### Abstract

It is found that within the two (electronic)-state approximation, the multidimensional surface intersection problem may be reduced to an equivalent local one-dimensional curve crossing problem. The unique direction along which the adiabatic surfaces avoid a crossing is found to be normal to the "surface of avoided intersection." One may apply this result to the surface hopping trajectory method of Tully and Preston without having to define the surfaces of avoided intersection beforehand. Furthermore, the Landau-Zener transition probability at such an avoided intersection may be calculated from information obtained along the trajectory. These results are applied to trajectory calculations of H_{2}
^{+} + H_{2} collisions.

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

Pages (from-to) | 3975-3984 |

Number of pages | 10 |

Journal | Journal of Chemical Physics |

Volume | 65 |

Issue number | 10 |

Publication status | Published - 1976 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*65*(10), 3975-3984.

**On the multidimensional surface intersection problem and classical trajectory "surface hopping".** / Stine, J. R.; Muckerman, James.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 65, no. 10, pp. 3975-3984.

}

TY - JOUR

T1 - On the multidimensional surface intersection problem and classical trajectory "surface hopping"

AU - Stine, J. R.

AU - Muckerman, James

PY - 1976

Y1 - 1976

N2 - It is found that within the two (electronic)-state approximation, the multidimensional surface intersection problem may be reduced to an equivalent local one-dimensional curve crossing problem. The unique direction along which the adiabatic surfaces avoid a crossing is found to be normal to the "surface of avoided intersection." One may apply this result to the surface hopping trajectory method of Tully and Preston without having to define the surfaces of avoided intersection beforehand. Furthermore, the Landau-Zener transition probability at such an avoided intersection may be calculated from information obtained along the trajectory. These results are applied to trajectory calculations of H2 + + H2 collisions.

AB - It is found that within the two (electronic)-state approximation, the multidimensional surface intersection problem may be reduced to an equivalent local one-dimensional curve crossing problem. The unique direction along which the adiabatic surfaces avoid a crossing is found to be normal to the "surface of avoided intersection." One may apply this result to the surface hopping trajectory method of Tully and Preston without having to define the surfaces of avoided intersection beforehand. Furthermore, the Landau-Zener transition probability at such an avoided intersection may be calculated from information obtained along the trajectory. These results are applied to trajectory calculations of H2 + + H2 collisions.

UR - http://www.scopus.com/inward/record.url?scp=0000810970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000810970&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000810970

VL - 65

SP - 3975

EP - 3984

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

ER -