Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.     

Quantum reaction rate from higher derivatives of the thermal flux-flux autocorrelation function at time zero

A quantum theory of thermal reaction rates is presented which may be viewed as an extension of the recently developed "quantum instanton" (QI) model [W. H. Miller, Y. Zhao, M. Ceotto, and S. Yang, J. Chem. Phys. 119, 1329 (2003)]. It is based on using higher derivatives of the flux-flux autocorrelation function C(t) (as given by Miller, Schwartz, and Tromp) at t=0 to construct a short time approximation for C(t). Tests of this theory on 1d and collinear reactions, both symmetric and asymmetric, show it to be more accurate than the original QI model, giving rate constants to approximately 5% for a wide range of temperature.     

A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Herman's nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Planck's over 2pi and the error is O(variant Planck's over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Planck's over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.     

Electronic structure and spectrum of UO2 2+ and UO2Cl4 2-

A theoretical study is presented of the electronic spectra of the UO(2) (2+) and UO(2)Cl(4) (2-) ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-A. Malmqvist et al., Chem. Phys. Lett. 357, 230 (2002); B. O. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys. 6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs(2)UO(2)Cl(4) crystals from Denning [Struct. Bonding (Berlin) 79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A 103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A. 105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.     

Steric guided change of electron transfer mechanism in benzene

In fluorescence quenching study via electron transfer (ET), the quenching rate constant (k(q)) values generally decrease with lowering of quencher concentration, since smaller concentration of quencher always leads to a red shift in the donor-acceptor (D-A) distance in ET [M. Tachiya, S. Murata, J. Phys. Chem. 96 (1992) 8441; S. Murata, M. Tachiya, J. Phys. Chem. 100 (1996) 4064; L. Burel, M. Mastafavi, S. Murata, M. Tachiya, J. Phys. Chem. A 103 (1999) 5882]. However, while doing a comparative study with different carbazole (CZ) derivatives-1,4-dicyanobenzene (DCB) systems in benzene (BZ), we observed a deviation from that normal behaviour. It was found that for all of them with lower quencher (DCB) concentration, k(q) values actually increase instead of the expected reduction. Exceptionally, for simple CZ (C12H9N) with decrease in concentration of DCB, k(q) values can even reach the order of energy transfer (10(11) s(-1)). Interestingly, it is not observed when toluene (TL) or xylene (XY) is used as solvent. To explain this unique observation, a sandwich type of molecular structure is predicted, where BZ sliding in between CZ and DCB brings them closer enough, imparting more through bond character to CZ-DCB interaction and hence a higher rate of ET (k(q)) is observed [L. Burel, M. Mastafavi, S. Murata, M. Tachiya, J. Phys. Chem. A. 103 (1999) 5882].     

An analytic model of rotationally inelastic collisions of polar molecules in electric fields

We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the "shape" of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne-OCS((1)Sigma) and Ar-NO((2)Pi) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett. 313, 491 (1999)] demonstrates the model's ability to qualitatively explain the field dependence of all the scattering features observed.     

Exact analytical evaluation of time dependent transmission coefficient from the method of reactive flux for an inverted parabolic barrier

The paper demonstrates an elegant way of combining the normal mode analysis and the method of reactive flux to evaluate the time dependent transmission coefficient for a classical particle coupled to a set of harmonic oscillators, surmounting a one dimensional barrier. The author's analysis reproduces the results of Kohen and Tannor [J. Chem. Phys. 103, 6013 (1995)] and Bao [J. Chem. Phys. 124, 114103 (2006)]. Moreover the use of normal mode analysis has a better physical meaning.     

Forward-backward semiclassical initial value series representation of quantum correlation functions

The forward-backward (FB) approximation as applied to semiclassical initial value representations (SCIVR's) has enabled the practical application of the SCIVR methodology to systems with many degrees of freedom. However, to date a systematic representation of the exact quantum dynamics in terms of the FB-SCIVR has proven elusive. In this paper, we provide a new derivation of a forward-backward phase space SCIVR expression (FBPS-SCIVR) derived previously by Thompson and Makri [Phys. Rev. E 59, R4729 (1999)]. This enables us to represent quantum correlation functions exactly in terms of a series whose leading order term is the FBPS-SCIVR expression. Numerical examples for systems with over 50 degrees of freedom are presented for the spin boson problem. Comparison of the FBPS-SCIVR with the numerically exact results of Wang [J. Chem. Phys. 113, 9948 (2000)] obtained using a multiconfigurational time dependent method shows that the leading order FBPS-SCIVR term already provides an excellent approximation.     

