STATISTICAL FORMALISM FOR ANALYSIS OF GAS ELECTRON-DIFFRACTION INTENSITIES OF BOLTZMANN VIBRATIONAL DISTRIBUTIONS

A new procedure is described that allows one to model molecular intens ities from gas electron diffraction (GED) in terms of cumulant expansi ons, without the need first to evaluate the cumulants by complex compu tational analyses based on spectroscopic data. By introducing a number of approximate constraints on cumulant coefficients, gamma(n), the co ntribution to the molecular scattering by each pair of atoms, i and j, is represented by three independent variables, i.e. the equilibrium d istance, r(e,ij), mean amplitude, I-g, and the first cumulant coeffici ent, gamma(1). These parameters are determined by least squares refine ment from the GED data, and the resulting values can be used to calcul ate the probability density, P(r(ij)), and effective pair potential, V -eff(r(ij)). By applying the simplified cumulant analysis scheme to GE D data of SF6 recorded in the temperature range 298-773 K, it is found that the resulting parameters are within error limits of those obtain ed from analyses including spectroscopic information. The development of the new intensity expression is important because it avoids the geo metrically inconsistent r(a) scheme of the traditional equation common ly used in GED investigations, and it can be applied to equilibrium en sembles at elevated temperatures, following heating or optical pumping , where the traditional equation is inoperable. Thus, the simplified c umulant analysis will serve as a much needed base for structural kinet ic studies of laser excited species by stroboscopic GED.