A comparative study between three experimentally known beryllium chelators (EDTA, NTP, and 10-HBQS) and two tetradentate tripodal di-pyridine-based receptors (HL and HL-NH2), specifically designed to bind Be2+ cations, has been undertaken in the aqueous phase at the B3LYP/6-311++G(d,p) computational level. The relative binding energies of these five ligand systems to a variety of first row and pre-transition metal cations have been calculated, specifically to investigate their binding strength to Be2+ and the binding enhancement that a second sphere hydrogen bonding interaction could afford to the pyridyl based systems. The complexes of EDTA were calculated to have the highest average binding energy; followed by those of NTP, HL-NH2, HL, and finally 10-HBQS. The calculated binding energy of the HL-NH2Be complex, which includes second sphere interactions, was found to be almost 9% greater than the HL Be complex, with an average binding energy increase of 13.5% observed across all metals upon inclusion of second sphere hydrogen bonding.