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1 state is ignored in our treatment.
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The relative signs of λ parameters reflect those of the corresponding normal coordinates. Only the magnitudes are shown in Table V, while the relative signs are apparent in Table VIII.
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note
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Nontotally symmetric modes can show up only in terms of (2v)×n, where n is an integer. The present study does not incorporate anharmonic effects in the adiabatic simulation.
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70
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33748281812
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note
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This observation can be used as a check on the convergence of the model Hamiltonian calculation with respect to the number of Lanczos recursion and basis set size.
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71
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Presumably, this scaling accounts for deficiencies in the treatment of dynamic electron correlation (triples) in the EOMIP-CCSD method. See Y. J. Bomble, J. C. Saeh, J. F. Stanton, P. G. Szalay, M. Kallay, and J. Gauss, J. Chem. Phys. 122, 154107 (2005).
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33748267769
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note
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Certainly, the resonance feature can be reproduced in the adiabatic simulation as long as the anharmonicity of the potential energy surface is taken into account. In the 1-imidazolyl system, the corresponding anharmonicity is associated with one totally symmetric mode (linear) and one vibronic coupling mode (quadratic). Nonadiabatic simulation with quadratic model potentials can accommodate the effects of such anharmonicity as the totally symmetric mode tunes the energy difference of the two vibronically coupled states. See Ref. 2.
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note
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The reduction in the number of vibronic coupling modes is made based on the magnitudes of the linear interstate coupling constants. We assume that the diabatic off-diagonal quadratic force constants, which mix these coupling modes, are zero in the treatment of the model potentials. Indeed, we find negligible off-diagonal elements in the force constant matrix evaluated at the anion geometry once contributions from the vibronic interactions are subtracted. Such observation has been made previously for the p-benzoquinone system (Ref. 28). It should be mentioned that the numbers of nuclear basis functions for the totally symmetric modes, on the other hand, cannot be determined simply from the magnitudes of the linear coupling constants because of the mode mixing (see Tables III, IV, and VI).
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74
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33748266755
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note
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1 states. Thus, the effects of this truncation on the final three-state simulation are negligible.
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33748263659
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note
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This high sensitivity may imply that a more elaborate treatment of vibronic coupling modes in the model potentials is necessary to provide a more correct representation of the spectral feature of peaks e and f.
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85
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note
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2 state), the quadratic coupling constants are evaluated from the harmonic vibrational frequencies of the anion and neutral states under the parallel mode approximation.
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0003002136
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