Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 60 / a / Solution

Define $h_{pq}=⟨p|\hat{h}|q⟩$, the one-electron kinetic plus nuclear-attraction integral, and physicists' two-electron integralsin atomic units. With $E_{\mathrm{NN}}$ the zero-electron nuclear-repulsion term, the Slater determinant expectation isThe occupied sums include spin-orbitals, so the exchange integral vanishes for incompatible spins without needing a separate closed-shell factor.