A relook at the compliance constants in redundant internal coordinates and some new insights

The compliance constants, the inverse of the force constant matrix elements offer the advantage that any one of them could be calculated directly without the need to calculate the full Hessian. Here we show that such a direct calculation produces accurate results. Since the diagonal G and the compliance matrix elements (G(ii),C(ii)) give unique values that are independent of the other internal coordinates, an internal frequency (nu) is defined which could be effectively used to study related molecules. The conventional coordinates used for benzene and cubane give some of the compliance constants, which differ from the values obtained by the direct method by 5%-40%, indicating that the coordinate systems used are deficient. We identify the source of this discrepancy and find a way to form the correct coordinate system in the sense that the Hessian method and the direct method will lead to the same compliance constants. This procedure takes away the simplicity of local coordinates at least in highly symmetric molecules and it is advantageous to have the potential energy distribution in redundant internal coordinates. A method is proposed for this purpose. All these imply that the most satisfactory way of describing the molecular force field is in terms of redundant internal compliance constants.