The lowest energy wavefunction can be thought of as a (anti)symmetric linear combination of an
electron in the ground state near nucleus A and the ground state near nucleus B
We can now compute the energy of these states.
The graph below shows the energies from our calculation for the space symmetric and antisymmetric states as well as the result of a more complete calculation (Exact ) as a function of the distance between the protons . Our calculation for the symmetric state shows a minimum arount 1.3 Angstroms between the nuclei and a Binding Energy of 1.76 eV. We could get a better estimate by introduction some parameters in our trial wave function and using the variational method.
The antisymmetric state shows no minimum and never goes below -13.6 eV so there is no binding in this state.
By setting , we can get the distance between atoms and the energy.
|Calculated||1.3 Å||-1.76 eV|
|Actual||1.06 Å||-2.8 eV|
Its clear we would need to introduce some wfn. parameters to get good precision.
Jim Branson 2013-04-22