A $180^\circ$ rotation leaves both metal centres fixed but reverses each transverse : $p_x\mapsto-p_x$ and $p_y\mapsto-p_y$. Its <matrix> is $-I_4$, so its <character of a representation> is \b[$\chi(C_6^3)=-4$], also obtained from $4\cos\pi$.

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 / b / Solution

 Solution (source code)