Energetics of the Bonding in H2 and

Under standard conditions, both molecules exist in their lowest vibrational energy levels. These are known as their zero-point vibrational states, in which the value of the vibrational quantum number is zero. The fact that molecules in their zero-point vibrational states possess vibrational energy is a consequence of the Uncertainty Principle this would be violated if the internuclear distance was unchanging. The dissociation limits for both species are identical the complete separation of the two atoms, which is taken as an arbitrary zero of energy. The difference between the zero of energy and the zero-point vibrational energy in both cases represents the bond dissociation energies, respectively, of H2+ and H2. 

To obtain an accurate assessment of the interelectronic repulsion energy of the H2 molecule it is essential to carry out calculations in which the hydrogen nuclei are a constant distance apart. The following calculations are for an internuclear distance of 74 pm for both molecules, which is the equilibrium internuclear distance in the dihydrogen molecule. 

There are only two forces operating in H2+ the attractive force between the nuclei and the single electron, and the repulsive force between the two nuclei. The interproton repulsion energy may be calculated from Coulomb s law  

I- H + Hf at infinite separation, E = 0 - actual H2+ both forces operating 

Q What is the repusion energy between two protons which are 106 pm apart, as they are in the ground state of the hydrogen molecule-ion  

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