The ability of B atoms on two different molecules to engage with one another in a noncovalent diboron bond is studied by ab initio calculations. Due to electron donation from its substituents, the trivalent B atom of BYZ 2 (Z=CO, N 2 , and CNH; Y=H and F) has the ability to in turn donate charge to the B of a BX 3 molecule (X=H, F, and CH 3 ), thus forming a B•••B diboron bond. These bonds are of two different strengths and character. BH(CO) 2 and BH(CNH) 2 , and their fluorosubstituted analogues BF(CO) 2 and BF(CNH) 2 , engage in a typical noncovalent bond with B(CH 3 ) 3 and BF 3 , with interaction energies in the 3-8 kcal/ mol range. Certain other combinations result in a much stronger diboron bond, in the 26-44 kcal/mol range, and with a high degree of covalent character. Bonds of this type occur when BH 3 is added to BH(CO) 2 , BH(CNH) 2 , BH(N 2 ) 2 , and BF(CO) 2 , or in the complexes of BH(N 2 ) 2 with B(CH 3 ) 3 and BF 3 . The weaker noncovalent bonds are held together by roughly equal electrostatic and dispersion components, complemented by smaller polarization energy, while polarization is primarily responsible for the stronger ones.