Polyatomic force constants from charge densities and field gradients

Cartesian-coordinate expressions for polyatomic molecule force constants are considered to investigate the relationship between these quantities and field gradients, ’’atomic force constants’’ or Laplacian terms as ∇2αW, and ’’perfectly following densities.’’ It is shown that for hydride molecules, AHN, the Laplacian quantities obey the approximate relationship ∇2AW?N∇2HW. For triatomic molecules (A–C–B), a ’’diatomics in molecules’’ argument is successful in predicting the quantities ∇2AW and ∇2BW, which are combinations of the stretching and bending force constants. This lends credence to the approximate universality of a relationship for diatomic molecules suggested by Anderson and Parr. Furthermore, it is shown that while only diagonal Cartesian constants are needed to completely describe the general quadratic valence force field (GQVFF) for linear triatomic molecules, nonlinear triatomics require Cartesian constants of the form ∂2W/∂XA∂YC to specify the GQVFF constants. However, the latter may be related to the field gradient tensor and perfectly following densities through the Eckart conditions imposed on Cartesian constants. Possiblities for further applications of the formulas are discussed.