### Abstract

We study a radiationless transition in a polyatomic molecule when the electronic energy of an excited electronic state is transferred to the vibrational degrees of freedom of the nuclei, and when some nuclear coordinates change abruptly. This jump between the donor energy surface and the acceptor one gives the initial conditions for the subsequent dynamics on the acceptor surface, and the partition of energy between competing accepting modes. In the Wigner representation, the physical problem of recognizing the accepting modes for a radiationless vibronic relaxation reduces to the mathematical problem of finding the maximum of a function of many variables under a constraint. The function is the initial Wigner function of the nuclei and the constraint is energy conservation. In a harmonic approximation for the potential surfaces, the problem is equivalent to finding the distance from a given point to a multidimensional ellipsoid. This geometrical problem is solved in closed form. For nonharmonic potentials, the optimization problem is solved perturbatively.

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

Pages (from-to) | 1769-1789 |

Number of pages | 21 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 7 |

DOIs | |

Publication status | Published - 22 Feb 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*35*(7), 1769-1789. https://doi.org/10.1088/0305-4470/35/7/321

**Most probable path in phase space for a radiationless transition in a molecule.** / Sergeev, Alexey V.; Segev, Bilha.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 35, no. 7, pp. 1769-1789. https://doi.org/10.1088/0305-4470/35/7/321

}

TY - JOUR

T1 - Most probable path in phase space for a radiationless transition in a molecule

AU - Sergeev, Alexey V.

AU - Segev, Bilha

PY - 2002/2/22

Y1 - 2002/2/22

N2 - We study a radiationless transition in a polyatomic molecule when the electronic energy of an excited electronic state is transferred to the vibrational degrees of freedom of the nuclei, and when some nuclear coordinates change abruptly. This jump between the donor energy surface and the acceptor one gives the initial conditions for the subsequent dynamics on the acceptor surface, and the partition of energy between competing accepting modes. In the Wigner representation, the physical problem of recognizing the accepting modes for a radiationless vibronic relaxation reduces to the mathematical problem of finding the maximum of a function of many variables under a constraint. The function is the initial Wigner function of the nuclei and the constraint is energy conservation. In a harmonic approximation for the potential surfaces, the problem is equivalent to finding the distance from a given point to a multidimensional ellipsoid. This geometrical problem is solved in closed form. For nonharmonic potentials, the optimization problem is solved perturbatively.

AB - We study a radiationless transition in a polyatomic molecule when the electronic energy of an excited electronic state is transferred to the vibrational degrees of freedom of the nuclei, and when some nuclear coordinates change abruptly. This jump between the donor energy surface and the acceptor one gives the initial conditions for the subsequent dynamics on the acceptor surface, and the partition of energy between competing accepting modes. In the Wigner representation, the physical problem of recognizing the accepting modes for a radiationless vibronic relaxation reduces to the mathematical problem of finding the maximum of a function of many variables under a constraint. The function is the initial Wigner function of the nuclei and the constraint is energy conservation. In a harmonic approximation for the potential surfaces, the problem is equivalent to finding the distance from a given point to a multidimensional ellipsoid. This geometrical problem is solved in closed form. For nonharmonic potentials, the optimization problem is solved perturbatively.

UR - http://www.scopus.com/inward/record.url?scp=0042383421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042383421&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/7/321

DO - 10.1088/0305-4470/35/7/321

M3 - Article

AN - SCOPUS:0042383421

VL - 35

SP - 1769

EP - 1789

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

ER -