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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

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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Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions

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ANNUAL REVIEW OF PHYSICAL CHEMISTRY 2000年 51卷 553-600页

作者： Tannor, DJ Garashchuk, S Weizmann Inst Sci Dept Chem Phys IL-76100 Rehovot Israel Univ Chicago James Franck Inst Dept Chem Chicago IL 60637 USA

Calculation of chemical reaction dynamics is central to theoretical chemistry. The majority of calculations use either classical mechanics, which is computationally inexpensive but misses quantum effects, such as tunneling and interference, or quantum mechanics, which is computationally expensive and often conceptually opaque. An appealing middle ground is the use of semiclassical mechanics. Indeed, since the early 1970s there has been great interest in using semiclassical methods to calculate reaction probabilities. However, despite the elegance of classical S-matrix theory, numerical results on even the simplest reactive systems remained out of reach. Recently, with advances both in correlation function formulations of reactive scattering as well as in semiclassical methods, it has become possible for the first time to calculate reaction probabilities semiclassically. The correlation function methods are contrasted with recent flux-based methods, which, although providing somewhat more compact expressions for the cumulative reactive probability, are less compatible with semiclassical implementation.

关键词： reaction rates cumulative reaction probability S-matrix wavepackets time-correlation functions semiclassical propagation

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NMR study of the rotational dynamics of linear homopolysaccharides in dilute solutions as a function of linkage position and stereochemistry

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CARBOHYDRATE RESEARCH 1999年第1-2期315卷 16-34页

作者： Tylianakis, M Spyros, A Dais, P Taravel, FR Perico, A Univ Crete Dept Chem GR-91409 Iraklion Crete Greece Univ Grenoble 1 CNRS Ctr Rech Macromol Vegetales F-38041 Grenoble France NRC Inst Chim Fis Macromol Sintet & Nat I-16149 Genoa Italy

Variable temperature and magnetic field dependent C-13 NMR relaxation measurements (T-1, T-2, and NOE) were carried out on a series of linear homopolysaccharides: alpha-(1-->3)-D-glucan, beta-(1-->3)-D-glucan in Me2SO-d(6), and alpha-(1-->6)-D-glucan in D2O and Me2SO-d(6) dilute solutions. The relaxation data of the backbone carbons were analyzed quantitatively by using a variety of theoretical unimodal and bimodal time-correlation functions in an attempt to describe the main carbohydrate chain dynamics as a function of linkage position and stereochemistry. Among these, the time-correlation function developed by Dejean, Laupretre, and Monnerie (DLM) offered the best quantitative description of the segmental motion of the carbohydrate chains. The internal rotation of the hydroxymethyl groups about the exocyclic C-5-C-6 bonds superimposed on segmental motion has been described as a diffusion process of restricted amplitude. Comparison of the dynamics of polysaccharides has been extended to include amylose and inulin studied previously. On the basis of the calculated correlation times for segmental motion, the flexibility of the carbohydrate chains decreases from inulin and dextran following the order;inulin > dextran > alpha- (1 --> 3)-D-glucan > beta-(1 --> 3)-D-glucan similar to amylose, whereas the rate and the amplitude of the internal rotation of the hydroxymethyl groups about the exocyclic C-5-C-6 bonds showed that the restriction of the hydroxymethyl internal rotation decreases from inulin to amylose following the order;inulin > alpha-(1 --> 3)-D-glucan similar to beta-(1 --> 3)-D-glucan > amylose. Solvent effects on segmental dynamics and the temperature-frequency superposition of the relaxation data of the three polysaccharides have been discussed as well. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： NMR-relaxation polysaccharides dynamics time-correlation functions

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CALCULATION OF THE MUTUAL DIFFUSION-COEFFICIENT BY EQUILIBRIUM AND NONEQUILIBRIUM MOLECULAR-DYNAMICS

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 1986年第2期7卷 305-317页

作者： ERPENBECK, JJ KINCAID, JM NBS DIV THERMOPHYSGAITHERSBURGMD 20899

A nonequilibrium molecular dynamics method for the calculation of the mutual diffusion coefficient for a mixture of hard spheres is described. The method is applied to a 50-50 mixture of equidiameter particles having a mass ratio of 0.1 for the two species, at a volume of three times close-packing. By extrapolating the results to the limit of vanishing concentration gradient and infinite system size, we obtain a value in statistical agreement with the result obtained using a Green-Kubo molecular dynamics procedure, which is also described. The non-equilibrium calculation yields a mutual diffusion coefficient which decreases slightly with increasing concentration gradient. The Green-Kubo timecorrelation function for mutual diffusion displays a slow decay with time, qualitatively similar to the long-time tail which has been predicted by the hydrodynamic theory of Pomeau.

关键词： hard spheres mixtures molecular dynamics Monte Carlo mutual diffusion time-correlation functions

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MOLECULAR-DYNAMICS CALCULATIONS OF SHEAR VISCOSITY time-correlation functions FOR HARD-SPHERES

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JOURNAL OF STATISTICAL PHYSICS 1981年第3期24卷 455-468页

作者： ERPENBECK, JJ WOOD, WW Los Alamos Scientific Laboratory University of California Los Alamos

The time-correlation function for shear viscosity is evaluated for hard spheres at volumes of 1.6 and 3 times the close-packed volume by a Monte Carlomolecular dynamics technique. At both densities, the kinetic part of the timecorrelation function is consistent, within its rather large statistical uncertainty, with the long-timet −3/2 tail predicted by the mode-coupling theory. However, at the higher density, the time-correlation function is dominated by the cross and potential terms out to 25 mean free times, whereas the mode-coupling theory predicts that these are asymptotically negligible compared to the kinetic part. The total time-correlation function decays roughly asαt −3/2, withα much larger than the mode-coupling value, similar to the recent observations by Evans in his nonequilibrium simulations of argon and methane. The exact value of the exponent is, however, not very precisely determined. By analogy with the case of the velocity autocorrelation function, for which results are also presented at these densities, it is argued that it is quite possible that at high density the asymptotic behavior is not established until times substantially longer than those attainable in the present work. At the lower density, the cross and potential terms are of the same magnitude as the kinetic part, and all are consistent with the mode-coupling predictions within the relatively large statistical uncertainties.

关键词： longtime tails molecular dynamics Monte Carlo Shear viscosity time-correlation functions velocity autocorrelation function

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