Term values rovibrational

The main difficulty in solving (2.153) lies in the evaluation of the potential energy term (2.154). Even in the case ofH2, calculation of V from the electronic waveftmctions for different values of R is no easy matter. Usually, therefore, the vibrational wave equation is solved by inserting a restricted form of the potential experimental data on the rovibrational levels are then expressed in terms of constants introduced semiempirically, as we shall show. 

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)... 

This pattern of transitions in the rovibrational spectrum of the diatomic is roughly similar to the appearance of a rovibronic spectrum. Equations 9.27 and 9.28 need to be adjusted to include the equilibrium term energy for the difference in energy between the potential minima for the initial and final electronic states and to separate the power series expansions in the vibrational and rotational energies. Parameters such as B (o, and depend on the potential energy curve of each individual electronic state. No simple equation relates these potential energy curves for different electronic states, and therefore distinct values for each of these parameters are given to each electronic state ... 

Rotational and Centrifugal Distortion Constants. The rotational constants of gaseous NH2 were obtained by fitting the rovibrational bands of the high-resolution IR spectrum to a Watson-type S-reduced Hamiltonian. The results in cm for the ground state of the ion are Ao = 23.0508 0.0019, Bo = 13.0684 0.0015, Cq = 8.11463 0.00048, Dj = 0.001082 0.000022, Djk=-0.00381 0.00012, Dk = 0.02065 0.00013, Di =-0.000492 0.000014, and 2= -0.0000461 0.0000054. The corresponding values for the v l and the Va = 1 states and the estimated equilibrium rotational constants of the ground state are also listed. The analysis was restricted to quartic distortion terms, because the inclusion of sextic terms did not result in a better fit of the bands. The Hamiltonian used does not include the effects of the rotational interactions which are noticeable in some bands [2]. Rotational constants... 

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