Hydrogen total electronic energy

The total electronic energy of the hydrogen molecule is calculated as... 

In section 6.9 we already introduced finite-size models of the atomic nucleus and analyzed their effect on the eigenstates of the Dirac hydrogen atom. This analysis has been extended in the previous sections to the many-electron case. It turned out that neither the electron-electron interaction potential functions nor the inhomogeneities affect the short-range behavior of the shell functions already obtained for the one-electron case. Table 9.5 now provides the total electronic energies calculated for the hydrogen atom and some neutral many-electron atoms obtained for different nuclear potentials provided by Visscher and Dyall [439], who also provided a list of recommended finite-nucleus model parameters recommended for use in calculations in order to make computed results comparable. 

Calculate the total electronic energy of a mole of hydrogen atoms. Calculate the total electronic energy of a mole of He atoms. What accounts for the difference in the two total energies ... 

These are two hydrogen-like Schrodinger equations. The eigenvalues E and 2 are hydrogen-like orbital energies. The total electronic energy in the zero-order approximation is... 

Bohr s planetary model of the atom states that electrons in a hydrogen atom move in a circular orbit of radius r around a proton. The proton is so heavy in comparison with the electron that the center of mass of this system coincides with the position of the nucleus. Following Bohr, calculate the total electron energy. 

Curve 1 shows the electronic energy of the hydrogen molecule neglecting interelectronic interaction (from Burrau s solution for the molecule-ion) curve 2, the electronic energy empirically corrected by Condon s method and curve 3, the total energy of the hydrogen molecule, calculated by Condon s method. 

As a summary of the results reported above, the bond in the hydrogen molecule may be described as resulting in the main from the resonance of the two electrons between the two nuclei, this phenomenon contributing 80 percent of the total bond energy. An additional 5 percent is contributed by the ionic structures H H+ and H+H , which are of equal importance. The remaining 15 percent of the energy of the bond can be ascribed to complex interactions included under the term deformation.11... 

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