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Evaluation of the quantum time-correlation functions employing the Hamilton-Jacobi dynamics framework

THEORETICAL CHEMISTRY ACCOUNTS 2019年第1期138卷 1-16页

作者： Ekanayake, Niranji Thilini Garashchuk, Sophya Univ South Carolina Dept Chem & Biochem Columbia SC 29208 USA

The quantum Hamilton-Jacobi equation (QHJE) is formally equivalent to the time-dependent Schrodinger equation, and the solutions to the QHJE can be easily interpreted in terms of trajectories providing a link between classical and quantum mechanics. The trajectory-based approaches to quantum molecular dynamics are, generally, appealing because they circumvent exponential scaling associated with exact quantum methods with the system size, and because, unlike classical molecular dynamics, such methods incorporate dominant quantum effects due to delocalization of wavefunctions describing the nuclei. We explore the utility of the QHJE framework for calculations of the time-correlation functions (TCFs) involving quantum evolution defined by the Boltzmann density operator and by the Hamiltonian time-evolution operator. The implementation is based on solutions to the imaginary-time counterpart to the QHJE, which yield approximations to the ground state wavefunction. The resulting nodeless wavefunction is used to generate a basis in coordinate space, which is efficient for evaluation of the low-lying excited states and of the quantum TCFs, including the Kubo-transformed TCFs, at low temperature. The QHJE/basis approach is illustrated on several model systems in and out of thermal equilibrium, i.e., the dimer and bound anharmonic potentials. If a system exhibits large amplitude motion, e.g., in case of the nonequilibrium dynamics, then the real-time trajectory propagation provides an alternative to the basis representation, as demonstrated on a model describing the inversion mode of the ammonia molecule and ion.

关键词： Quantum dynamics time-correlation functions Excited states Trajectory dynamics

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Generalized Langevin Equation Theory of Thermal Conduction across Material Interfaces

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PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS 2021年第9期258卷 2000454-2000454页

作者： Zeng, Yi Avritte, Jalaan T. Dong, Jianjun Auburn Univ Dept Mech Engn Auburn AL 36849 USA Auburn Univ Dept Phys Auburn AL 36849 USA

The thermal conduction across material interfaces is studied using a generalized Langevin equation (gLE) theory. A general statistical formula of thermal interfacial conductance (TIC) is derived at the slow fluctuation limit in terms of the time auto-correlation functions of interfacial heat current (QACF) < q(t) q(0)> and the heat capacity C-V. At the bulk limit of C-V -> 8, this general TIC formula reduces to the previously proposed Green-Kubo type of TIC formula. Beyond the bulk limit, the TIC of a material with finite CV can be calculated using the first and second moments of the interfacial QACF. These statistical TIC formulas provide the basis to adopt equilibrium molecular dynamics simulations to calculate the TIC of real material interfaces beyond the bulk limit, including the interfaces at the nanoscale. The TIC of two types of non-Markov model interfaces with analytic forms of QACF is predicted by the reported gLE theory, and the results of these non-Markov interfaces are compared with those of a Markov interface.

关键词： Green-Kubo formulas Langevin equations molecular dynamics simulations thermal conduction thermal interfacial conductance time-correlation functions

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Photoinduced quantum dynamics in molecules and at adsorbates

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MOLECULAR PHYSICS 2010年第21-23期108卷 3223-3234页

作者： Salam, A. Micha, D. A. Wake Forest Univ Dept Chem Winston Salem NC 27109 USA Univ Florida Dept Chem Quantum Theory Project Gainesville FL 32611 USA Univ Florida Dept Phys Quantum Theory Project Gainesville FL 32611 USA

A problem of long-standing scientific interest is the interaction of electromagnetic fields with atomic and molecular species both in isolation and within a medium, and the ensuing spectroscopy and chemical dynamics. This paper presents an overview of theoretical and computational methods, both fully quantum mechanical or semi-classical in nature, developed over many years at the Quantum Theory Project of the University of Florida for dealing with photo-induced processes such as molecular dissociation or desorption of adsorbates from metal surfaces. In the former case, photoinduced transition rates are computed from transition operators via eikonal functions, or more generally with a time correlation function in which the radiation and material degrees of freedom are treated separately. Application to the photodissociation of methyl iodide is outlined. For molecular photodesorption, the system is partitioned into two self-consistently coupled regions, and a density matrix formalism in Liouville space is employed to study its time evolution in the general case when the substrate is also photoexcited. Pulsed laser irradiation of the substrate, described by optical Bloch and kinetic rate equations, results in electronic to vibrational energy transfer from metal to adsorbate and subsequent photodesorption. The theory has been applied to the CO/Cu(001) system to calculate desoprtion yields. Also treated is the optical control of yields via chirping effects, which has been predicted to both suppress or enhance the amount of CO leaving the surface.

