Time-dependent discrete variable representations for quantum wave packet propagation

Eun Ji Sim, Nancy Makri

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

We present an efficient method for exact wave function propagation with several degrees of freedom based on time-dependent discrete variable representations (TD-DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD-DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD-DVR grids offer optimal representations in time-dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time-dependent Hamiltonians. TD-DVR grids based on the time-dependent self-consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.

Original languageEnglish
Pages (from-to)5616-5625
Number of pages10
JournalThe Journal of Chemical Physics
Volume102
Issue number14
DOIs
Publication statusPublished - 1995 Jan 1

Fingerprint

Hamiltonians
Wave packets
wave packets
Wave functions
propagation
grids
Degrees of freedom (mechanics)
degrees of freedom
self consistent fields
wave functions

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

@article{f2634fffea0844079827f87190e3636a,
title = "Time-dependent discrete variable representations for quantum wave packet propagation",
abstract = "We present an efficient method for exact wave function propagation with several degrees of freedom based on time-dependent discrete variable representations (TD-DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD-DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD-DVR grids offer optimal representations in time-dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time-dependent Hamiltonians. TD-DVR grids based on the time-dependent self-consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.",
author = "Sim, {Eun Ji} and Nancy Makri",
year = "1995",
month = "1",
day = "1",
doi = "10.1063/1.469293",
language = "English",
volume = "102",
pages = "5616--5625",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "14",

}

Time-dependent discrete variable representations for quantum wave packet propagation. / Sim, Eun Ji; Makri, Nancy.

In: The Journal of Chemical Physics, Vol. 102, No. 14, 01.01.1995, p. 5616-5625.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Time-dependent discrete variable representations for quantum wave packet propagation

AU - Sim, Eun Ji

AU - Makri, Nancy

PY - 1995/1/1

Y1 - 1995/1/1

N2 - We present an efficient method for exact wave function propagation with several degrees of freedom based on time-dependent discrete variable representations (TD-DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD-DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD-DVR grids offer optimal representations in time-dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time-dependent Hamiltonians. TD-DVR grids based on the time-dependent self-consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.

AB - We present an efficient method for exact wave function propagation with several degrees of freedom based on time-dependent discrete variable representations (TD-DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD-DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD-DVR grids offer optimal representations in time-dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time-dependent Hamiltonians. TD-DVR grids based on the time-dependent self-consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.

UR - http://www.scopus.com/inward/record.url?scp=0012072566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012072566&partnerID=8YFLogxK

U2 - 10.1063/1.469293

DO - 10.1063/1.469293

M3 - Article

AN - SCOPUS:0012072566

VL - 102

SP - 5616

EP - 5625

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

ER -