The estimation of molecular properties using momentum–space wavefunctions

A method for estimating molecular properties from ab initio molecular electronic wavefunctions is described. The method involves Fourier transformation of the wavefunction followed by integration over polar angle coordinates to generate a one-dimensional `molecular transformʹ invariant to the choice of position space coordinates. Parameters defining the shape of the low-momentum segment of the transform are then fitted to known values of the property under consideration for a given collection of molecules. Whilst the method is illustrated using polarizability and hyperpolarizability, it is advocated more for its usefulness in estimating properties that are not definable as quantum mechanical first, second or higher order properties.