### Abstract

The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.

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

Article number | 044108 |

Journal | Journal of Chemical Physics |

Volume | 124 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2006 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*124*(4), [044108]. https://doi.org/10.1063/1.2162172

**Effects of anharmonicity on nonadiabatic electron transfer : A model.** / Yeganeh, Sina; Ratner, Mark A.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 124, no. 4, 044108. https://doi.org/10.1063/1.2162172

}

TY - JOUR

T1 - Effects of anharmonicity on nonadiabatic electron transfer

T2 - A model

AU - Yeganeh, Sina

AU - Ratner, Mark A

PY - 2006

Y1 - 2006

N2 - The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.

AB - The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.

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UR - http://www.scopus.com/inward/citedby.url?scp=31544462359&partnerID=8YFLogxK

U2 - 10.1063/1.2162172

DO - 10.1063/1.2162172

M3 - Article

AN - SCOPUS:31544462359

VL - 124

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

M1 - 044108

ER -