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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.

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.

The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure. (C) 2005 American Institute of Physics.

In "outer sphere" electron transfer reactions, motions of the solvent molecules surrounding the donor and acceptor govern the dynamics of charge flow. Are the relevant solvent motions determined simply by bulk solvent properties such as dielectric constant or viscosity? Or are molecular details, such as the local solvent structure around the donor and acceptor, necessary to understand how solvent motions control charge transfer? In this paper, we address these questions by using ultrafast spectroscopy to study a photoinduced electron transfer reaction with only electronic degrees of freedom: the charge-transfer-to-solvent (CTTS) reaction of Na- (sodide). Photoexcitation of Na- places the excited CTTS electron into a solvent-bound excited state; motions of the surrounding solvent molecules in response to this excitation ultimately lead to detachment of the electron. The detached electron can then localize either in an "immediate" contact pair (in the same cavity as the Na atom), which undergoes back electron transfer to regenerate Na- in similar to1 ps, or in a "solvent-separated" contact pair (one solvent shell away from the Na atom), which undergoes back electron transfer in tens to hundreds of picoseconds. We present detailed results for the dynamics of each step of this reaction in several solvents: the ethers tetrahydrofuran, diethyl ether and tetrahydropyran and the amine solvent hexamethylphosphoramide (HMPA). The results are interpreted in terms of a kinetic model that both incorporates spectral shifting of the reaction intermediates due to solvation dynamics and accounts for anisotropic spectral diffusion in polarized transient hole-burning experiments. We find that the rate of CTTS detachment does not correlate simply with any bulk solvent properties, but instead appears to depend on the details of how the solvent packs around the solute. In contrast, the rate for back electron transfer of solvent-separated contact pairs varies inversely with solvent polarity, indicating a barrier to recombination and suggesting that this reaction lies in the Marcus inverted regime. For immediate contact pairs, the rate of recombination varies directly with solvent polarity in the ethers but is slowest in the highly polar solvent HMPA, suggesting that the spatial extent of the solvated electron in each solvent is one of the major factors determining the recombination dynamics. The fact that each step in the reaction varies with solvent in a different way implies that there is not a single set of solvent motions or spectral density that can be used to model all aspects of electron transfer. In addition, all of the results and conclusions in this paper are compared in detail to related work on this system by Ruhman and co-workers; in particular, we assign a fast decay seen in the near-IR to solvation of the CTTS p-to-p excited-state absorption, and polarization differences observed at visible probe wavelengths to anisotropic bleaching of the Na- CTTS ground state. (C) 2003 American Institute of Physics.

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

In the milestoning framework, and more generally in related transition interface sampling schemes, one significantly enhances the calculation of relaxation rates for complex equilibrium kinetics from molecular dynamics simulations between the milestones or interfaces. The goal of the present paper is to advance milestoning applications into the realm of non-equilibrium statistical mechanics, in particular, to calculate entire time correlation functions. In order to accomplish this, we introduce a novel methodology for obtaining the flux through a given milestone configuration as a function of both time and initial configuration and build upon it with a novel formalism describing autocorrelation for Langevin motion in a discrete configuration space. The method is then applied to three different test systems: a harmonic oscillator, which we solve analytically, a two-well potential, which is solved numerically, and an atomistic molecular dynamics simulation of alanine dipeptide.

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.

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.

Reactions in real chemical systems often take place on vastly different time scales, with "fast" reaction channels firing very much more frequently than "slow" ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system's evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized. (C) 2005 American Institute of Physics.

Tau-leaping methods have recently been proposed for the acceleration of discrete stochastic simulation of chemically reacting systems. This paper considers the numerical stability of these methods. The concept of stochastic absolute stability is defined, discussed, and applied to the following leaping methods: the explicit tau, implicit tau, and trapezoidal tau.(C) 2004 American Institute of Physics.

The torque generated by RNA polymerase as it tracks along double-stranded DNA can potentially induce long-range structural deformations integral to mechanisms of biological significance in both prokaryotes and eukaryotes. In this paper, we introduce a dynamic computer model for investigating this phenomenon. Duplex DNA is represented as a chain of hydrodynamic beads interacting through potentials of linearly elastic stretching, bending, and twisting, as well as excluded volume. The chain, linear when relaxed, is looped to form two open but topologically constrained subdomains. This permits the dynamic introduction of torsional stress via a centrally applied torque. We simulate by Brownian dynamics the 100 mus response of a 477-base pair B-DNA template to the localized torque generated by the prokaryotic transcription ensemble. Following a sharp rise at early times, the distributed twist assumes a nearly constant value in both subdomains, and a succession of supercoiling deformations occurs as superhelical stress is increasingly partitioned to writhe. The magnitude of writhe surpasses that of twist before also leveling off when the structure reaches mechanical equilibrium with the torsional load. Superhelicity is simultaneously right handed in one subdomain and left handed in the other, as predicted by the "transcription-induced twin-supercoiled-domain" model [L. F. Liu and J. C. Wang, Proc. Natl. Acad. Sci. U.S.A. 84, 7024 (1987)]. The properties of the chain at the onset of writhing agree well with predictions from theory, and the generated stress is ample for driving secondary structural transitions in physiological DNA. (C) 2004 American Institute of Physics.

In this paper we examine the different formulations of Gillespie's stochastic simulation algorithm (SSA) [D. Gillespie, J. Phys. Chem. 81, 2340 (1977)] with respect to computational efficiency, and propose an optimization to improve the efficiency of the direct method. Based on careful timing studies and an analysis of the time-consuming operations, we conclude that for most practical problems the optimized direct method is the most efficient formulation of SSA. This is in contrast to the widely held belief that Gibson and Bruck's next reaction method [M. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000)] is the best way to implement the SSA for large systems. Our analysis explains the source of the discrepancy. (C) 2004 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.

In this paper we describe how the density matrix renormalization group can be used for quantum chemical calculations for molecules, as an alternative to traditional methods, such as configuration interaction or coupled cluster approaches. As a demonstration of the potential of this approach, we present results for the H2O molecule in a standard gaussian basis. Results for the total energy of the system compare favorably with the best traditional quantum chemical methods. © 1999 American Institute of Physics.