### Abstract

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

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

Article number | 024119 |

Journal | The Journal of Chemical Physics |

Volume | 131 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

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### ASJC Scopus subject areas

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

### Cite this

*The Journal of Chemical Physics*,

*131*(2), [024119]. https://doi.org/10.1063/1.3173276

**Nuclear quantum effects in electronically adiabatic quantum time correlation functions : Application to the absorption spectrum of a hydrated electron.** / Túri, L.; Hantal, György; Rossky, Peter J.; Borgis, Daniel.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 131, no. 2, 024119. https://doi.org/10.1063/1.3173276

}

TY - JOUR

T1 - Nuclear quantum effects in electronically adiabatic quantum time correlation functions

T2 - Application to the absorption spectrum of a hydrated electron

AU - Túri, L.

AU - Hantal, György

AU - Rossky, Peter J.

AU - Borgis, Daniel

PY - 2009

Y1 - 2009

N2 - A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

AB - A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

UR - http://www.scopus.com/inward/record.url?scp=67650754976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650754976&partnerID=8YFLogxK

U2 - 10.1063/1.3173276

DO - 10.1063/1.3173276

M3 - Article

VL - 131

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

M1 - 024119

ER -