Ab initio MP2/aug'-cc-pVTZ calculations have been carried out on B4H4 and B-4(CH3)(4) to investigate the base properties of these molecules with T-d symmetry. Each face of the tetrahedral structure of B4H4 and B-4(CH3)(4) is stabilized by a two-electron, three-center B-B-B bond. The face uses these two electrons to act uniquely as an electron-pair donor for the formation of stable hydrogen-bonded and halogen-bonded complexes with C-3 nu symmetry. The hydrogen-bonded complexes are B4H4:HY and B-4(CH3)(4):HY, with HY = HNC, HF, HCl, HCN, and HCCH; the halogen-bonded complexes are B4H4:ClY and B-4(CH3)(4):ClY, with ClY = CIF, ClCl, ClNC, ClCN, ClCCH, and ClH. The absolute values of the binding energies of the hydrogen-bonded complexes B-4(CH3)(4):HY and of the halogen-bonded complexes B-4(CH3)(4):ClY are significantly greater than the binding energies of the corresponding complexes with B4H4. The binding energies of each series correlate with the distance from the hydrogen-bonded H atom or halogen-bonded Cl atom to the centroid of the interacting face. Charge transfer stabilizes all complexes and occurs from the B-2-B-3-B-4 orbital of the face to the antibonding H-X orbital of HY in hydrogen-bonded complexes and to the antibonding Cl-X orbital of ClY in halogen-bonded complexes, with X being the atom of Y that is directly bonded to either H or Cl. For fixed HY, EOM-CCSD spin spin coupling constants J(X-B-1) are greater than J(X-B) for complexes B4H4:HY, even though the X-B1 distances are longer. B-1 and B-n are the atoms at the apex and in the interacting face, respectively. Similarly, for complexes B4H4:ClY, J(Cl-B-1) is greater than J(Cl-B-n). In the halogen-bonded complexes, both coupling constants correlate with the corresponding distances.