 Bonding orbital

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 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.