Vibronic energy levels

The general form of the energy of the harmonic oscillator indicates that the vibrational energy levels are equally spaced. Due to the vector character of the dipole transition operator, the transition between vibronic energy levels is allowed only if the following selection rule is satisfied ... 

Any external electric field is minute in comparison with the internal field generated by the system of electrons and nuclei inside a molecule. The effect of the operator (8.4) is therefore always much smaller than the electronic energy of the molecule. In most cases, the effects of electric-field perturbations are also much smaller than the vibrational energy of the molecule. The interaction with an external DC field can thus be treated as a perturbation to the vibronic energy levels of molecules. 

In Fig. 3, the computed vibronic energy levels are shown for 0Renner-Teller Hamiltonian of the type/g4. Looking at Figs 2 and 3, we can see that for small g values (near g = 0) the behavior of the vibronic energy levels without and with quartic terms is similar. However, with increasing g, relevant... 

The bond lengths were calculated as the Boltzmann average of the geometric properties of the individual vibronic energy levels. 

Fig. 6 The vibronic energy levels as a function of (a) the first-order coupling with (A2 = 0), and (b) the second-order coupling constant for a fixed value of Ai/fm = 1.65...

The beauty of Ham s theory is its simplicity. The Ham factors for any particular problem can be classified by symmetry. This means that any other operator which is a function of the Ua2 will be reduced by the same factor. Note that Ham s treatment implies that that the linear coupling is large compared to the additional terms in the Hamiltonian that are subsequently evaluated as perturbations of the ground vibronic energy levels. 

Fig. 14 Vibronic energy levels in the linear E e case (in units of hco) versus dimensionless coupling constant k (after Muramatsu and Sakamoto [60]). Encircled is the domain of coupling constants where the vibronic ground state is well energy separated from excited vibronic states and the concept of vibronic pseudo spin applies...

Fig. 15 Vibronic energy levels versus the warping factor p (both E and P are in units of 4a, where a is rotational quantum) in a JT elementary cell with quadratic coupling E (S> e [after O Brien [62]). Encircled is the domain of a very small tunneling energy gap where the concept of extended vibronic pseudo spin applies...

In this section we consider the role of molecular vibrations in resonant L NLO properties. Tliese properties govern the intensity of light absorption (or emission) accompanying tlie transition between two vibronic energy levels. Of interest here is one- and two-photon absorption (OPA and TPA). Applications of TPA, in particular, include three-dimensional optical data storage and photodynamic therapy. 

The vibronic energy levels and vibrational amplitude functions X <+), and Xd > where a = 2,5e, or 5a) may be found by si ving the secular equation, Eq. (18). In this matrix equation,... 

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