Spin-vibronic coupling

Although spin-orbit coupling is the principal mechanism of singlet-triplet interconversion, a secondary mechanism, spin-vibronic coupling also plays a role, becoming important - as may occur - when spin-orbit coupling is prohibited by symmetry. It is illustrated for diphenylcarbene in Fig. 9.2. 

For groups with real, one-dimensional, representations, i.e. D2/1 and its subgroups, the formal requirement can be expressed in analogy to Equation 9.33  

Rx and belong to a , and Ry - rotation in the zx plane - to a. When Equation 9.33 is applied in the overall symmetry of the triplet component, like that of the singlet, is A. Since its space symmetry is also 4, the spin function has to transform like iZy, the only totally symmetric rotation. 

M can interconvert with Ty and of because both R and Ry belong to 5, as does the space function, so the overall symmetry of both is A. These results are exactly the same as that obtained with Equation 9.35, but the distinction drawn in Fig. 9.2 between the components produced by spin-orbit and spin-vibronic coupling respectively has disappeared spin-vibronic coupling in the parent group has become spin-orbit coupling in the subgroup. 

In anticipation of the discussion of photochemical reactions in the next chapter, it might be noted that spin-orbit coupling alone cannot promote intersystem crossing between the first excited, open shell, singlet and the triplet. Both have the same space symmetry, so their interconversion would require the presence of a totally symmetric rotation - non-existent in C2v to produce a triplet component with an Ai spin-function. Direct intersystem crossing in the parent methylene therefore has to rely on spin-vibronic coupling with the antisymmetric stretching vibration, of Fig. 4.3, its only non-totally symmetric 

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Table 18- The T, - So oscillator strengths calculated with direct spin-vibronic coupling along 62s modes ( , i=4,5). Results are displayed for different basis sets and for the active space described in text.

To understand this discrepancy, three different theories have been proposed such as Chudnovsky et al. s dislocation-induced tunneling [85], Cornia et al. s solvent-disorder model [86], and Pederson et al. s spin-vibron coupling for isotopically impure samples [87], Magnetic tunneling measurements [88,89] and high-frequency EPR spectroscopy [84,90]... 

Clearly, this cannot occur in first-order spin vibronic coupling since the perturbing singlet must be u. As a result both r(ft) and F(vib) must be g if the triplet is u. Xor can this occur via the mechanisms expressed in... 

Figure 9.2. Spin-orbit and spin-vibronic coupling in diphenylcarbene. The triplet component induced by spin-orbit coupling is printed in bold letters. (0 displacement towards displacement towards -x)...

Combined Vibronic and Spin-Orbit Coupling in Linear Molecules... 

Introduction of the vibronic coupling (s / 0) causes removal of the above degeneracy and leads to the general vibronic-spin-orbit pattern presented in the central part of Figure 3. Each vibronic level is characterized by a particular K... 

The vibronic structure of a electronic state at variable strengths of the vibronic and spin-orbit coupling is presented in Figure 5. The splitting of the... 

Figure 5, Low-eriergy vibronic spectrum in a electronic state of a linear triatomic molecule. The parameter c determines the magnitude of splitting of adiabatic bending potential curves, is the spin-orbit coupling constant, which is assumed to be positive. The zero on the...

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

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