Vibronic coupling operator

The vibronic coupling operates upon the nuclear and electronic functions of the electronic states involved in the internal conversion (Equation 6.74). Mk is the effective mass associated with the /cth vibrational mode. Because of the different spin labels of the states involved in the intersystem crossing, the spin-orbit coupling gives a finite value to the electronic coupling in Equation 6.74. 

As stated earlier, the vibronic coupling operator, (s dH/dQ e), determines which normal vibration is resonance-enhanced via the 5-term. This term... 

The notations g, i, j, e, and v were explained in Sec. 1-20. Other notations are as follows s, another excited electronic state h<,the vibronic coupling operator dS /dQay M and being the electronic Hamiltonian and the ath normal coordinate of the electronic ground state, respectively E i and the energies... 

Totally symmetric modes are not subject to symmetry restrictions. Their potentials may contain odd and even terms in Q so that the harmonic-oscillator approximation imposes unwarranted symmetry restrictions. Similarly, the corresponding vibronic coupling operator may contain both odd and even terms so that the distinction between pseudo-Jahn-Teller and pseudo-Renner-Teller coupling disappears. Since the potential energy minimum of a totally symmetric mode is different in different electronic states, the pseudo-Jahn Teller/Renner-Teller limit is quite different from the limiting cases discussed in Section I V,B,C. Finally, the transition moments... 

Since and (as well as S>2 and 2) will furnish identical matrix elements of the vibronic coupling operator we can combine the coefficients as ci -H cl = di and < + C2 = di yielding for the total energy correction Eq. (28) when applying Eq. (30) only on... 

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