Molecular orbital ($\psi (\mathbf{r})$)

A molecular orbital is a one-Electron spatial wavefunction for the combined atomic nuclei of a molecule. For a normalized molecular orbital, the Born rule gives the position probability density $|\psi (\mathbf{r}){|}^2$, with ${\int }_{{\mathbb{R}}^3}|\psi {|}^2{d}^3\mathbf{r}=1$. The molecular orbital is the amplitude, rather than its squared modulus or a classical trajectory.

In the independent-orbital approximation, a doubly occupied molecular orbital contributes $2|\psi {|}^2$ to the Electron number density, whose integral is two. An empty molecular orbital contributes zero, even though its shape is still part of the model. The molecular hydrogen example therefore uses one occupied spatial molecular orbital for two Electrons, distinguished by their spins. A negative real probability amplitude means a relative quantum phase of $\pi$, not positive electric charge; multiplying the whole wavefunction by $-1$ changes only its global phase.