Hydrogen molecule

Finally, make a copy of your file ``Hatom.m'' called ``H2.m''. In ``H2.m'', set rhohat equal to the sum of the expansion coefficients for two densities, that from the hydrogen potential you calculated above for a hydrogen nucleus at rI=[8;8;8] and a second just like it but centered at rI=[8;8;8]+[1.5;0;0]. Be sure also to include the fact that the $H_2$ molecule has two electrons.

You should find a total energy (when you add the nuclear-nuclear part from Problem 3.1) of -1.136 hartree. Subtracting from this twice the energy you found for the isolated atom then gives your prediction for the energy relative to the two atoms being isolated at infinite separation from each other. Your result for this ``bonding energy'' should be negative, indicating that the atoms prefer to be together rather than isolated.

Using this approach, compute the total ``bonding energy'' of the hydrogen molecule for the separations 0.50, 1.00, 1.25, 1.50, 1.75, 2.00, 4.00 and 6.00 bohr. Make a plot of your results. From the plot, determine the bond-length of $H_2$ and compare with the experimental result from a standard reference such as the CRC handbook. Show the plot to the grader to get credit for this problem!