Theory of the two-center bond

Tight-binding theory, with universal parameters, provides direct prediction of bond energies, bond lengths, and force constants for ordinary molecular and solid-state two-center bonds. Corrections, which are dominated by nonorthogonality of orbitals on neighboring atoms, are included and are seen to be given approximately by a two-body repulsion proportional to the inverse fourth power of internuclear distance. The bond properties depend upon metallicity, increasing in a series such as C, Si, Ge, and Sn, and are strongly affected by the coupling between the bond and its environment at high metallicity. This effect, called metallization, is calculated in perturbation theory. The properties depend also strongly upon the polarity of the bond and upon the decrease in the effect of metallization with increasing polarity. Finally, the properties depend upon bond order. This effect is characterized by a $\pi$-bonding strength, which for a resonating bond is enhanced by a factor of the square root of the number of sites between which the bond resonates. Formulas are derived for the bond energies, lengths, and force constants in terms of these parameters and are compared with experiment.