Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 24 / b / i

A doubly occupied spatial orbital gives a spin-singlet Slater determinant:Equivalently, $\Psi =\psi ({\mathbf{r}}_1)\psi ({\mathbf{r}}_2)[\alpha (s_1)\beta (s_2)-\beta (s_1)\alpha (s_2)]/\sqrt{2}$. The spatial factor is symmetric, and the normalized antisymmetric spin factor enforces the Pauli exclusion principle. Here $\mathbf{x}$ includes position and spin.