### Abstract

A wide variety of problems involving molecular motion in liquids can be formulated in terms of the generalized Langevin equation (GLE). The friction coefficient on a molecular bond or on some more complicated reaction coordinate is then required. An often used approximation is to set the dynamic friction constant equal to the autocorrelation function of the fluctuating force exerted on the frozen bond by the remaining unfrozen coordinates. The true friction involves projection operators and should differ from this approximation. In this paper we derive various identities and show that the rigid bond approximation is the high frequency limit of the true dynamic friction coefficient. We compute the "true" dynamic friction and the friction approximated on the basis of the rigid or frozen bond and show that the asymptotic limit is very accurate even for frequencies not much larger than the peak frequency of the solvent spectral density. Two different dynamical systems are studied using MD simulations with our newly devised NAPA integrator for systems with disparate time scales. In one the molecule is not allowed to rotate and in the other it is allowed to rotate. Interestingly, even for very long rotational reorientation times, small but significant differences in the long time decay of the bond dynamic friction are observed for rotational and nonrotational molecules - differences, however, that do not produce large differences in the static friction constants.

Original language | English (US) |
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Pages (from-to) | 5084-5095 |

Number of pages | 12 |

Journal | The Journal of Chemical Physics |

Volume | 93 |

Issue number | 7 |

DOIs | |

State | Published - 1990 |

### ASJC Scopus subject areas

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

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## Cite this

*The Journal of Chemical Physics*,

*93*(7), 5084-5095. https://doi.org/10.1063/1.458647