Bending overtone

As mentioned in the introduction, this is a convenient system for theoretical and experimental study because the OH stretch absorbs in the same region as in liquid water, but in this case, this stretch is decoupled from the other stretches in the system, and even from the bend overtone. 

The Hamiltonians of the previous sections describe realistic vibrational spectra of linear triatomic molecules except when accidental degeneracies (resonances, cf. Section 3.3) occur. A particularly important case is that in which the bending overtone (02°0) is nearly degenerate with the stretching fundamental (10°0) of the same symmetry Fermi, 1929, resonance). This situation occurs when the coefficient in Eq. (4.67) is nearly equal to -A (Figure 4.13). The Majorana... 

Sym. stretch Antisym. stretch bend Overtone bend... 

The bend overtone progression (0, V2, 0) exhibits surprisingly regular Morse-like vibrational spacings [5, 12, 19], described by... 

Figure 23 A proposal for dephasing in ethanol by solvent-assisted intramolecular vibrational redistribution (IVR). The yym-methyl stretch is initially excited, but rapidly equilibrates with one or more modes within kT (the ayym-methyl stretch and/or CH bend overtones). Dephasing occurs with this rapid equilibration time Tivr- However, significant population remains in the sym-methyl stretch after equilibration. Relaxation from this group of state to lower states causes the final relaxation of the population to zero, which is measured as Tj in energy relaxation experiments. (Adapted from Ref. 7.)...

The problem in investigating these two mechanisms is spectroscopically distinguishing the C-H bend overtone (v = 2) from the fundamental (v = 1). The Raman cross section of the two-quantum v = 2 0 transition... 

In the specific example of ACN (46) (point group C3V), there is one C-H stretch and one C-H bend of ai-symmetry and a pair of doubly degenerate stretches and bends of e-symmetry (84). In Fig. 5, the ACN Raman spectrum in the C-H bending region can be seen. The spectrum consists of a sharper ai-symmetry bend 1372 cm-1 and a broader e-symmetry bend at 1440 cm 1. The e-symmetry bend is broadened by Fermi resonance because the e-bend overtones (2 x 1440 cm 1) are degenerate with the e-stretches ( 3000 cm-1). The ai-bend and stretch have no Fermi resonance because the bend overtone (2 x 1372 cm 1) is not degenerate with the stretch (2943 cm-1). In the gas phase, the anharmonicity of the e-bend is 25 cm-1 [85], For an e-bend v = 1 0 transition at 1440 cm-1, the... 

It would help if the e-bend overtone could be frequency-shifted away from the fundamentals. That would be possible if the e-bend were inho-mogeneously broadened (see Section IV.G.). Then we could pump the C-H stretch around 3000 cm-1 and excite only bend overtones in the - 4500 cm 1 region, away from the region between the two fundamentals. Figure 20c,d shows the results of pumping ACN at 3000 cm-1. At t = 0, a new peak is observed in the C-H bend spectrum near 1500 cm-1, whose spectral width is about the same as the apparatus-limited bandwidth. This... 

It should be noted that in a model calculation (76) for the gas phase H20 self-relaxation, the accepting mode for the transition to the bend overtone is the 0-0 stretch in the modeled hydrogen-bonded pair, rather than the D20 librations invoked in the solution case. This might represent a real difference between relaxation in the two phases, but the 0-0 frequency adopted in the model seems to be (57,77) about a factor of 2 too high, which would rather overemphasize the ease of transfer into this mode. 

Figure 6 The differences between energies of bend overtones in H O with 7=2 and K = 2 and the energies of the corresponding 7 = 0 states are plotted as a function of the number of quanta in the bend. The results of variational, eighth, sixth, fourth, and second-order perturbative calculations are denoted by, , O, A, and 0 respectively. The perturbative results model the rotation-vibration coupling as a polynomial expansion in the bend quantum number. Given the actual form of this coupling, as obtained from the variational calculation, the slow convergence of CVPT is not surprising. (From Ref. 49.)...

Figure 1 Left Enol-keto tautomerism in salicylaldimine (SA) and normal mode displacements for skeleton modes i/u and U3o- Middle H/D diabatic potential energy curves Ua Qu) for mode 1 14 (lowest states ground state, bending and stretching fundamental, first bending overtone arrows indicate laser excitation). Right two-dimensional (Qu.Qso) cuts through the adiabatic PES (obtained upon diagonalizing the field-free part of Eq. (1)) which has dominantly H/D stretching character but includes state and mode couplings (contours from 0 to 7400 cm ).

From 13000 to 16500 cm (polyads 5-9). The A B symmetric stretch-bending bands are stronger than the bending overtones the intensity increases quickly. 

In particular, there is a reasonably strong feature at 86.7 cm with a width of about 0.2 cm and a weaker, sharper feature at 89.0 cm . These could be associated with branch heads of the (200) (000) and (210) (000) bending overtone bands with predicted origins at 84.5 and 88.5 cm , respectively. The calculated spectruun of this... 

---