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Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

J. Chem. Phys. 125, 014109 (2006); doi:10.1063/1.2209676

Published 7 July 2006

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Valerie Rodriguez-Garcia
Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435

Kiyoshi Yagi and Kimihiko Hirao
Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan and CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan

Suehiro Iwata
Center for Quantum Life Sciences, Hiroshima University, Hiroshima 739-8526, Japan and Graduate School of Science, Hiroshima University, Hiroshima 739-8526, Japan

So Hirata
Quantum Theory Project, Department of Chemistry, University of Florida
Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X-tilde   2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X-tilde   2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+. ©2006 American Institute of Physics
History: Received 10 April 2006; accepted 9 May 2006; published 7 July 2006
Permalink: http://link.aip.org/link/?JCPSA6/125/014109/1
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KEYWORDS and PACS

Keywords
PACS
  • 33.70.Ca
    Molecular oscillator and band strengths, lifetimes, transition moments, and Franck–Condon factors
  • 31.15.Dv
    Coupled cluster theory (atoms and molecules)
  • 31.15.Ne
    Self-consistent-field methods (atoms and molecules)
  • 31.25.Qm
    Electron-correlation calculations for polyatomic molecules
  • 31.50.-x
    Potential energy surfaces (atoms and molecules)
  • 33.60.-q
    Photoelectron spectra of molecules
  • YEAR: 2006

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0021-9606 (print)   1089-7690 (online)
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