Molecular integral evaluation kinetic-energy integrals

The calculation for the hydrogen molecule ion makes plain the basic problem with attempting to extend the numerical approach to molecular calculations. Even, for the simplest molecular species, we have to build a spreadsheet with multiple worksheets devoted to the calculation of the components of the potential and kinetic energies and, this, without any consideration of the extra need in neutral species to evaluate the two-electron potential term. It is appropriate, therefore, to extend the direct approach of Chapter 5, for the calculation of the two-electron integral components for helium, to the calculation of all the integrals in any calculation. 

Given an equation of state, such as the van der Waals equation, the above integral can be evaluated to obtain an explicit expression for Cy. Equation (6.2.9) shows that,/or any equation of state in which p is a linear function ofT, Cv.reai = Gy ideal- This is tTue for the van der Waals equation. The energy due to the molecular interactions depends on the intermolecular distance or density (M V). Because this does not change at constant the value of Cy is unaffected by the molecular forces Cy is the change in kinetic energy of the molecules per unit change in temperature. 

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