关键词： quantum dynamics photoinduced rates time-correlation functions density matrix photodissociation photodesorption

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Interference and quantization in semiclassical response functions

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JOURNAL OF CHEMICAL PHYSICS 2008年第12期128卷 124106-1-124106-1页

作者： Gruenbaum, Scott M. Loring, Roger F. Cornell Univ Baker Lab Dept Chem & Chem Biol Ithaca NY 14853 USA

Application of the Herman-Kluk semiclassical propagator to the calculation of spectroscopic response functions for anharmonic oscillators has demonstrated the quantitative accuracy of these approximate dynamics. In this approach, spectroscopic response functions are expressed as multiple phase-space integrals over pairs of classical trajectories and their associated stability matrices. Here we analyze the Herman-Kluk semiclassical approximation to a linear response function and determine the origin of the capacity of this method to reproduce quantum effects in a response function from classical dynamical information. Our analysis identifies those classical trajectories that contribute most significantly to the response function on different time scales. This finding motivates a procedure for computing the linear response function in which the interference between pairs of classical trajectories is treated approximately, resulting in an integral over a single average trajectory, as in a purely classical calculation. (c) 2008 American Institute of Physics.

关键词： INITIAL-VALUE REPRESENTATION 2-DIMENSIONAL INFRARED-SPECTROSCOPY time-correlation functions NONLINEAR RESPONSE COHERENT STATES VIBRATIONAL SPECTROSCOPY ANHARMONIC VIBRATION MORSE OSCILLATOR RAMAN RESPONSE PHASE-SPACE

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Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water

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JOURNAL OF CHEMICAL PHYSICS 2008年第7期128卷 74506-1-74506-11页

作者： Fanourgakis, George S. Xantheas, Sotiris S. Pacific NW Natl Lab Chem & Mat Sci Div Richland WA 99352 USA

We present a new parametrization of the flexible, polarizable Thole-type model for water [J. Chem. Phys. 116, 5115 (2002);J. Phys. Chem. A 110, 4100 (2006)], with emphasis in describing the vibrational spectra of both water clusters and liquid water. The new model is able to produce results of similar quality with the previous versions for the structures and energetics of water clusters as well as structural and thermodynamic properties of liquid water evaluated with classical and converged quantum statistical mechanical atomistic simulations. At the same time it yields accurate redshifts for the OH vibrational stretches of both water clusters and liquid water. (C) 2008 American Institute of Physics.

关键词： CENTROID MOLECULAR-DYNAMICS time-correlation functions AB-INITIO CALCULATIONS BINDING-ENERGIES INFRARED-SPECTRA 1ST PRINCIPLES EMPIRICAL POTENTIALS COMPUTER-SIMULATION ORDER CORRECTION PATH-INTEGRALS

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Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices

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JOURNAL OF CHEMICAL PHYSICS 2008年第24期128卷 244108-1-244108-1页

作者： Ma, Z. Coker, D. F. Boston Univ Dept Chem Boston MA 02215 USA

This paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantum-classical description. This approach is applied to studying vibrational pure dephasing of ground state molecular iodine in a rare gas matrix. The Feynman-Kleinert optimized harmonic approximation for the full system density operator is used to sample initial conditions for the bath degrees of freedom. This extremely efficient approach is compared to alternative initial condition sampling techniques at low temperatures where classical initial condition sampling yields dephasing rates that are nearly an order of magnitude too slow compared to quantum initial condition sampling and experimental results. (C) 2008 American Institute of Physics.

关键词： PATH CENTROID DENSITY time-correlation functions CLASSICAL TRAJECTORY APPROACH RELAXATION RATE CONSTANTS MOLECULAR-DYNAMICS IMPURITY MOLECULES ENERGY RELAXATION CONDENSED-PHASE ANHARMONIC MOLECULES SEMICLASSICAL THEORY

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Statistical-mechanical theory of ultrasonic absorption in molecular liquids

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JOURNAL OF CHEMICAL PHYSICS 2007年第4期126卷 44504-1-44504-页

作者： Kobryn, Alexander E. Hirata, Fumio Inst Mol Sci Dept Theoret Study Okazaki Aichi 4448585 Japan Grad Univ Adv Studies SOKENDAI Dept Funct Mol Sci Okazaki Aichi 4448585 Japan

We present results of the theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of a microscopical, i.e., statistical-mechanical, framework capable of explaining the long living puzzle of excess ultrasonic absorption in liquids. Typically, an ultrasonic wave in a liquid can be generated by applying a periodically alternating external pressure with an angular frequency that corresponds to the ultrasound. If the perturbation introduced by such a process is weak, its statistical-mechanical treatment can be done with the use of a linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency-dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions, we refer to the site-site memory equations in the mode-coupling approximation for first-order memory kernels, while equilibrium properties such as site-site static structure factors, and direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM, or one of its generalizations. All of the formalism is phrased in a general manner, hence the results obtained are expected to work for arbitrary types of molecular liquids including simple, ionic, polar, and nonpolar liquids. (c) 2007 American Institute of Physics.

