Energy levels rovibrational

Rovibrational Energy Levels of a Triatomic Molecule with a Simple Lanczos Method. 

Calculations of Rovibrational Energy Levels of Hydrogen Peroxide (HOOH). 

Figure 2.5 Energy-level diagram of the nonrigid three-dimensional rovibrator [Eq. (2.105)]. Here N = 3 and e, k, k >0.

The energy levels corresponding to Eq. (2.109) are shown in Figure 2.7. These are the energy levels of the three-dimensional (re 0) rovibrator (Figure 2.8). The expression (2.109) can be rewritten in terms of the vibrational quantum... 

One recognizes that these are the energy levels of the Morse rovibrator discussed in Chapter 1. In particular,... 

Fig. 4 Lower rotational energy levels of Hj in the Vj state and the ground state. They are specified by J, G, U and J, K, respectively see text. The allowed rovibrational transitions are shown by vertical lines.

S. Carter and N. C. Handy, A theoretical determination of the rovibrational energy levels of the water molecule. J. Chem. Phys. 87, 4294-4301 (1987). 

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)... 

Schwenke, D.W. Variational calculations of rovibrational energy levels and hansition intensities for tehatomic molecules, J. Chem. Phys. 1996,100,2867-84. 

Kozin, I.N., Law, M.M., Hutson, J.M., Tennyson, J. Calculating energy levels of isomerizing tetra-atomic molecules. 1. The rovibrational bound states of Ar2HF, J. Chem. Phys. 2003,118,4896-904. 

Pseudomolecular Energy Level Patterns. In intrashell states, the two electrons have the same principal quantum number so are nominally at the same distance from the nucleus. The electrons hence exhibit strongly correlated, collective motions and the energy levels and wavefunctions resemble those for molecular rovi-bational states. Kellman and Herrick [92] discovered these patterns and showed that many features could be interpreted in terms of an empirical rovibrator model, e-core-e, analogous to a linear triatomic molecule. This model has since been examined and refined by anal-... 

One of the eonsequences of adiabatic approximation is the potential energy hypersurface V (R) for the motion of nuclei. To obtain the wave function for the motion of nuclei (and then to construct the total product-like wave function for the motion of electrons and nuclei), we have to solve the Schrodinger equation with V (R) as the potential energy. This is what this hypersurface is for. We will find rovibrational energy levels and the corresponding wave functions, which will allow us to obtain rovibrational spectra (frequencies and intensities) to compare with experimental results. 

Rovibrational energy levels of with energies above the barrier to linearity,... 

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