(Color online) Three-dimensional structures of phosphoric acid and tetrahydrofuran. The small circles are hydrogen atoms.
Schematic structures of cyclopentane (I), THF (II), and the DNA sugar deoxyribose (III) that show the similarities between these compounds. The hydrogen atoms that fill the carbon valences are not shown. The ring conformation we have used in the calculations is not planar but puckered, as indicated in Fig. 1 for THF, therefore the carbon is below the plane and above; here they are indicated both above for ease of drawing.
Partial elastic electron scattering cross sections from THF (solid line); the dot-dashed line represents the static-exchange results. Calculations involve partial waves up to and the dipole physics outside the -matrix box is included exactly for those partial waves. Top: Cross section comparison with theoretical (dotted) (Ref. 15) and experimental (dashed) (Ref. 13) results; the open squares are the actual experimental data points. Bottom: Time-delay plot to highlight the presence of resonances. The full curve is the total time delay, while the numbered curves correspond to the few highest eigenvalues that exhibit resonant behavior. The total time delay was rescaled to show all curves on the same graph more easily.
Unconverged fixed nuclei elastic cross sections for electron scattering by THF and cyclopentane. The two molecular structures are similar (THF has an oxygen atom instead of a –– group) and so are their electron scattering cross sections. Cyclopentane has essentially zero dipole moment, therefore the low energy part of its cross section does not rise the way it does in THF.
(Color online) Left: Time-delay eigenfunctions for THF on resonance at [top, where the widely spaced dotted curve (labeled “2”) in Fig. 3 is dominant] and [bottom, where instead the dashed curve (labeled “1”) in Fig. 3 dominates]. A slice of the three-dimensional eigenfunctions is shown on the plane that contains , while is above the plane and below. The red contours identify positive areas and the blue contours identify negative areas of the real part of the wave function. Right: Virtual orbitals for energies (top) and (bottom) from HF at the level. The full lines identify positive areas and the broken lines identify negative areas. The correspondence between the two top plots and the two bottom plots is very pronounced, allowing to identify the two main contributions to the resonance. Although the molecule is not planar, this projection is much easier to read than the three-dimensional structures.
partial elastic cross section (top) and time-delay analysis (bottom). Calculations again involve partial waves up to and the dipole physics outside the -matrix box is included exactly for those partial waves. Two broad resonances are present at 7.7 and , and the cross section is smaller than in the DNA bases and comparable to THF.
Energies, widths, and dominant partial waves of the resonances discussed in the text.
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