Forbidden transitions, between states opposite symmetry

A rule of quantum mechanics states that transitions between states of opposite symmetry are forbidden this is why the intensity of the outer lines falls to zero in the limit of An = 0. In between, in the strong coupling zone, the outer lines are diminished in intensity and this gives the leaning or house shape of the AB system. 

The essential point that distinguishes between allowed and forbidden reactions is the role of the D+A configuration. If the D+A configuration is allowed by symmetry to mix into the transition state wave-function then the transition state will be stabilized and will take on character associated with that configuration. For the ethylene dimerization, D+A is precluded from mixing with DA due to their opposite symmetries. As was discussed in detail in Section 2 (p. 130), DA cannot mix with D+A" since and n orbitals are orthogonal (106). Thus for ethylene dimerization the concerted process... 

Electric dipole transition can take place only between the states of different parities. In the free ion, therefore, direct inner shell transitions d d and /— / are forbidden. For the ions in crystals, however, this prohibition is removed by the mixing of orbitals having opposite parity. Such mixing may be induced by a) absence of a center of S5mimetry of the crystal field (existence of the hemihedral part of the crystal field) and b) destruction of the center of symmetry by odd vibrations. This was first pointed out by Van Vleck. In most salts of the 3d group ions the mechanism (b) plays the dominant role for the optical absorptions caused by the transitions between d" states. ... 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

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