Error matrices in gas-electron diffraction : I. Effects of systematic errors in intensities

Abstract

Electron diffractionists have largely ignored the effect of systematic errors in intensities upon derived molecular parameters. The present investigation proposes a treatment of such errors in terms of certain coefficients characterizing systematic errors which are included as variables interacting with molecular parameters in the information matrix. A simple method is devised to limit coefficient variances to reasonable values. Simple analytical approximations are derived to account for parameter regression slopes. Model systems with poorly resolved internuclear distances are tested. It is found that systematic errors may have a substantial effect, particularly in the case of amplitudes of vibration and the resolution of closely similar internuclear distances. Different types of vibrational averages [e.g., rg(0) versus rg(1)] are influenced to different extents. The resolution of internuclear distances is influenced less by systematic errors if the internuclear distances correspond to atomic scattering factors with distinctly different angular dependencies. Investigations in which a knowledge of highly correlated parameters is crucial should include a treatment analogous to that proposed above.