Knowledge Bank

An algorithm is described for the calculation of uncertainties in the Cartesian displacements obtained using harmonic oscillator assumptions. The method involves an extension of a derivation given by Nakagawa, $etal.1,2$ for determining the variation in the normal coordinate transformation matrix produced by numerical changes in the force field. The force constant correlation matrix determined from familiar least squares techniques is used to determine the Cartesian displacement dispersions and their correlations. Examples of the effect of correlation and non-correlation between force constants will be given for benzene, 1,2,4-trichlorobenzene and coumarin.