  We construct a tight-binding model of
[(C$_2$H$_5$)$_3$NH]$_2$Cu$_2$(C$_2$O$_4$)$_3$ from Wannier orbital overlaps.
Including interactions within the Jahn-Teller distorted Cu-centered $e_g$
Wannier orbitals leads to an effective Heisenberg model. The hyper-honeycomb
lattice contains two symmetry distinct sublattices of Cu atoms arranged in
coupled chains. One sublattice is strongly dimerized, the other forms isotropic
antiferromagnetic chains. Integrating out the strongest (intradimer) exchange
interactions leaves extremely weakly coupled Heisenberg chains, consistent with
the observed low temperature physics.

Strongly Correlated Electrons;Materials Science