  From first principles, we calculate the Heisenberg interactions between
neighboring dimers in several compounds within the
Et$_{n}$Me$_{4-n}X$[Pd(dmit)$_2$]$_2$ (Et = ethyl, Me = methyl, dmit =
2-thioxo-1,3-dithiole-4,5-dithiolate) family using an atomistic approach; with
broken-symmetry density functional theory. In all materials, we find a scalene
triangular model where the strongest exchange coupling along one
crystallographic axis is up to three times larger than the others and that
frustration further enhances this quasi-one-dimensionality. We calculate the
N\'eel ordering temperature via the chain random phase approximation (CRPA). We
show that the difference in the frustrated interchain couplings is equivalent
to a single bipartite interchain coupling, favoring long-range magnetic order.
We find that the N\'eel ordering temperatures are in good agreement with the
experimentally measured values for most compounds.
