Tutorial 3    Electronic structure of the C60 molecule
======================================================


This tutorial will explain use of NRLMOL to study the electronic structure of C60 molecule.
The C60 molecule is spherical carbon molecule - also called bucky ball. It was found in the laboratory 
at Rice university in 1985 by Harold Kroto, James R. Heath, Sean O'Brien, Robert Curl, and Richard Smalley.
The 1996 nobel prize was awarded to Kroto, Curl and Smalley for the discovery of C60 and related molecules.
This molecule posses very high symmetry- icosahedral symmetry. 

.. figure:: input_data/c60.png
   :scale: 30%
   :align: right



We will make use of this symmetry in 
our calculations. All carbon atoms in C60 are equivalent to each other, that is, once the position of one 
carbon atom is specified  the position of remaining carbon atoms can be obtained using the point group 
operations of the icosahedral group. This tutorial will explain how to accomplish this and make 
use of symmetry to simplify the calculations.
 
We assume that the code us compiled with appropriate set of parameters needed for arrays. The following set of 
parameters will work.

.. literalinclude:: input_data/PARAMS_C60



As you know by now, CLUSTER file is the main input file of NRLMOL. For C60 the 
CLUSTER file is 

.. literalinclude:: input_data/CLUSTER.C60


Note that we have only one atom listed and the point group is listed to be **Ih**.  If you 
are using point group symmetry then only positions of inequivalent atoms need to be listed. 
The NRLMOL will generate full geometry of the system using the point group operations.
It is *strongly* recommended that you visualize the geometry generated - XMOL.DAT or XMOL.xyz files
using molecular viewer such as JMOL or MOLEKEL or any other of your choice.

Now run the calculation.
    $ **rm -f GEOCNVRG SYMBOL**

    $ **./cluster > print.SCF**

Open the **GEOCNVRG** file and write down the energy.  It should be 


.. literalinclude:: input_data/GEOCNVRG.C60


and the forces are 

.. literalinclude:: input_data/FRCOUT.C60

Note that forces on only one atom (inequivalent) are listed.

The eigenvalues are stored in file called "EVALUES". Please inspect it. Look at the degeneracy 
of the eigenvalues. Identify HOMO, LUMO etc. The file is also displayed below for your convenience.

.. literalinclude:: input_data/EVALUES.C60 
   :emphasize-lines: 12,15-18


To be added: Discussion of orbital degeneracies- plot of wave functions