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.

Pick at least one of your favorite atoms from the periodic table and run the computer program graphatom to determine: (Please send email to natalie@wfu.edu if you have any questions.)

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.

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 login to the wfu.edu computer. In order to setup your session, there are a number of preliminary steps that will be helpful. Below are listed two alternative methods:

1. If you have never used a Unix machine before, this method may be preferable. It creates or modifies a control file called ".login"
   • login wfu.edu -- type your user name and password at the prompts
   • type ls -l
   • You should see at least two files in your list -- .login and .cshrc or .tcshrc . If you do (not) see these files, then you should load the following in your windows buffer:

     set path=($PATH .  /usr/bin /usr/sbin /bin /usr/local/bin\
       /users/faculty/phylib/bin/ ~natalie/www-home/s01phy345/programs/ .)
      
     # Set the default X server.
     if ($?DISPLAY == 0) then
         if ($?REMOTEHOST) then
             setenv DISPLAY ${REMOTEHOST}:0
         else
             setenv DISPLAY :0
         endif
     endif
     
     # Set X-Window title
     @ havexwindows=($term == "xterm")
     if ($havexwindows) then
         ~/public/bin/set_xterm_title `hostname`
     endif
      
     if ( (! $?ENVONLY) && $?prompt ) then
      setenv PROMPT "`whoami`@<`hostname|cut -d \. -f 1`>`pwd`:"
      set prompt="$PROMPT"
      alias cd 'set old=$cwd;chdir \!*;set prompt="`whoami`@<`hostname|cut -d \. -f 1`>`pwd`:"'
     endif
     
     setenv TERM vt100
     set term=vt100
     

   • Then type cat >(>) .login (ENTER)
   • (PASTE)
   • type (CONTROL-d)
   • This creates (modifies) your ".login" file.
   • To activate this .login file, type source .login
     
2. This method involves more steps which should be done every time you start a new session. It has the advantage that it has been successfully used by others.
   • login wfu.edu -- type your user name and password at the prompts
   • In order to easily find the executable files, type

     set path=($path /users/faculty/phylib/bin ~natalie/www-home/s01phy345/programs/ . )

   • In order to enable graphics output to your Thinkpad, make sure that you have activated x-windows and that you set the parameters:
     setenv DISPLAY 152.17.xxx.xxx:0
     where the xxx's refer to your local IP address, which can be determined from the windows program --C:\WINDOWS\winipcfg.exe.

• 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