= Bonding orbital
{title2=$\sigma_g$}
{wiki}
= Bonding molecular orbital
{synonym}
Occupying a <bonding molecular orbital> favours a <chemical bond>. For the two equivalent $1s$ <atomic orbitals> of the <hydrogen atom>, the sum $\sigma_g=\sigma_+$ has constructive <interference> between the <protons>. The resulting <electron> density in that region helps stabilize the combined system. Its lower <energy> in this model follows from the <Quantum Hamiltonian>, not from the plus sign alone; 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].
For example, $(\sigma_g)^2$ in <molecular hydrogen> supplies $N_b=2$, hence <bond order> one when $N_a=0$. The sum in the <molecular orbital theory> toy has midpoint <probability density> $0.303468$, whereas the difference has zero there. The normalization factors must be included in this comparison.
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