This program, GPED.exe, will calculate the electron diffraction
pattern produced by individual, randomly oriented, molecules. Such diffraction patterns
have radial symmetry so that only the radial pattern density is of interest. Realistic
noise, such as that caused by other background gases, can be added to the radial pattern.
Once this pattern is obtained over some limited collection angles, it can be inverted
to give a pair correlation function (PCF). This PCF represents the distribution of atomic
distances within the molecule and it would be the result of any laboratory experiment.
This program was
specifically designed to investigate the feasibility of electron diffraction on molecules
levitated in a radio frequency trap.
GPED.exe is a Windows executable. The executable and a few support files are located in
a zipped file here.
Using the program, a brief introduction:
- On startup the program will request a
*.geo file that contains the
molecular geometry. The file
C60.geo and a few others are provided.
Initially, the molecule will be visible as well as its pair-distance histogram. The
pair-distance histogram is analogous to the continuous pair-correlation function.
- For all atom types in the molecule an atomic scattering factor file
is required (
*.scf). A handful of these are provided. They bear names of the
atomic name and atomic charge. Usually these are accessed automatically if they are within
the ScatteringFactors subdirectory.
Click Compute Scatter and the
calculation should take a few seconds. All plots are interactive and can be zoomed and
scaled. Techniques for
using this specialized graphical user interface can be found here.
Plots with and without multiplication by s (the radial distance) are shown. One
separates the atomic and molecular components as well.
Realistic noise can be added to the simulation as caused by a column of He gas in the
electron beam. Select Pressure, GasTemperature, and He column dimensions in
millimeters. numHeAtoms is computed
Click Compute PCF to compute new
noise (or just Compute Noise) and the
pair-correlation function shown on lower right. The PCF is overlaid with the pair-distance
histogram for comparison.
Smoothing of the PCF is a simple technique for reducing the effects of noise and limited
data collection. Increasing the parameter alpha
will generate smoothing - an exponentially decaying weight starting at s=0. Also
if the molecule under consideration is known to have a limited size, this information can
be used to remove additional noise. Set the min and max atomic distances as r.ij. Repeat Compute
PCF to see the effects of these changes.
The effects of finite molecular temperature can be crudely approximated with the q_lij_rij setting. This attributes small
distributions to the atomic positions. Note that for C60 a setting of 0.0055 is
expected to correspond to a temperature of 1000K. A few more notes
on this approximation are here.
Finally the results (all plotted curves) can be saved as ASCII files with Save Results. Data files with names beginning
with "s_", such as "s_molecular_xy.dat" have values multiplied by the
variable s for convenient viewing, as is common for electron powder diffraction.
Some additional information on using the AlphaSquared
graphical user interface can be found here.
- Select the range over which diffraction is to be collected. Here
denoted s0 to s1 with count
steps. Click on these controls and enter new numbers as desired. Typically s0
> 0 and s1 is 5-20 Angstrom-1.
and numScatteredE controls the
number of molecules and the number of scattered electrons in the simulation. These are
most important in relation to the noise generation discussed below. Low numbers of
scattered electrons reproduce shot noise accurately.
Note that the molecule viewing panel is interactive.
this program is intended for experimental simulation not mass distribution. No harm can be
done in running the program incorrectly. However, due to its highly technical and
exploratory nature, many features are indicated only in the source code. If you have
interest in those features, please contact me.
Source code is available from the author on request. It uses the AlphaSquared graphical user interface.
Development of this program was funded primarily by The Rowland Institute for Science, under the direction
of Joel Parks. The program was written exclusively by Douglas Cameron.