Wave equation vibrational

The corresponding rotation-vibration wave equation in the Born-Oppenheimer approximation, in which all coupling of electronic and nuclear motions is neglected, is... 

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 simplest molecular problem, viz. H, can be attacked by numerical methods to jdeld accurate vibrational and rotational energy levels in the electronic ground state. This calculation was done by Wind (66a) using the electronic energy Eg(R) determined by him 66b) to a very high degree of accuracy and the rotation-vibration wave equation derived by Cohen, Hiskes and Riddell (76)... 

We can therefore substitute for Erot(R) in the vibrational wave equation (2.146) to give... 

The vibrational wave function pv is a function of the internal coordinates (the normal coordinates are usually used) and is a solution of the vibrational wave equation. In Sec. 2-4 it was shown that the kinetic and potential energies of vibration arc given by the expressions... 

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