Extended near-infrared resonance raman investigations of an organic mixed-valence system: Diazatetracyclodiene radical cation

Journal of Physical Chemistry A

Volumn 103, Issue 50, 1999, Pages 11172-11180

  Williams, Robert D ^a   Hupp, Joseph T ^a   Ramm, Michael T ^b   Nelsen, Stephen F ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000073758     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp992789+     Document Type: Article

References (95)

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66. -1.
67. 8 × Δ
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69. s.
70. 2 so that large intensities are expected for large Raman shifts (although strictly only for frequencies less than Γ).
71. s and are not high enough in frequency to mimic the large F values that we have obtained.
72. 5 For a discussion of the effects of partial and complete ion pairing upon intervalence absorption line shapes and energies, see the following. Blackbourn, R. L.; Hupp, J. T. J. Phys. Chem. 1990, 94, 1788.
73. FORTRAN code for calculating absolute cross sections was obtained courtesy of Prof. Anne Myers at the University of Rochester.
74. -Γt) + t/τ where T is the temperature and D and Λ are used to describe the characteristic magnitude and frequency of the solvent perturbation, respectively. In this equation, the real part contributes spectral broadening while the imaginary part contributes the Franck-Condon shift.
75. 2/molecule.
76. -1 mode) that were similar to those from the previous calculation.
77. This was done by increasing the κ value from 0.01 to 1, where κ is the line shape parameter given by Λ/D.
78. ab equals the experimentally obtained value.
79. 46 Upon moving through the curve-crossing region, the wave packet (or a fraction of the wave packet) may jump to the lower diabatic surface and continue its evolution there (see Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437). An accurate calculation would need to follow the wave packet evolution and keep track of curve crossing, which for the high-high-frequency vibrations present in this system might involve several oscillations. In the absence of appreciable damping, upper-surface/lower-surface wave packet interference effects might also be needed to be considered.
80. The need to propagate on adiabatic surfaces has been recognized previously. In fact, adiabatic surfaces have already been used by Zink and co-workers to calculate intervalence absorption bands for mixed-valence complexes (Simoni, E.; Reber, C.; Talaga, D.; Zink, J. I. J. Phys. Client. 1993, 97, 12678.
81. Zink, J. I.; Reber, C. Coord. Chem. Rev. 1991, 111, 1.). Adaptation and extension of their approach to include absolute scattering cross sections, several vibrational modes, detailed solvent reorganizational effects, and detailed dephasing effects would almost certainly resolve the problems encountered here. Their analysis also elegantly handles wave packet curve-crossing and partial curve-crossing effects. Wave packet propagation on adiabatic surfaces (although not yet extended to the calculation of absorbance and Raman excitation profiles) has also been addressed by Coalson and co-workers. See, for example, the following.
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83. -1.
84. 2, where f is a force constant and Δa is the change in bond length.
85. -1 and a transition length of 0.84 Å.
86. k) between the minima on the adiabatic surfaces is less than the displacement between the minima on the diabatic surfaces (see Figure 3). However, this correction is comparatively small and has been ignored.
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88. f(FC) is equation presented
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94. -1.
95. tot where C is the quartic factor, taken to be 0.2.