The distributed-memory SMC program has been applied to a number of elastic and inelastic electron-molecule scattering problems, emphasizing polyatomic gases of interest in low-temperature plasma applications [JTIS:88a], [Manos:89a]. Initial applications [Hipes:90a], [Winstead:91d] on the Mark IIIfp were to elastic scattering by ethylene (CH), ethane (CH), propane (CH), disilane (SiH), germane (GeH), and tetrafluorosilane (SiF). We have since studied elastic scattering by other systems, including phosphine (PH), propylene (CH) and its isomer cyclopropane, n-butane (CH), and 1,2-trans-difluoroethylene, both on the Mark IIIfp and on the Intel machines. We have also examined inelastic collisions with ethylene [Sun:92a], formaldehyde (CHO), methane (CH), and silane (SiH). Below we present selected results of these calculations, where possible comparing to experimental data.
Figure 8.10 shows integral elastic cross sections-that is, cross sections summed over all angles of scattering, plotted as a function of the electron's kinetic energy-for the two CH isomers, cyclopropane and propylene. Scattering from propylene requires some special consideration, because of its small dipole moment [Winstead:92a]. These calculations were performed in the static-exchange approximation, neglecting polarization and excitation effects, on 256-node partitions of the Delta. The results in Figure 8.10 should be considered preliminary, since studies to test convergence of the cross section with respect to basis set are in progress, but we do not expect major changes at the energies shown. Corresponding experimental values have not been reported, but the total scattering cross section, of which elastic scattering is the dominant component, has been measured [Floeder:85a], [Nishimura:91a], and these data are included in Figure 8.10. Both the calculation and the measurements show a clear isomer effect in the vicinity of the broad maximum, which gradually lessens at higher energies. At the level of approximation (static-exchange) used in these calculations, the maxima in the cross sections are expected to appear shifted to higher energies and somewhat broadened and lowered in intensity. Thus, for propylene, where some discrepancy is seen between the two measurements, our calculation appears to support the larger values of [Nishimura:91a].
Figure 8.11: Differential Cross Sections for Elastic Scattering of Electrons by Disilane and Ethane. Experimental points for ethane (circles) are from Ref. [Tanaka:88a]; disilane data (squares) are from Ref. [Tanaka:89a].
Figure 8.11 shows the plotting of the calculated differential cross section, that is, the cross section as a function of scattering angle, for elastic scattering of electrons from ethane and its analogue disilane. These results were obtained on the Mark IIIfp within the static-approximation. Agreement with experiment [Tanaka:88a;89a], is quite good; although there are quantitative differences where the magnitude of the cross section is small, the qualitative features are well reproduced for both molecules.
Calculations of electronic excitation cross sections are shown in Figures 8.12 and 8.13. In Figure 8.12, we present the integral cross section for excitation of the state of ethylene [Sun:92a], obtained on the Mark IIIfp in a two-channel approximation. This excitation weakens the C-C bond, and its cross section is relevant to the dissociation of ethylene by low-energy electron impact. As seen in the figure, the cross section increases rapidly from threshold (experimental value ) and reaches a fairly high peak value before beginning a gradual decline. The threshold rise is largely due to a d-wave () contribution, seen as a shoulder around above threshold, which may arise from a core-excited shape resonance. Relative measurements of this cross section [Veen:76a], which we have placed on an absolute scale by normalizing to our calculated value at the broad maximum, show a much sharper structure near threshold, but are otherwise in good agreement.
Figure 8.12: Integral Cross Section for Electron-Impact Excitation of the State of Ethylene. Solid line: present two-channel result; dashed line: relative measurement of Ref. [Veen:76a], normalized to the calculated value at the broad maximum.
Figure 8.13 shows the cross section for electron-impact excitation of the and states of formaldehyde, obtained from a three-channel calculation. Portions of this calculation were done on the Mark IIIfp, the iPSC/860, and the Delta. Experimental data for these excitations are not available, but an independent calculation at a similar level of theory has been reported [Rescigno:90a], and is shown in the figure. Since the complex-Kohn calculation of [Rescigno:90a] included only partial waves up to , we show both the full SMC result, obtained from , and a restricted SMC result, obtained with f projected onto a spherical-harmonic basis , . The agreement between the restricted SMC result and that of [Rescigno:90a] is in general excellent; however, comparison to the full SMC result indicates that such a restriction introduces some errors at higher energies.
Figure 8.13: Calculated Integral Cross Sections for Electron-Impact Excitation of the and States of Formaldehyde, Obtained from Three-Channel Calculations. Solid lines: present SMC results; short-dashed lines: SMC results, limited to ; long-dashed lines: complex-Kohn calculations of Ref.\ [Rescigno:90a].