### 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 language | English |
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Pages (from-to) | 5616-5625 |

Number of pages | 10 |

Journal | The Journal of Chemical Physics |

Volume | 102 |

Issue number | 14 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*The Journal of Chemical Physics*,

*102*(14), 5616-5625. https://doi.org/10.1063/1.469293

}

*The Journal of Chemical Physics*, vol. 102, no. 14, pp. 5616-5625. https://doi.org/10.1063/1.469293

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

Research output: Contribution to journal › Article

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 -