### Abstract

For accurate description of vibration/rotation eigenstates of molecules, and for discussion of reactions and relaxation processes, simple independent-mode pictures are generally inadequate. Mean-field methods, in which each mode acts subject to a mean potential (static or dynamic) that is just the exact potential averaged over all other modes of the system, are attractive for treating such problems for several reasons: they are conceptually simple, numerically tractable, quantitatively quite accurate, and generally applicable to a wide variety of molecular species, energies, and coupling conditions. For these reasons, such mean-field, or self-consistent-field, techniques have been applied to molecular problems quite extensively within the last decade. We discuss several aspects of recent and current work on mean-field applications to molecular problems. In the class of static mean-field, or self-consistent-field, methods such situations include inversion of vibration/ rotation spectra to obtain potential energy surfaces, distorted-wave Born approximation work on vibrational predissociation lifetimes of long-lived van der Waals complexes, and an extension of the Slater theory for unimolecular decay rates in the weak-coupling regime. Applications of time-dependent SCF, or TDSCF, include a linearized approximation for investigation of long-time processes and study of the Fourier representation to derive random-phase approximations for direct calculation both of excitation energies and of instabilities and lifetimes. Several intriguing problems remain in the general area of mean-field methods for molecular systems: these include optimal choice of coordinate systems, selection of initial state in dynamical problems, and methods for tractable extension of mean-field approximations.

Original language | English |
---|---|

Pages (from-to) | 3252-3260 |

Number of pages | 9 |

Journal | Journal of Physical Chemistry |

Volume | 92 |

Issue number | 11 |

Publication status | Published - 1988 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*92*(11), 3252-3260.

**Mean-field models for molecular states and dynamics : New developments.** / Gerber, R. B.; Ratner, Mark A.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 92, no. 11, pp. 3252-3260.

}

TY - JOUR

T1 - Mean-field models for molecular states and dynamics

T2 - New developments

AU - Gerber, R. B.

AU - Ratner, Mark A

PY - 1988

Y1 - 1988

N2 - For accurate description of vibration/rotation eigenstates of molecules, and for discussion of reactions and relaxation processes, simple independent-mode pictures are generally inadequate. Mean-field methods, in which each mode acts subject to a mean potential (static or dynamic) that is just the exact potential averaged over all other modes of the system, are attractive for treating such problems for several reasons: they are conceptually simple, numerically tractable, quantitatively quite accurate, and generally applicable to a wide variety of molecular species, energies, and coupling conditions. For these reasons, such mean-field, or self-consistent-field, techniques have been applied to molecular problems quite extensively within the last decade. We discuss several aspects of recent and current work on mean-field applications to molecular problems. In the class of static mean-field, or self-consistent-field, methods such situations include inversion of vibration/ rotation spectra to obtain potential energy surfaces, distorted-wave Born approximation work on vibrational predissociation lifetimes of long-lived van der Waals complexes, and an extension of the Slater theory for unimolecular decay rates in the weak-coupling regime. Applications of time-dependent SCF, or TDSCF, include a linearized approximation for investigation of long-time processes and study of the Fourier representation to derive random-phase approximations for direct calculation both of excitation energies and of instabilities and lifetimes. Several intriguing problems remain in the general area of mean-field methods for molecular systems: these include optimal choice of coordinate systems, selection of initial state in dynamical problems, and methods for tractable extension of mean-field approximations.

AB - For accurate description of vibration/rotation eigenstates of molecules, and for discussion of reactions and relaxation processes, simple independent-mode pictures are generally inadequate. Mean-field methods, in which each mode acts subject to a mean potential (static or dynamic) that is just the exact potential averaged over all other modes of the system, are attractive for treating such problems for several reasons: they are conceptually simple, numerically tractable, quantitatively quite accurate, and generally applicable to a wide variety of molecular species, energies, and coupling conditions. For these reasons, such mean-field, or self-consistent-field, techniques have been applied to molecular problems quite extensively within the last decade. We discuss several aspects of recent and current work on mean-field applications to molecular problems. In the class of static mean-field, or self-consistent-field, methods such situations include inversion of vibration/ rotation spectra to obtain potential energy surfaces, distorted-wave Born approximation work on vibrational predissociation lifetimes of long-lived van der Waals complexes, and an extension of the Slater theory for unimolecular decay rates in the weak-coupling regime. Applications of time-dependent SCF, or TDSCF, include a linearized approximation for investigation of long-time processes and study of the Fourier representation to derive random-phase approximations for direct calculation both of excitation energies and of instabilities and lifetimes. Several intriguing problems remain in the general area of mean-field methods for molecular systems: these include optimal choice of coordinate systems, selection of initial state in dynamical problems, and methods for tractable extension of mean-field approximations.

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UR - http://www.scopus.com/inward/citedby.url?scp=0000566869&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000566869

VL - 92

SP - 3252

EP - 3260

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 11

ER -