Rovibrational eigenvalues

These extra eigenvalues are shown as a function of energy for both Ai and A2 symmetries of the rovibronic wavefunction in Fig. 10. There are two maxima near 4.41 and 4.62 eV for Ai symmetry, 4.49 and 4.70 eV for A2 symmetry. They correspond to resonances with lifetimes close to 15 fs for Ai symmetry and 10 fs for A2 symmetry. Resonances with similar lifetimes have been computed in [60, 61] and detected experimentally in [68]. The energies of the bound rovibrational states... 

The eigenvalues of this Hamiltonian operator can be related directly to the conventional Dunham expansion in rovibrational quantum numbers given by... 

The most important difference with the local eigenvalues obtained for the bent case [Eq. (4.33)] is found in the double dependence on the vibrational angular momentum quantum number Ig, which appears in the expectation values of both C- 2 and C 2 operators. In the bent-to-linear correlation pattern for rovibrational energy levels (Fig. 33) we achieve the exact linear limit for /I 0 (we recall that the bent limit is obtained with A[2 = 2Aj2). This means that in the eigenvalues (4.54), the dominant term in Ig is derived from the Cjj operator. However, it is possible to account for minor adjustments of energy terms explicitly dependent on Ig, by adding (small) contributions related to the operator Cjj- In the linear case, it is convenient to use, in place of the absolute value, the square of this operator, in such a way that the vibrational spectrum recalls the usual Dunham series (written in normal quantum numbers)... 

The eigenvalues of can be written in different ways, according to the conversion laws for rovibrational quantum numbers for linear or bent molecules [see Eqs. (4.33) and (4.54)] ... 

In this article I shall discuss only the calculation of vibrational spectra. To calculate rovibrational energy levels one must choose not only internal coordinates, to describe the vibrations of the molecule, but also define a molecule-fixed axis system (which rotates with the molecule). The Hamiltonian matrix is also much larger than for the vibrational (J = 0) case (one must calculate eigenvalues of matrices approximately JNy x JNy, where is the size of the vibrational basis). 

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