### Abstract

We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4, S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 104 - 106, which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.

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

Article number | 174110 |

Journal | Journal of Chemical Physics |

Volume | 123 |

Issue number | 17 |

DOIs | |

Publication status | Published - Nov 1 2005 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*123*(17), [174110]. https://doi.org/10.1063/1.2046670

**Theory and method for calculating resonance Raman scattering from resonance polarizability derivatives.** / Jensen, L.; Zhao, L. L.; Autschbach, J.; Schatz, George C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 123, no. 17, 174110. https://doi.org/10.1063/1.2046670

}

TY - JOUR

T1 - Theory and method for calculating resonance Raman scattering from resonance polarizability derivatives

AU - Jensen, L.

AU - Zhao, L. L.

AU - Autschbach, J.

AU - Schatz, George C

PY - 2005/11/1

Y1 - 2005/11/1

N2 - We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4, S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 104 - 106, which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.

AB - We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4, S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 104 - 106, which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.

UR - http://www.scopus.com/inward/record.url?scp=27644564718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644564718&partnerID=8YFLogxK

U2 - 10.1063/1.2046670

DO - 10.1063/1.2046670

M3 - Article

AN - SCOPUS:27644564718

VL - 123

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 17

M1 - 174110

ER -