Vibronic rotatory strength

Nafie and Freedman (1983) derived the vibronic coupling theory of infrared transition intensities using only ground state wave functions. According to this theory the rotatory strength can be given as ... 

More numerous, however, are aromatic compounds with an effectively planar n system, the optical activity of which comes from chiral perturbations. Benzene derivatives such as phenylalanine (3) are particularly important. The Lb band of the benzene chromophore (A = 260 nm) is neither magnetically nor electrically allowed. The symmetry selection rule may be broken by vibronic interactions or due to substituents. The interpretation of the observed rotatory strength is not easy, but empirical sector rules have been proposed. (Cf. Charney, 1979 Pickard and Smith, 1990.)... 

In cases where the adiabatic approximation breaks down, the only well-defined transitions are vibronic transitions with rotatory strengths given by... 

This excursion into electronic versus vibronic rotatory strengths and the adiabatic versus the nonadiabatic approximation may be highly relevant to the detailed interpretation of transition metal complex chiroptical spectra. In most optically active transition metal complexes, the symmetry of the metal ion-donor atom cluster remains rather high (nearly 0 or nearly D h) and, as a result, it is common to find many near-degeneracies (or even exact degeneracies) among the spectroscopic states of interest. Even in... 

For a more complete description of the vibronic levels associated with the Tig(A2 + E) electronic excited state, the wave functions Tj [Eq. f32)] must be augmented to include vibrational wave functions associated with all of the normal modes other than a = 2,5a, and 5e. Here we shall restrict our attention to just those vibronic levels derived from the vibrational modes a = 2,5a, and 5e. Assuming no vibronic couplings involving the ground electronic state of our model system, the rotatory strength of a transition between the lowest vibrational level of the ground electronic state and the j-th vibronic level of the Tjg (t2g + eg) coupled state may be written as... 

According to the restricted model adopted in this section (II.C.), all of the rotatory strength associated with the Ajg(Ai) Tig(A2 + E) electronic transition is distributed among the vibronic levels derived from (A2 + E) (ai + 2e) couplings. The total (or net) rotatory strength of the Aig - Tig transition is, therefore, given by... 

A2 + Ea + A + E ) e coupling can lead to mixed polarization within the vibronic CD band envelops of both the Ai A2 and Ai Ea transitions. In the absence of vibronic coupling, the Ai - A2 transition would be polarized parallel to the trigonal axis of the system, whereas the Ai - Ea transition would be polarized perpendicular to the trigonal axis. In the presence of vibronic coupling, vibronic components of both parallel and perpendicular polarization may appear in both the Ai - A2 and Ai Ea CD bands. Secondly, from Eqs. (61) and (62) we see that the net CD associated with the Ajg - Tig transition need not vanish even when the zeroth-order net electronic rotatory strength, r(°(Ai A2) + r(° Ai - Ea), is zero. 

The chiroptical behaviour of cisoid conjugated dienes, already known to be controlled by a combination of diene helicity and axial chirality effects, is further influenced by methyl substituents on the unsaturated carbon atoms. The observed methyl group contributions are not susceptible to a simple interpretation, for in some cases [e.g. at C-2 or C-3 in a 2,4-diene (24), or at C-3 in a 19-nor-l,3-diene (25)] the signs of methyl group contributions to Ae and to the rotatory strength (R) are opposite. Computer resolution showed that the c.d. and u.v. absorption curves are of composite form, with up to five vibronic components. Moreover the wavelength shifts accompanying methyl substitution do not accurately follow the Fieser-Woodward rules. It is concluded that... 

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