= Solution
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 \b[$d_{x^2-y^2}$], 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 \b[antiferromagnetic interactions in both directions with comparable magnitudes]. The axial oxygen donors are much less effective exchange routes.
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