We present a study on the dimers of the 4-cyano, 4'n-alkyl biphenyl (nCB) aimed at capturing information connected to the measured odd-even effects on the mesophase properties. The interaction energy of dimers of the 4-cyano, 4'n-alkyl biphenyl (nCB) is computed by a model atomistic potential. The latter has been derived for the 5CB molecule by ab initio calculations that include correlation energy, with an approach that has already provided accurate results. The analyzed intermolecular energy profiles for selected parallel and antiparallel conformations along the nCB series (n = 5,6,7,8), present some features that might be at the root of the odd-even effect of this class of compounds. Preliminary molecular dynamics results yield a stable nematic phase for each homologue, whose computed order parameter show an evident odd even alternation, in good agreement with the experimental findings.