关键词： INTERACTION-SITE-MODEL time-correlation functions EXTENDED RISM EQUATION DILUTED WATER SOLUTIONS GLOBULAR-PROTEINS DIFFUSION-COEFFICIENT COUPLING THEORY COLLECTIVEEXCITATIONS IRREVERSIBLE PROCESSES VOLUMETRIC PROPERTIES

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Chemical reaction rates using the semiclassical Van Vleck initial value representation

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JOURNAL OF CHEMICAL PHYSICS 2007年第9期126卷 94104-1-94104-页

作者： Venkataraman, Charulatha Miller, William H. Univ Calif Berkeley Dept Chem Berkeley CA 94720 USA Univ Calif Berkeley Kenneth S Pitzer Ctr Theoret Chem Berkeley CA 94720 USA Univ Calif Berkeley Div Chem Sci Lawrence Berkeley Natl Lab Berkeley CA 94720 USA

A semiclassical initial value representation formulation using the Van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] propagator has been used to calculate the flux correlation function and thereby reaction rate constants. This Van Vleck formulation of the flux-flux correlation function is computationally as simple as the classical Wigner [Trans. Faraday Soc. 34, 29 (1938)] model. However, unlike the latter, it has the ability to capture quantum interference/coherence effects. Classical trajectories are evolved starting from the dividing surface that separates reactants and products, and are evolved negatively in time. This formulation has been tested on model problems ranging from the Eckart barrier, double well to the collinear H+H-2. (c) American Institute of Physics.

关键词： THERMAL RATE CONSTANTS TRANSITION-STATE THEORY QUANTUM INSTANTONAPPROXIMATION time-correlation functions DISCRETE VARIABLE REPRESENTATION STATISTICAL-MECHANICALTHEORY COMPLEX MOLECULAR-SYSTEMS POTENTIAL-ENERGY SURFACE MONTE-CARLO SIMULATIONS PATH INTEGRALMETHODS

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Inclusion of inversion symmetry in centroid molecular dynamics: A possible avenue to recover quantum coherence

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JOURNAL OF CHEMICAL PHYSICS 2006年第16期125卷 64103-1-64103-页

作者： Huh, Yoonjung Roy, Pierre-Nicholas Univ Alberta Dept Chem Edmonton AB T6G 2G2 Canada

Inversion symmetry is included in the operator formulation of the centroid molecular dynamics (CMD). This work involves the development of a symmetry-adapted CMD (SA-CMD), here particularly for symmetrization and antisymmetrization projections. A symmetry-adapted quasidensity operator, as defined by Blinov and Roy [J. Chem. Phys. 115, 7822 (2001)], is employed to obtain the centroid representation of quantum mechanical operators. Numerical examples are given for a single particle confined to one-dimensional symmetric quartic and symmetric double-well potentials. Two SA-CMD simulations are performed separately for both projections, and centroid position autocorrelation functions are obtained. For each projection, the quality of the approximation as well as the accuracy are similar to those of regular CMD. It is shown that individual trajectories from two separate SA-CMD simulations can be properly combined to recover trajectories for Boltzmann statistics. Position autocorrelation functions are compared to the exact quantum mechanical ones. This explicit account of inversion symmetry provides a qualitative improvement on the conventional CMD approach and allows the recovery of some quantum coherence.

关键词： LIQUID PARA-HYDROGEN FERMI-DIRAC STATISTICS time-correlation functions REACTION-RATE CONSTANTS BOSE-EINSTEIN TRANSPORT-PROPERTIES NONLINEAR OPERATORS FORMULATION SIMULATIONS FORMALISM

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Semiclassical calculation of nonadiabatic thermal rate constants: Application to condensed phase reactions

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JOURNAL OF CHEMICAL PHYSICS 2006年第11期124卷 114508,1-8页

作者： Zhao, Y Li, X Zheng, ZL Liang, WZ Univ Sci & Technol China Hefei Natl Lab Phys Sci Microscale Hefei 230026 Peoples R China Univ Sci & Technol China Dept Phys Chem Hefei 230026 Peoples R China

The nonadiabatic transition state theory proposed recently by Zhao [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932);Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.

关键词： TRANSITION-STATE THEORY ELECTRON-TRANSFER REACTIONS CURVE CROSSINGPROBLEMS QUANTUM INSTANTON APPROXIMATION time-correlation functions PATH-INTEGRAL CALCULATION MONTE-CARLO SIMULATIONS UNIFORM RATE EXPRESSION UNIMOLECULAR REACTIONS MOLECULAR-DYNAMICS

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