### Abstract

We develop a generalized Langevin equation approach for treating gas phase molecular collisions. First, the exact classical equations of motion for the "slow" degrees of freedom (say translation and rotation) in a collision are rewritten in a generalized Langevin form in which the influence of "fast" (internal) degrees of freedom is isolated explicitly in random force and friction terms. Approximations to the friction terms are then introduced to take advantage of weak correlations between fast and slow variables so that a purely markovian nonlinear Langevin equation is obtained. These approximations utilize a reference friction term (which is generated by integrating a single fully correlated trajectory corresponding to zero initial vibrational energy) to treat non-markovian effects, and a markovian correction factor to account for fluctuations about the reference. Applications to vibrationally inelastic scattering in colinear models of He + H_{2} and Kr + CO_{2} are presented which indicate that this approach is capable of a quantitative description of the collision dynamics as long as good time scale separations between slow and fast variables exist. Indeed, accurate results (often <10% errors) are obtained even in the limit of high initial vibrational excitation and large energy transfers. The present generalized Langevin method assumes some restrictions on the form of the potential energy function in the hamiltonian, but methods for treating more general problems including rearrangement collisions are discussed.

Original language | English |
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Pages (from-to) | 295-307 |

Number of pages | 13 |

Journal | Chemical Physics |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 15 1978 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Spectroscopy
- Atomic and Molecular Physics, and Optics

### Cite this

**A generalized Langevin equation approach to molecular collision dynamics.** / Schatz, George C.

Research output: Contribution to journal › Article

*Chemical Physics*, vol. 31, no. 2, pp. 295-307. https://doi.org/10.1016/0301-0104(78)87044-X

}

TY - JOUR

T1 - A generalized Langevin equation approach to molecular collision dynamics

AU - Schatz, George C

PY - 1978/6/15

Y1 - 1978/6/15

N2 - We develop a generalized Langevin equation approach for treating gas phase molecular collisions. First, the exact classical equations of motion for the "slow" degrees of freedom (say translation and rotation) in a collision are rewritten in a generalized Langevin form in which the influence of "fast" (internal) degrees of freedom is isolated explicitly in random force and friction terms. Approximations to the friction terms are then introduced to take advantage of weak correlations between fast and slow variables so that a purely markovian nonlinear Langevin equation is obtained. These approximations utilize a reference friction term (which is generated by integrating a single fully correlated trajectory corresponding to zero initial vibrational energy) to treat non-markovian effects, and a markovian correction factor to account for fluctuations about the reference. Applications to vibrationally inelastic scattering in colinear models of He + H2 and Kr + CO2 are presented which indicate that this approach is capable of a quantitative description of the collision dynamics as long as good time scale separations between slow and fast variables exist. Indeed, accurate results (often <10% errors) are obtained even in the limit of high initial vibrational excitation and large energy transfers. The present generalized Langevin method assumes some restrictions on the form of the potential energy function in the hamiltonian, but methods for treating more general problems including rearrangement collisions are discussed.

AB - We develop a generalized Langevin equation approach for treating gas phase molecular collisions. First, the exact classical equations of motion for the "slow" degrees of freedom (say translation and rotation) in a collision are rewritten in a generalized Langevin form in which the influence of "fast" (internal) degrees of freedom is isolated explicitly in random force and friction terms. Approximations to the friction terms are then introduced to take advantage of weak correlations between fast and slow variables so that a purely markovian nonlinear Langevin equation is obtained. These approximations utilize a reference friction term (which is generated by integrating a single fully correlated trajectory corresponding to zero initial vibrational energy) to treat non-markovian effects, and a markovian correction factor to account for fluctuations about the reference. Applications to vibrationally inelastic scattering in colinear models of He + H2 and Kr + CO2 are presented which indicate that this approach is capable of a quantitative description of the collision dynamics as long as good time scale separations between slow and fast variables exist. Indeed, accurate results (often <10% errors) are obtained even in the limit of high initial vibrational excitation and large energy transfers. The present generalized Langevin method assumes some restrictions on the form of the potential energy function in the hamiltonian, but methods for treating more general problems including rearrangement collisions are discussed.

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U2 - 10.1016/0301-0104(78)87044-X

DO - 10.1016/0301-0104(78)87044-X

M3 - Article

VL - 31

SP - 295

EP - 307

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

IS - 2

ER -