Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 2 / a

The four shortest contacts are the three Cu–N bonds and Cu–OR bond. They define an approximately square equatorial set. The two remaining Cu–O contacts are longer and define a strongly elongated axial direction, as expected for the Jahn-Teller effect of $d^9$ Cu(II).

Choose $z$ along the long contacts and $x,y$ towards the short equatorial donors. The singly occupied, predominantly metal magnetic orbital is then $d_{x^2-y^2}$, with substantial Ligand in coordination chemistry admixture. All three pyrazine nitrogen donors lie in this equatorial set, so both ladder directions have strong metal–Ligand in coordination chemistry orbital overlap. Neighboring copper centers communicate through comparable pyrazine superexchange pathways. Virtual electron transfer between half-filled orbitals stabilizes the antiparallel arrangement, giving antiferromagnetic interactions in both directions with comparable magnitudes. The axial oxygen donors are much less effective exchange routes.

At high temperature, $\chi T$ tends towards the nearly constant Curie constant of weakly correlated $S=\frac{1}{2}$ centers. On cooling, $\chi T$ falls because neighboring spins increasingly correlate antiparallel. The broad maximum in $\chi$ marks the crossover from the high-temperature Curie-like regime to substantial short-range order.

At still lower temperature, the Magnetic susceptibility becomes small because the antiferromagnetic ladder favors a singlet-like ground state and has few thermally accessible magnetic excitations. An even-leg spin ladder can have a spin gap, which reinforces this suppression. A broad Magnetic susceptibility maximum and falling $\chi T$ support short-range antiferromagnetic correlations; they do not establish a three-dimensional Néel transition. Such a transition would require independent evidence, rather than identifying the broad maximum itself as the ordering temperature.