These lectures and labs present a brief introduction to computational physics using examples from self-consistent field calculations of the electronic energy and density of various atoms throughout the periodic table. In order to prepare for the assignment, you will need to load some software on your computers as explained in the instructions.

Here are some notes on some basics of numerical analysis.

Pick at least one of your favorite atoms from the periodic table and run the computer program graphatom to determine:

1. A plot of the electron density for that atom.
2. A plot of the one-electron wavefunctions (labeling the curves -- 1s, 2s,... 2p, 3p... etc.)
3. A list of the total energy and the one-electron eigenvalues for the ground state and at least one excited or ionic state. Alternatively, you can use the program frozencore to determine the total energy differences. Note -- the energy units are Rydberg == 13.60569172 eV. In the next meeting, we will compare your results with experimental values.

(Please send email to natalie@wfu.edu if you have any questions.)

In this session, we will focus on running the programs graphatom and frozencore for a few materials and comparing the results with experimental ionization energies or excitation energies.

The program frozencore is designed to study which electrons act as valence electrons. The initial input is very similar to that of graphatom. After the ground state configuration has converged, you will then be asked to identify "core" and "valence" contributions. You can then calculate the energy for the same atom with a new set of valence occupation values (simulating either an excited state or a positive ion), comparing the "frozen core" approximation with a fully converged ("relaxed core") calculation.

1. Run frozencore for your favorite atom in its ground state and at least one excited or ionized state, comparing the energy differences between the frozen core, relaxed core, and experimental result.
2. For the same atom, run graphatom at least twice for the ground state and one excited or ionized state. Compare the shapes of at least two of the wave functions in the ground and excited or ionized state. For this purpose, it will be helpful to make two subdirectories. For example, you can issue the commands:

   mkdir groundstate
   cd groundstate
   graphatom
    (input appropriate data)
   cd ..
   mkdir ionizedstate
   cd ionizedstate
   graphatom
    (input appropriate data)
   cd ..
   gplot -f ./groundstate/wfn0 1 4 lines -f ./ionizedstate/wfn0 1 4 lines
   

   In this example, the gplot command allows you to plot the s-like wave functions (stored in the files named wfn0). The numbers "1 4" mean that you are plotting the results in column 1 (r-values) versus the results in column 4 (in this case, the 3s radial wave functions).

1. graphatom
2. frozencore

Note: In order to run these programs, you will need to run KeyAccess, Exceed, and SSH as described above. Within the SSH windown, login to the wfu.edu computer using your login ID and password.

• man (command name) -- on line help information. If you don't know the command name, you can type "man -k (topic name)"
• ls -l -- lists the file names in your directory
• cat (file name) -- lists file contents
• more ( file name) -- same as "cat", but pauses at the end of each screen full of data.
• lpr -Polin305or file name -- sends file to printer
• chmod 755 plot* -- this makes all files beginning with the filename "plot" into executable files
• which program name -- the result of this command will tell you whether you can "find" the program you wish to execute.
• echo $PATH -- this will display which directories are accessed when you type commands.