Second-order, nondegenerate mixing

Orbital mixing. Simple spherical orbitals are shown to illustrate the concept. A. The first-order, degenerate mixing. B. The second-order, nondegenerate mixing. 

One doesn t need a real degeneracy to benefit from this effect. Consider a nondegenerate two-level system, 84, with the two levels of different symmetry (here labeled A, B) in one geometry. If a vibration lowers the symmetry so that these two levels transform as the same irreducible representation, call it C, then they will interact, mix, and repel each other. For two electrons, the system will be stabilized. The technical name of this effect is a second order Jahn-Teller deformation.67... 

The effect of suUur participation on the orbital g -shifts in the EPR spectra, illustrated in Pig. 20, accounts for the qualitatively different spectra observed for tyrosyl phenoxyl and Tyr-Cys phenoxyl radicals (Gerfen et al., 1996). The rhombicity of the simple tyrosyl radical EPR spectrum is a consequence of the splitting between gx and gy principal g -values. These g -shifts deviate from the free electron g--value ge = 2.00023) as a result of orbital angular momentum contributions. While a nondegenerate electronic state (such as the A" ground state for ere) contains no hrst-order unquenched orbital momentum, second-order spin-orbit mixing between close-lying a and a" functions results... 

At second order in optical fields (x = 2), only nonquadrature passive processes, harmonic generation and parametric three-wave mixing, are possible. In fully nondegenerate second order processes, three frequency components of the field at [Pg.71]

Much more commonly, vibronic interactions involve mixing of two nondegenerate electronic states of different symmetry, under the influence of an appropriate nonsymmetric vibration, which leads to a stabilization of the state of lower energy. This type of vibronic interaction is called a second-order Jahn-Teller (SOJT) effect. SOJT effects occur whenever two electronic states, and Tg, which belong to different irreducible representations, are mixed by a vibration that lowers the molecular symmetry. Therefore, except in diatomics, SOJT effects occur whenever any symmetry element is present in a molecule. 

---