theory, the number of explicitly treated electronic degrees of freedom in a multielectron problem is reduced by forcing the wave functions of the few electrons of interest (the valence electrons) to be orthogonal to those of the remaining electrons (the core electrons); this results in a new Schrodinger equation for the valence electrons in which the effects of the core electrons are treated implicitly via an extra term known as the pseudopotential. Although this pseudopotential must be evaluated iteratively, our reformulation of the theory allows the exact pseudopotential to be found without ever having to evaluate the potential energy operator, providing enormous computational savings. In this paper, we present a detailed computational procedure for implementing our reformulation of the PK theory, and we illustrate our procedure on the largest system for which an exact pseudopotential has been calculated, that of an excess electron interacting with a tetrahyrdrofuran (THF) molecule. We discuss the numerical stability of several approaches to the iterative solution for the pseudopotential, and find that once the core wave functions are available, the full e(-)-THF pseudopotential can be calculated in less than 3 s on a relatively modest single processor. We also comment on how the choice of basis set affects the calculated pseudopotential, and provide a prescription for correcting unphysical behavior that arises at long distances if a localized Gaussian basis set is used. Finally, we discuss the effective e(-)-THF potential in detail, and present a multisite analytic fit of the potential that is suitable for use in molecular simulation. (c) 2006 American Institute of Physics.

Since charge-transfer-to-solvent (CTTS) reactions represent the simplest class of solvent-driven electron transfer reactions, there has been considerable interest in understanding the solvent motions responsible for electron ejection. The major question that we explore in this paper is what role the symmetry of the electronic states plays in determining the solvent motions that account for CTTS. To this end, we have performed a series of one-electron mixed quantum/classical nonadiabatic molecular dynamics simulations of the CTTS dynamics of sodide, Na-, which has its ground-state electron in an s orbital and solvent-supported CTTS excited states of p-like symmetry. We compare our simulations to previous theoretical work on the CTTS dynamics of the aqueous halides, in which the ground state has the electron in a p orbital and the CTTS excited state has s-like symmetry. We find that the key motions for Na- relaxation involve translations of solvent molecules into the node of the p-like CTTS excited state. This solvation of the electronic node leads to migration of the excited CTTS electron, leaving one of the p-like lobes pinned to the sodium atom core and the other extended into the solvent; this nodal migration causes a breakdown of linear response. Most importantly, for the nonadiabatic transition out of the CTTS excited state and the subsequent return to equilibrium, we find dramatic differences between the relaxation dynamics of sodide and the halides that result directly from differences in electronic symmetry. Since the ground state of the ejected electron is s-like, detachment from the s-like CTTS excited state of the halides occurs directly, but detachment cannot occur from the p-like CTTS excited state of Na- without a nonadiabatic transition to remove the node. Thus, unlike the halides, CTTS electron detachment from sodide occurs only after relaxation to the ground state and is a relatively rare event. In addition, the fact that the electronic symmetry of sodide is the same as for the hydrated electron enables us to directly study the effect of a stabilizing atomic core on the properties and solvation dynamics of solvent-supported electronic states. All the results are compared to experimental work on Na- CTTS dynamics, and a unified picture for the electronic relaxation for solvent-supported excited states of any symmetry is presented. (C) 2003 American Institute of Physics.

Even with modern computers, it is still not possible to solve the Schrodinger equation exactly for systems with more than a handful of electrons. For many systems, the deeply bound core electrons serve merely as placeholders and only a few valence electrons participate in the chemical process of interest. Pseudopotential theory takes advantage of this fact to reduce the dimensionality of a multielectron chemical problem: the Schrodinger equation is solved only for the valence electrons, and the effects of the core electrons are included implicitly via an extra term in the Hamiltonian known as the pseudopotential. Phillips and Kleinman (PK) [Phys. Rev. 116, 287 (1959)]. demonstrated that it is possible to derive a pseudopotential that guarantees that the valence electron wave function is orthogonal to the (implicitly included) core electron wave functions. The PK theory, however, is expensive to implement since the pseudopotential is nonlocal and its computation involves iterative evaluation of the full Hamiltonian. In this paper, we present an analytically exact reformulation of the PK pseudopotential theory. Our reformulation has the advantage that it greatly simplifies the expressions that need to be evaluated during the iterative determination of the pseudopotential, greatly increasing the computational efficiency. We demonstrate our new formalism by calculating the pseudopotential for the 3s valence electron of the Na atom, and in the subsequent paper, we show that pseudopotentials for molecules as complex as tetrahydrofuran can be calculated with our formalism in only a few seconds. Our reformulation also provides a clear geometric interpretation of how the constraint equations in the PK theory, which are required to obtain a unique solution, are themselves sufficient to calculate the pseudopotential. (c) 2006 American Institute of Physics.