What factors are responsible for the 458 kJ/mol bond between two hydrogen atoms?

Is the bond due to electron density being shifted from around the atom to the bond midpoint? Or does it have a quantum mechanical basis?

The geometric variables for molecular hydrogen, H₂ are given in Figure 1

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We'll start from simple trial wave functions, Eqns. \eqref{eq:h2_17} and \eqref{eq:h2_18}.

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\begin{equation} \psi = {\phi _a}^{(1)}{\phi _b}^{(2)}\alpha \beta \label{eq:h2_17} \end{equation}
\begin{equation} \psi = {\phi _b}^{(1)}{\phi _a}^{(2)}\alpha \beta \label{eq:h2_18} \end{equation}

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We'll examine their energies and then introduce the concept of resonance and consider the resonance between these limiting forms.

Each hydrogen interacts with each proton (Electron Nuclear Attraction), each hydrogen has kinetic energy, the protons interact (Nuclear Repulsion), and the electrons interact (E-E Coulomb). Electron-electron interpentration occurs at a greater distance that electon-nuclear penetration. These terms are plotted in Figure 2, referenced to two hydrogen atoms.

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