Gas Phase Electron Diffraction Simulator

GPED Simulator

Gas Phase Electron Diffraction

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.

C60 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.
- 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.

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.
- 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.
- numClusters 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.

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 automatically later.

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.
Note that the molecule viewing panel is interactive.

signal Note that 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.