Bonding and antibonding orbitals of H₂

Build the molecular orbitals of the simplest molecule from two 1s atomic orbitals, then stretch and compress the bond to see how the bonding advantage disappears.

Goal

Compare the σ bonding and σ* antibonding clouds, and find the bond length where overlap is strongest.

Apparatus and reagents

A pair of hydrogen 1s orbitals at distance $R$; the viewer combines them as $\sigma = \frac{1}{\sqrt{2}}(1s_a + 1s_b)$ and $\sigma^{*} = \frac{1}{\sqrt{2}}(1s_a - 1s_b)$.

Explanation

Molecular orbital theory combines atomic orbitals into wavefunctions spread over the whole molecule. For $\ce{H2}$ the two 1s orbitals add in phase to give $\sigma$ (electron density between the nuclei screens their repulsion and binds the molecule) or out of phase to give $\sigma^{*}$ (a nodal plane leaves density outside, so filling it weakens the bond). The energy gap between σ and σ* shrinks as $R$ grows — at dissociation both combinations cost the same energy. This LCAO picture is the simplest case solved by Hartree–Fock and by density-functional codes for real molecules.

Virtual experiment: a simplified model to build intuition. It does not replace real lab work or safety training; never repeat chemistry at home without supervision.