Non-Totally Symmetric Modes

Distortions along non-totally symmetric modes may occur in certain excited states. These distortions are non-symmetry preserving the point group of the molecule changes in the excited state. The specific examples in this paper are the linear to bent geometry changes of metal nitrosyls (e.g., from Ci(V to C3 in [Fe(CN)5N0]2+.)... 

Figure 1-19 shows the Raman spectra of CC14 obtained with 90° scattering geometry. In this case, the pp values obtained were 0.02 for the totally symmetric (459 cm-1) and 0.75 for the non-totally symmetric modes (314 and 218 cm-1). For pp values in other scattering geometry, see Ref. 26. 

The relative contributions of A-and 6-term scattering under resonance conditions is a subject of considerable interest and different conclusions have been found for different systems. For example the A-term predominates for n-electron systems, e. g. polyenes, especially for their main intense absorption band (Warshel 1977). Vibrational wavefunc-tions of non-totally symmetric modes are more nearly orthogonal. Thus, vibrations may only derive their intensities from the 6-teim. A-term and 6-term enhancement can be distinguished experimentally by their excitation profiles. For A-term scattering a peak in the excitation profile is expected at the origin of the resonant electronic transition and subsidiary peaks at successive excited state vibrational levels. The amplitudes of the peaks depend on the successive Frank-Condon factors. For 6-term scattering excitation profile maxima are expected at the 0 0 and 1 0 positions for each of the mixing... 

The sets of coupling constants and the Hamiltonians, (8), (15) define the highdimensional potential energy surfaces of the lowest five electronic states of the various cations treated. Typically 6-8 totally symmetric modes and 8-10 non-totally symmetric modes are found to have non-negligible coupling constants in the C2v systems in the two cases with higher symmetry these numbers apparently decrease, e.g. to 3 relevant totally symmetric modes for the 1,4-difluoro isomer. Only few selected constants are included in Table 3 and we refer to the original papers for full details [62,68,69]. 

Although the multidimensional PES for the totally symmetric modes are harmonic oscillators, we emphasize that (pronounced) anharmonicity of the adiabatic PES comes into play as soon as non-totally symmetric modes are included [6]. The minima of the diabatic PES can be determined by retaining only the totally... 

The predicted relative rates do not increase as sharply as the experimental rates. Preliminary calculations imply that frequency changes (of ca. 100 cm-1) in the lower frequency non totally symmetric modes and/or the promoting mode appear to affect the relatives rates by no more than a few percent. These cannot account therefore for the discrepancy. Included in Table 1 are also the calculated ratios where xa has been increased by 10% while xM has been decreased by 10%. Such parameter changes are well within their experimental errors for the perhydro case. These changes tend to provide increased agreement with experiment. In the perdeutero case, the parameters were only guestimated, and they therefore could be further adjusted in order to obtain improvement with... 

Non-Totally Symmetric Modes and Herzberg-Teller Scattering... 

The classic cases of the HT mechanism concern coupling between two electronic states of different symmetry or between the different components of two degenerate states of the same symmetry. An important example of the first case occurs when electric dipole transitions to one of the two states are forbidden (e.g. the Laporte-forbidden d—d and f-f transitions). In this case, the forbidden transition may acquire absorption intensity by HT mixing with an allowed transition via a non-totally symmetric mode of appropriate symmetry (the irreducible representation of the active mode must be contained in the direct product of the irreducible representations for the two states coupled by the HT mechanism). 

Enhanced scattering in the Qj band may also result from interference between the FC scattering of totally symmetric modes with shifted potentials and HT scattering by the non-totally symmetric mode concerned. 44)... 

The absorption intensity of the 0-1 vibronic sideband is entirely borrowed by HT coupling. The observation that this 0-1 transition is of comparable intensity to the 0-0 transition suggests the feasibility of resonance Raman processes in which both the absorption and emission moments are borrowed. This second-order HT coupling displays itself in the appearance of first overtones and combination bands of non-totally symmetric modes. These are observed extensively in the haem proteins 35). 

Fig. 5. The Herzberg-Teller scattering mechanism. A and B illustrate the first-order contributions to fundamental scattering for non-totally symmetric modes where the excited-state potential curves are unshifted relative to those of the ground state. C and D show the dominant second-order contributions to overtone scattering.

Combination-Band Progressions Involving One or Two Quanta of a Non-Totally Symmetric Mode... 

The purpose of this section is to draw attention briefly to two interesting examples of progressions involving both totally symmetric and non-totally symmetric modes. First, the resonance Raman spectra (50) of various salts of the [AuBr4]" ion (D4h symmetry) show progressions in the i i (Aig) Au—Br stretching frequency based on one quantum of V2 (Big) (up to 2 f j) and also based on a quantum of J 4( 2g) (up to 1 4 + 5 J i). Excitation was at 457.9 nm, which lies near the absorption maximum (22,500 cm ) of a broad band assigned (51) to a superposition of two electric-dipole-allowed transitions, both of the type a dx2 yj(Au) - 7r p(Br),... 

The definition of the depolarisation ratio, pi, is illustrated in Fig. 1 for linearly-polarised incident radiation and a 90° scattering geometry. In the normal Raman effect it is well known that the measurement of p may identify the symmetry of the vibrational mode responsible for a given Raman band pi < 3/4 (pi = 0 in cubic or higher symmetries) for totally symmetric modes and Pi= 3/4 for non-totally symmetric modes. In the resonance Raman effect, the value of P, and its dependence on the exciting frequency, may be more informative. This is because the symmetries of... 

For non-totally symmetric modes in any point group, there are no trace contributions. Therefore G° = 0 and Pi is given by the special formula... 

Additional information about the vibration can be obtained through the depolarization ratio. This is the ratio of the intensity of scattered light that is polarized in a plane perpendicular to the incident radiation relative to that the scattered light that is polarized parallel to the incident polarization, p = For totally symmetric modes, p = 0, while 0 < p < 3/4 for non-totally symmetric modes [i, 3]. The polarization ratio can actually be greater than 3/4 for a resonantly enhanced Raman band [3]. 

Non totally symmetric modes are enhanced (Fq = Tg x Does not vanish even off resonance... 

Figure 9 (Henneker et al., 1978a) shows an example of Raman scattering by a non totally symmetric mode involved in (linear) Herzberg-Teller coupling of two excited states, d> and <1> . It is an elaboration of Fig. 7 in that the result of resonance with both excited states is shown. For convenience, we have assumed that both transitions -> and <5, -> are allowed and have the same transition moment, but different polarization. This assumption makes the Rayleigh profile symmetric relative to the two states, but has no effect on the structure of the fundamental REP since its matrix elements are proportional to the product of the two transition moments. The difference in intensity of the overtones in the and <1> band region reflects the frequency differences cOg — co and cOg — co . Figure 9 is based...

We have constructed several linear vibronic coupling model Hamiltonians augmented with diagonal quadratic terms for the non-totally symmetric modes. The total Hamiltonian of the molecule in the diabatic representation reads... 

As a final distinction, we mention a difference between trigonal (such as or Dsh) and tetragonal (such as C4 , D, D2d) point groups. In the first case doubly degenerate modes are JT active, in the second case nondegenerate, non-totally symmetric modes are JT active [3]. In the former case the JT-split PESs have... 

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