Vibrational borrowing

The position of the 0 O band defines the energy of the excited state relative to that of the ground state, E0 0 = hv0 0. It can usually be located accurately in gas-phase spectra, especially in high-resolution spectra that can be obtained in low-temperature molecular beams. In solution, however, many molecules do not exhibit any vibrational fine structure in their electronic absorption spectra, so that it is difficult to determine v0 0. Moreover, the intensity dependence illustrated in Figure 2.10 holds only for symmetry-allowed transitions (see Section 4.4). That symmetry-forbidden transitions are observable at all as weak absorptions is due to vibrational borrowing vibronic transitions to upper (non-totally symmetric) vibrational levels become weakly allowed when the total symmetry of the vibronic transition is considered. Forbidden 0 0 bands are sometimes (barely) detectable in solution spectra due to symmetry perturbations induced by the solvent, but possible contributions from hot bands (Section 2.1.4) must be taken into account. 

This situation occurs for vddely separated electronic states and leads to the familiar phenomenon of vibrational borrowing due to asymmetric modes. In this case, we vwite the Hamiltonian as... 

Al(HE), Ga(HE) as well as In(HE) porphyrin are typical porphyrins incorporated with a tervalent metal ion Characteristic Q and B bands in the visible and near-ultraviolet region, respectively, arise from the (7T,7T ) excitations in the porphyrin ring with only minor perturbation from the outershell electrons of the central metal ion. The Q band is of forbidden character, however, the Q band can borrow the intensity by vibronic couplings from the allowed B band (30). The intensity of the Q(1,0) band is much less sensitive to the peripheral substituents, the axial ligands and the central metal ions, while that of the Q(0,0) band without excitation in the skeletal vibrational modes is rather sensitive to various substituents. 

For atomic systems the integrated areas under the absorption and emission spectral curves provide values of t (Section 3.9). For molecules, various sources of error vitiate the result, specially when electronic hands overlap and one band can borrow intensity from the other. Existence of vibrational peaks quite often present problems in measuring the area under the absorption curve accurately. But if one can measure t/ and tj>f, t0 can be calculated from the expression (10.2). 

The experimental evidences for these conclusions derive mainly from low-temperature spectra of isolated molecules in rigid matrices.62,63 The diffuseness observed ranges from a few tenths of a cm-1 to thousands of cm-1. In the case of a relatively simple molecule like naphthalene that has two nearby states (S at 31,680 cm-1, and S2 at 34,420 cm-1) a careful study of the second state shows many relatively sharp lines emerging from a diffuse background.64,65 It appears that these sharp transitions can be associated with vibrational levels of the lower electronic state, and that the intensity is borrowed from the second state by the mixing of vibronic states having different electronic parentage in the Born-Oppenheimer representation. 

The first term in Equation (1.47) is identical with the expression derived in the last section for electronically allowed transitions. It is presently assumed to be very small or zero. (A/o f - 0 for symmetry-forbidden transitions.) The second term results from vibronic mixing and represents a first-order vibronic contribution to the transition moment. It is seen that in this description the forbidden transition 0->f steals or borrows intensity from the allowed transition 0- b. If A/o f is exactly zero all observed components of the electronic transition will be polarized along the direction of the transition dipole moment A o b. The 0- 0 transition (v = v = 0) will have zero intensity and only vibrational levels of overall symmetry given by the direct product of symmetries of the states % and % will appear. 

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