Statistical formalism for analysis of gas electron diffraction intensities of Boltzmann vibrational distributions
by Ischenko, A. A.; Lobastov, V. A.; Schafer, L.; Ewbank, J. D.
A new procedure is described that allows one to model molecular intensities from gas electron diffraction (GED) in terms of cumulant expansions, without the need first to evaluate the cumulants by complex computational analyses based on spectroscopic data. By introducing a number of approximate constraints on cumulant coefficients, gamma(n), the contribution to the molecular scattering by each pair of atoms, i and j, is represented by three independent variables, i.e. the equilibrium distance, r(e,ij), mean amplitude, I-g, and the first cumulant coefficient, gamma(1). These parameters are determined by least squares refinement from the GED data, and the resulting values can be used to calculate the probability density, P(r(ij)), and effective pair potential, V-eff(r(ij)). By applying the simplified cumulant analysis scheme to GED data of SF6 recorded in the temperature range 298-773 K, it is found that the resulting parameters are within error limits of those obtained from analyses including spectroscopic information. The development of the new intensity expression is important because it avoids the geometrically inconsistent r(a) scheme of the traditional equation commonly used in GED investigations, and it can be applied to equilibrium ensembles at elevated temperatures, following heating or optical pumping, where the traditional equation is inoperable. Thus, the simplified cumulant analysis will serve as a much needed base for structural kinetic studies of laser excited species by stroboscopic GED.
- Journal
- Journal of Molecular Structure
- Volume
- 377
- Issue
- 3
- Year
- 1996
- Start Page
- 261-269
- URL
- https://dx.doi.org/10.1016/0022-2860(95)09140-8
- ISBN/ISSN
- 1872-8014; 0022-2860
- DOI
- 10.1016/0022-2860(95)09140-8