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 / ii / Solution

Let $S_{12}=⟨{\varphi }_1|{\varphi }_2⟩$ be real, with each atomic orbital normalized. ThenTogether with orthonormal spin functions, this also normalizes the Slater determinant: its norm squared is $⟨\psi |\psi {⟩}^2$. Under the subsequent zero-overlap assumption,using the specified nonnegative branch for $c_1$.