Determination of CNDO/2 dipole moment derivatives from interpolating polynomials

A numerical differentiation technique is presented from which dipole moment derivatives are estimated from sets of CNDO/2 calculated dipole moment values. The dipole moment values are evaluated over a range of molecular geometries, which are obtained by distorting the molecule along CH-stretching local coordinates. The technique effectively fits the dipole moment values to an interpolating polynomial, but the utilization of difference tables and lozenge diagrams makes the explicit determination of the polynomial unnecessary.First, second, and third order pure derivatives, and second order mixed derivatives, are estimated for methane and ethane. Several testing procedures for the numerical technique are discussed. On this basis, the accuracy of these derivatives is judged to be very good.