Choose transverse directions parallel and perpendicular to the vertical mirror plane. At each metal the parallel is unchanged, whereas the perpendicular changes sign. Thus each two-dimensional block has <trace> $1-1=0$. The total <character of a representation> is \b[$\chi(\sigma_d)=0$]. A mirror plane passing through an orbital centre does not imply that every orbital on that centre contributes $+1$.

Solution

Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2B / Section A / 28 / c / Solution

 Solution (source code)