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

The reference, singly excited and doubly excited determinants are mutually orthogonal. Singles have amplitude $O(\lambda )$ and doubles $O({\lambda }^2)$, so only the reference norm and squares of single-excitation amplitudes contribute through second order:There is no reference-double cross term. The stated expansion has no cubic contribution because its single and double sectors are orthogonal.