= Antibonding orbital
{title2=$\sigma_u^*$}
{wiki}
= Antibonding molecular orbital
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Occupying an <antibonding molecular orbital> opposes a <chemical bond>. For equivalent $1s$ <atomic orbitals> of the <hydrogen atom>, the difference $\sigma_u^*=\sigma_-$ vanishes on the plane halfway between the <protons>: every point there is equally far from both centres, so the amplitudes cancel. This nodal plane removes the contribution of this <molecular orbital> to <electron> density on that plane; it does not make an entire finite region empty. The $1s$-derived <antibonding molecular orbital> lies above its <bonding molecular orbital> partner in <energy>. See https://ocw.mit.edu/courses/5-61-physical-chemistry-fall-2017/e9f9413400be87f6a0a512e757d52e3c_MIT5_61F17_lec25.pdf[Field, MIT 5.61, lecture 25, pp. 1–2].
In the $\mathrm{He}_2$ minimal model, $(\sigma_u^*)^2$ adds $N_a=2$ and cancels the <bond order> contribution of $(\sigma_g)^2$. Opposite signs on the two lobes describe <probability amplitudes>, while both lobes have nonnegative <probability density> after squaring. The star is an orbital label, not an extra <electron> or an <electric charge>.
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