Diagonal-corrected vibrational model

Romelt, J. (1983). Prediction and interpretation of collinear reactive scattering resonances by the diagonal corrected vibrational adiabatic hyperspherical model, Chem. Phys. 79, 197-209. 

To clarify these questions we have studied the quantal and semiclassical theory of reactive resonances. In section II the Diagonal corrected Vibrational Adiabatic Hyperspherical (DIVAH) model 21, ) is reviewed. This theory was the first to provide quantitative predictions (with a typical accuracy of 0.1 kcal/mole) of collinear quantal resonance energies. Furthermore the DIVAH model led us to the new and very surprising phenomenon of vibrationally bonded molecules (29-41). The connection and interrelation with semiclassical RPO theory (25.30.42-47) which predicted and interpreted these results, is presented in section III. Having... 

Romelt [19,20] has prcsented an approximate method called the Diagonal corrected Vibrational Adiabatic Hypersi erical (DFVAH) model. In the DIVAH model all but the diagonal terms of P and Q are ignored. Now the coupled equations in Eq. (13) become a set of n uncoupled equations ... 

If atoms are bound to a common atom, one wonld expect a van der Waals interaction between than. However, if this interaction were included explicitly, since the atoms are quite close together (2-3 A), one wonld have to be carefnl abont the exact shape of this curve to get a correct energy variation with the vibrational motion. A first approximation would be just to find the minimum energy point and add the Urey-Bradley term (the harmonic approximation). And this is a reasonable approximation. But the mathonatics is more simple if one uses a stretch-bend term rather than a Urey-Bradley (UB) term. So this stretch-bend term is important, even in hydrocarbons, and it is easy to see why in the UB model. It is almost as easy to see why in the stretch-bend model. When we need a cross term in the F matrix, it is because the two diagonal elements are not completely independent. That is, they interact. That interaction can be well represented in the present case by just linear terms as in Eq. (4.7). (If the linear terms were to be inadeqnate by themselves, quadratic or higher terms could also be added, but these are not needed here or in most of molecular mechanics.)... 

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