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Is a "homogeneous" description of dynamic heterogeneities possible?

We study the simplest model of dynamic heterogeneities in glass forming liquids: one-spin facilitated kinetic Ising model introduced by Fredrickson and Andersen [G. H. Fredrickson and H. C. Andersen, Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 83, 5822 (1985)]. We show that the low-temperature, long-time behavior of the density autocorrelation function predicted by a scaling approach can be obtained from a self-consistent mode-couplinglike approximation.     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.     

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.     

Soft core thermodynamics from self-consistent hard core fluids

In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA)-an accurate liquid state theory that has been restricted so far to hard core systems-to arbitrary soft core systems we study a combination of SCOZA with a recently developed perturbation theory. The latter was constructed by Ben-Amotz and Stell [J. Phys. Chem. B 108, 6877 (2004)] as a reformulation of the Weeks-Chandler-Andersen [J. Chem. Phys. 54, 5237 (1971)] perturbation theory directly in terms of an arbitrary hard sphere reference system. We investigate the accuracy of the combined approach for the Lennard-Jones fluid in comparison with simulation data and pure perturbation theory predictions and determine the dependence of the thermodynamic properties and the phase behavior on the choice of the effective hard core diameter of the reference system.     

PEACH 4 with ABINIT-MP: a general platform for classical and quantum simulations of biological molecules

A program package for molecular simulations of biological molecules was developed. The package, "PEACH version 4 with ABINIT-MP version 20021029," was constructed by incorporating ABINIT-MP, a program for the fragment molecular orbital (FMO) method [Chem.Phys. Lett. 313 (1999) 701], into PEACH, a program package for classical molecular dynamics simulations (MD). A few capabilities of the package were demonstrated. First, high parallel efficiency of FMO was demonstrated in a single point calculation of a protein. Second,FMO-MD simulations [Chem. Phys. Lett. 372 (2003) 342] of a peptide were performed with and without explicit solvent, and the simulations showed the influence of the solvent on the electronic state of the peptide.     

Fixed node diffusion Monte Carlo using a genetic algorithm: a study of the CO-(4)He(N) complex, N = 1…10

The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO-(4)He(N) complexes with N≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped (4)He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO-(4)He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N～ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (～0.7 cm(-1)) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.     

Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems

We address the problem of eliminating fast reaction kinetics in stochastic biochemical systems by employing a quasiequilibrium approximation. We build on two previous methodologies developed by [Haseltine and Rawlings, J. Chem. Phys. 117, 6959 (2002)] and by [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)]. By following Haseltine and Rawlings, we use the numbers of occurrences of the underlying reactions to characterize the state of a biochemical system. We consider systems that can be effectively partitioned into two distinct subsystems, one that comprises "slow" reactions and one that comprises "fast" reactions. We show that when the probabilities of occurrence of the slow reactions depend at most linearly on the states of the fast reactions, we can effectively eliminate the fast reactions by modifying the probabilities of occurrence of the slow reactions. This modification requires computation of the mean states of the fast reactions, conditioned on the states of the slow reactions. By assuming that within consecutive occurrences of slow reactions, the fast reactions rapidly reach equilibrium, we show that the conditional state means of the fast reactions satisfy a system of at most quadratic equations, subject to linear inequality constraints. We present three examples which allow analytical calculations that clearly illustrate the mathematical steps underlying the proposed approximation and demonstrate the accuracy and effectiveness of our method.     

Space-time contours to treat the interaction between an intense electric field and a molecular system

A few years ago, we developed an approach to treat molecular systems exposed to an external, intense, time-dependent field (J. Phys. Chem. A 2003, 107, 4724; J. Chem. Phys. 2003, 119, 6998). Within this study, we encountered two novel concepts: the dressed (namely, field affected) time-dependent nonadiabatic coupling term and the space-time contours. In the present article, we analyze the newly introduced nonadiabatic coupling term and discuss its importance for dynamical studies. We also refer to the just mentioned space-time contour and present the more efficient contour for realistic situations. The scope of the above-mentioned articles is extended with the aim of defining quasi-adiabatic states for such situations. Strictly speaking, molecular systems exposed to intense, fast oscillating fields are not expected to form adiabatic states. Still we consider such a situation and end up with three possibilities for quasi-adiabatical time-dependent states eventually to be used within the Born-Oppenheimer approximation.