Vibronic correction

The theoretical method, as developed before, concerns a molecule whose nuclei are fixed in a given geometry and whose wavefimctions are the eigenfunctions of the electronic Hamiltonian. Actually, the molecular structure is vibrating and rotating and the electric field is acting on the vibration itself. Thus, in a companion work, we have evaluated the vibronic corrections (5) in order to correct and to compare our results with experimental values. 

Table 2 Vibronic correction for the static polarizability of CO (from Ref. 5)...

These results are compared with those obtained by Oddershede and Svendsen (18) using SOPPA or Sunil and Jordan (19) using MP4 or a coupled cluster approach, but without vibronic correction. 

The terms in braces in Eq. (78) may show constructive or destructive interference, depending on the sign of B and the sign of and hence Moreover, the sign and the magnitude of the vibronic correction varies with V. Similar arguments apply to the overtone REPs. 

This correction is responsible for the warping of the adiabatic potential surface near the nuclear configuration with electron degeneracy. The analytic form of the adiabatic potential surface becomes a non-linear (not only polynomial) function of nuclear displacements in which potential constants of two kinds occur. The force constants K , Ku, Kjik, etc. contain the pure nuclear term Fj, Fa, Fak, etc. as well as the electron-nuclear (vibronic) term X, Xa, Xak, etc. The vibronic constants Xj, Xy, etc. enter into the vibronic correction term e. They determine a warping of the adiabatic potential surface and they can couple vibration modes of different symmetry, e.g. Xy for i j. 

Finally, Englman presented the third-order vibronic correction in the form of... 

Other source of band shift is vibronic corrections, but they are much smaller than the shift caused by the electronic structure method. In the case of the first energy band of benzene (Fig. 3-left), we can employ Eq. (20) to estimate the vibronic shift. At TD-CAM-B3LYP/TZVP-mod level, AEo.i = 5.548 eV and AEg, = 5.421 eV, and therefore 8i = -0.06 eV, which is much smaller than the shift observed between theory and experiment in Fig. 3-left, about —0.6 eV from maximum to maximum. 

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