Counting molecular force constants

Vibrations typically correspond to small excursions from the equilibrium geometry, and the energy scale of the potential surface is defined with respect to a zero at that geometry, where by definition all first derivatives (9V/9Sj)e vanish. The higher derivatives d V/dSidSj)e, (d V/dSidSjdSk)e, are the quadratic, cubic,. .. force constants. As coefficients in the Taylor expansion 

The observations provide an opportunity to demonstrate one aspect of the utility of the GT calculator files on the CDROM. It is straightforward to calculate that while the C2v point symmetry H2O molecule exhibits 4 independent quadratic, 6 independent cubic and 

The same ideas extend straightforwardly to deal with property surfaces describing the dependence of a molecular property on geometry, for example, the dipole moment and polarisability derivatives that control the activity of a vibrational mode in IR and Raman spectroscopy. Extension to the case of redundant internal coordinates, the typical situation for polyatomic molecules, is also straightforward. 

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The total energy expression also derives contributions from ion-ion repulsion interactions. This is approximated by a sum of pairwise repulsive terms and included in Urep. This sum also contains the corrections arising from the double counting of electron-electron interactions in 17ei[8. Ho is a constant that merely shifts the zero of energy. The contribution to the total force from Hrep is rather straightforward. One can then easily do molecular dynamics simulations by numerically solving Newton s equation,... 

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