Laser Induced Electron Diffraction (LIED)is a method of molecular imaging using a molecule's own electrons. The process follows the three-step model: tunnel ionization, acceleration, and rescattering. Data from rescattered electrons encodes structural information. Codes are used to analyze the data as well as create theoretical models to compare to experimental data. My goal this summer was to develop these codes to more easily analyze this data. Developed programs are demonstrated on CH4 (methane).
K. Chirvi, J. Biegert Struct. Dynamics, 11, 041301 (2024) Visualization of Three Step Model
Experimentalist collect time of flight data of the rescattered photoelectrons at a range of scattering angles. The data is converted into momentum including the appropriate Jacobian for electron yield. This study follows Quantitative Rescattering Theory (QRS) [1] for calculation of Experimental DCS. QRS requires a range in the momentum transfer parameter q, which depends on theta and p. In this study we use the FABLES method (Fixed Angle Broadband Laser Induced Electron Scattering) to extract the DCS, which involves studying the yield of varying momentum values along a constant scattering angle of 180 degrees.
I developed a code that inputs cartesian parameters a priori from the National Institute of Standards in Technology (NIST) and calculates molecular distances pairwise to determine bond length. The results are then plotted into a Histogram of length vs bond frequency.
Bond Length Histogram for CH4. Methane consists of only 4 equal distance bonds of the same type, but the code can account for other types of bonds when present.
CH4 Ball and Stick model made using Application Avogadro: an open-source molecular builder and visualization tool. Version 1.XX. http://avogadro.cc/
I additionally created a code to convert radial data obtained by experiment to momentum parallel and perpendicular to the laser polarization. The data is then interpolated and plotted as a heatmap.
Momentum as a function of perpendicular and parallel momentum. Represented data conveys poor statistics and is not necessarily accurate, but rather serves the purpose of illustrating the ability of the program. 
Schematic detailing how momentum is recorded and converted.
For theoretical models, we use the Density Functional Theory Software ‘Octopus’ [2]to solve the Kohn-Sham Orbitals. The software was run through the HPC at Kennesaw State University. Using programs written by Dr. Chi Hong Yuen at Kennesaw State University, supporting material pertaining to the molecule can be plotted and included. We also used codes developed by Dr. Chi Hong Yuen to calculate the Tunnel Ionization rate, which is important in calculating the theoretical DCS of the molecule. The TI-Rate is calculated using ADK Theory [3].
Tunnel Ionization rate of CH4 at Euler Angle orientation calculated using Ammosov-Delone-Krainov Theory (ADK). The tunnel ionization rate weighs the results of the DCS.
Theoretical Orbitals of CH4
To calculate the DCS, we use the Tunnel Ionization Weighted Independent Atom Model. We calculate the DCS for constant energy with a range in angle and, separately, for constant angle with varying energy.
These methods will be applied to experiments taking place in August with a 4um and 100KHz laser. These experiments will bring much more data to the picture and allow for a drastic improvement in statistics for LIED results. Future studies will investigate methane and deuterated methane (CH4 and CD4) as well as butane isomers. The ultimate goal is to study molecular dynamics via pump probe experiments.
