A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids

被引:79
作者
Liu, Jian [1 ]
Miller, William H.
机构
[1] Univ Calif Berkeley, Dept Chem, Berkeley, CA 94720 USA
关键词
atom-molecule reactions; hydrogen neutral atoms; hydrogen neutral molecules; initial value problems; potential energy surfaces; reaction kinetics theory; Wigner distribution; TRANSITION-STATE THEORY; THERMAL RATE CONSTANTS; QUANTUM-STATISTICAL-MECHANICS; INITIAL-VALUE REPRESENTATION; BACKWARD SEMICLASSICAL DYNAMICS; VIBRATIONAL-ENERGY RELAXATION; TIME-CORRELATION FUNCTIONS; PARA-HYDROGEN; BOLTZMANN OPERATOR; CONDENSED-PHASE;
D O I
10.1063/1.3202438
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
A simple model is presented for treating local imaginary frequencies that are important in the study of quantum effects in chemical reactions and various dynamical processes in molecular liquids. It significantly extends the range of accuracy of conventional local harmonic approximations (LHAs) used in the linearized semiclassical initial value representation/classical Wigner approximation for real time correlation functions. The key idea is realizing that a local Gaussian approximation (LGA) for the momentum distribution (from the Wigner function involving the Boltzmann operator) can be a good approximation even when a LHA for the potential energy surface fails. The model is applied here to two examples where imaginary frequencies play a significant role: the chemical reaction rate for a linear model of the H+H(2) reaction and an analogous asymmetric barrier-a case where the imaginary frequency of the barrier dominates the process-and for momentum autocorrelation functions in liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). We also generalize the LGA model to the Feynman-Kleinert approximation.
引用
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页数:19
相关论文
共 65 条
[11]   Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters [J].
Frantsuzov, PA ;
Mandelshtam, VA .
JOURNAL OF CHEMICAL PHYSICS, 2004, 121 (19) :9247-9256
[12]   VARIATIONAL APPROACH TO QUANTUM STATISTICAL-MECHANICS OF NONLINEAR-SYSTEMS WITH APPLICATION TO SINE-GORDON CHAINS [J].
GIACHETTI, R ;
TOGNETTI, V .
PHYSICAL REVIEW LETTERS, 1985, 55 (09) :912-915
[13]   The short-time intramolecular dynamics of solutes in liquids .1. An instantaneous-normal-mode theory for friction [J].
Goodyear, G ;
Stratt, RM .
JOURNAL OF CHEMICAL PHYSICS, 1996, 105 (22) :10050-10071
[14]   Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics [J].
Habershon, Scott ;
Braams, Bastiaan J. ;
Manolopoulos, David E. .
JOURNAL OF CHEMICAL PHYSICS, 2007, 127 (17)
[15]   WIGNER PHASE SPACE METHOD - ANALYSIS FOR SEMICLASSICAL APPLICATIONS [J].
HELLER, EJ .
JOURNAL OF CHEMICAL PHYSICS, 1976, 65 (04) :1289-1298
[16]   Quantum time correlation functions and classical coherence [J].
Hernandez, R ;
Voth, GA .
CHEMICAL PHYSICS, 1998, 233 (2-3) :243-255
[17]   A comparative study of imaginary time path integral based methods for quantum dynamics [J].
Hone, TD ;
Rossky, PJ ;
Voth, GA .
JOURNAL OF CHEMICAL PHYSICS, 2006, 124 (15)
[18]   A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium [J].
Hone, TD ;
Voth, GA .
JOURNAL OF CHEMICAL PHYSICS, 2004, 121 (13) :6412-6422
[19]   Instantaneous normal mode approach to liquid state dynamics [J].
Keyes, T .
JOURNAL OF PHYSICAL CHEMISTRY A, 1997, 101 (16) :2921-2930
[20]  
Kubo R., 1991, Statistical Physics II: Nonequilibrium Statistical Mechanics.