Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels
- 11 April 2003
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 118 (16), 7174-7182
- https://doi.org/10.1063/1.1562158
Abstract
An application of the initial value representation (IVR) of semiclassical (SC) theory to approximate the quantum mechanical time evolution operator, exp [−iĤt/ℏ], requires an integral over the phase space of initial conditions of classical trajectories. The integrand of this integral is complex, i.e., has a phase, from which quantum coherence (in fact, all quantum) effects arise, but which also makes SC-IVR calculations more difficult than ordinary classical molecular dynamics simulations (the semiclassical version of the “sign problem”). A number of approaches have been devised to ameliorate the sign problem, and here we show how a time averaging procedure—the integrand of the phase space integral is time-averaged over the classical trajectory originating from each initial condition—can be profitably used in this regard, particularly so for the calculation of spectral densities (from which vibrational energy levels can be identified). This time averaging procedure is shown to greatly reduce the number of initial conditions (i.e., the number of classical trajectories) that are needed to converge IVR phase space averages. In some cases useful results can be obtained with only one classical trajectory. Calculations are carried out for vibrational energy levels of H 2 and H 2 O to illustrate the overall procedure.Keywords
This publication has 22 references indexed in Scilit:
- The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics SimulationsThe Journal of Physical Chemistry A, 2001
- Finite Temperature Correlation Functions via Forward−Backward Semiclassical DynamicsThe Journal of Physical Chemistry A, 2001
- Semiclassical Calculation of Chemical Reaction Dynamics via Wavepacket Correlation FunctionsAnnual Review of Physical Chemistry, 2000
- Semiclassical initial value representation for rotational degrees of freedom: The tunneling dynamics of HCl dimerThe Journal of Chemical Physics, 1998
- Spiers Memorial Lecture Quantum and semiclassical theory of chemical reaction ratesFaraday Discussions, 1998
- Semiclassical dynamics in up to 15 coupled vibrational degrees of freedomThe Journal of Chemical Physics, 1997
- Semiclassical dynamics of chaotic motion: Unexpected long-time accuracyPhysical Review Letters, 1991
- A semiclasical justification for the use of non-spreading wavepackets in dynamics calculationsChemical Physics, 1984
- The semiclassical way to molecular spectroscopyAccounts of Chemical Research, 1981
- Time-dependent approach to semiclassical dynamicsThe Journal of Chemical Physics, 1975