TITLE

Quantal cumulant dynamics: General theory

AUTHOR(S)
Shigeta, Yasuteru; Miyachi, Hideaki; Hirao, Kimihiko
PUB. DATE
December 2006
SOURCE
Journal of Chemical Physics;12/28/2006, Vol. 125 Issue 24, p244102
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The authors have derived coupled equations of motion of cumulants that consist of a symmetric-ordered product of the position and momentum fluctuation operators in one dimension. The key point is the utilization of a position shift operator acting on a potential operator, where the expectation value of the shift operator is evaluated using the cumulant expansion technique. In particular, the equations of motion of the second-order cumulant and the expectation values of the position and momentum operators are given. The resultant equations are expressed by those variables and a quantal potential that consists of an exponential function of the differential operators and the original potential. This procedure enables us to perform quantal (semiclassical) dynamics in one dimension. In contrast to a second-order quantized Hamilton dynamics by Prezhdo and Pereverzev which conserves the total energy only with an odd-order Taylor expansion of the potential [J. Chem. Phys. 116, 4450 (2002); 117, 2995 (2002)], the present quantal cumulant dynamics method exactly conserves the energy, even if a second-order approximation of the cumulants is adopted, because the present scheme does not truncate the given potential. The authors propose three schemes, (i) a truncation, (ii) a summation of derivatives, and (iii) a convolution method, for evaluating the quantal potentials for several types of potentials. The numerical results show that although the truncation method preserves the energy to some degree, the trajectory obtained gradually deviates from that of the summation scheme after 2000 steps. The phase space structure obtained by the truncation scheme is also different from that of the summation scheme in a strongly anharmonic region.
ACCESSION #
23761800

 

Related Articles

  • Theory of thermal unimolecular reactions at high pressures. II. Analysis of experimental results. Cobos, C. J.; Troe, J. // Journal of Chemical Physics;8/1/1985, Vol. 83 Issue 3, p1010 

    The simplified version, proposed in Part I, of the statistical adiabatic channel model for thermal unimolecular bond fission reactions and the reverse radical association reactions is applied to 26 experimental systems in which limiting high pressure rate coefficients have been determined. From...

  • Ring polymer molecular dynamics with surface hopping. Shushkov, Philip; Li, Richard; Tully, John C. // Journal of Chemical Physics;12/14/2012, Vol. 137 Issue 22, p22A549 

    We propose a ring polymer molecular dynamics method for the calculation of chemical rate constants that incorporates nonadiabatic effects by the surface-hopping approach. Two approximate ring polymer electronic Hamiltonians are formulated and the time-dependent Schrodinger equation for the...

  • Separation of classical equations of motion based on symmetry. Banerjee, Ajit; Adams, Noah P. // Journal of Chemical Physics;11/1/1989, Vol. 91 Issue 9, p5444 

    We show that an invariance of a system of N particles simplifies the solution of the classical equations of motion.A transformation can be constructed in a straightforward manner to yield a set of active and redundant coordinates in which Hamilton’s equations are separable. That is, the...

  • Molecular potential energy surfaces by interpolation. Ischtwan, Josef; Collins, Michael A. // Journal of Chemical Physics;6/1/1994, Vol. 100 Issue 11, p8080 

    A moving interpolation technique which provides an accurate representation of potential energy surfaces for polyatomic molecules is presented. The method uses the ab initio energy, energy gradient, and second derivatives calculated at dynamically important configurations. The interpolant of the...

  • A theoretical study of the reaction of Ti[sup +] with ethane. Moc, Jerzy; Fedorov, Dmitri G.; Gordon, Mark S. // Journal of Chemical Physics;6/15/2000, Vol. 112 Issue 23 

    The doublet and quartet potential energy surfaces for the Ti[sup +]+C[sub 2]H[sub 6]→TiC[sub 2]H[sub 4][sup +]+H[sub 2] and Ti[sup +]+C[sub 2]H[sub 6]→TiCH[sub 2][sup +]+CH[sub 4] reactions are studied using density functional theory (DFT) with the B3LYP functional and ab initio...

  • A new time-dependent approach to the direct calculation of reaction rates. Manthe, Uwe // Journal of Chemical Physics;6/15/1995, Vol. 102 Issue 23, p9205 

    A wave packet dynamical approach to the direct calculation of the rate constant of a chemical reaction is presented. Based on the position-flux correlation function of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889 (1983)] a reaction rate operator is introduced, which can be viewed as the...

  • Analysis of certain factors in the direct dynamics method: Variational rate constant of the NH3+OH→NH2+H2O reaction. Espinosa-García, J.; Corchado, J. C. // Journal of Chemical Physics;11/15/1994, Vol. 101 Issue 10, p8700 

    The minimum energy path for the NH3+OH→NH2+H2O reaction was traced and the coupling between the reaction coordinate and normal modes was analyzed along it. Following the ‘‘direct dynamics’’ methodology, the rate constants were calculated for the temperature range...

  • Accurate ab initio potential energy surface, thermochemistry, and dynamics of the Cl(2P, 2P3/2) + CH4 → HCl + CH3 and H + CH3Cl reactions. Czakó, Gábor; Bowman, Joel M. // Journal of Chemical Physics;1/28/2012, Vol. 136 Issue 4, p044307 

    We report a high-quality, ab initio, full-dimensional global potential energy surface (PES) for the Cl(2P, 2P3/2) + CH4 reaction, which describes both the abstraction (HCl + CH3) and substitution (H + CH3Cl) channels. The analytical PES is a least-squares fit, using a basis of permutationally...

  • Molecular dynamics simulations of the effects of truncation of the Taylor expansion of the potential energy on the thermodynamic properties of a crystal. Lacks, Daniel J.; Shukla, Ramesh C. // Journal of Chemical Physics;9/8/1996, Vol. 105 Issue 10, p4185 

    Molecular dynamics simulations are carried out on a Lennard-Jones crystal, for the potential energy surfaces generated from the full Hamiltonian and the Taylor expansion of the potential energy truncated at the quartic term, to determine the accuracy of the quartic truncation with regard to the...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics