Are One-Electron Bonds Any Different from Standard Two-Electron Covalent Bonds?

The nature of the chemical bond is perhaps the central subject in theoretical chemistry. Our understanding of the behavior of molecules developed amazingly in the last century, mostly with the rise of quantum mechanics (QM) and QM-based theories such as valence bond theory and molecular orbital theory. Such theories are very successful in describing molecular properties, but they are not able to explain the origin of the chemical bond. This problem was first analyzed in the 1960s by Ruedenberg, who showed that covalent bonds are the direct result of quantum interference between one-electron states. The generality of this result and its quantification were made possible through the recent development of the generalized product function energy partitioning (GPF-EP) method by our group, which allows the partitioning of the electronic density and energy into their interference and quasi-classical (noninterference) contributions. Furthermore, with GPF wave functions these effects can be analyzed separately for each bond of a molecule. This interference energy analysis has been applied to a large variety of molecules, including diatomics and polyatomics, molecules with single, double, and triple bonds, molecules with different degrees of polarity, linear or branched molecules, cyclic or acyclic molecules, conjugated molecules, and aromatics, in order to verify the role played by quantum interference. In all cases the conclusion is exactly the same: for each bond in each of the molecules considered, the main contribution to its stability comes from the interference term. Two-center one-electron (2c1e) bonds are the simplest kind of chemical bonds. Yet they are often viewed as odd or unconventional cases of bonding. Are they any different from conventional (2c2e) bonds? If so, what differences can we expect in the nature of (2c1e) bonds relative to electron-pair bonds? In this Account, we extend the GPF-EP method to describe bonds involving N electrons in M orbitals (N < M) and show its application to (2c1e) bonds. As examples we chose the molecules H, HC·CH, BH, [Cu·BH(PH)], and an alkali-metal cation dimer, and we evaluated the components of the electronic energy and density, which account for the formation of the bond, and compared the results with those for the respective analogous molecules exhibiting the "conventional" two-electron bond. In all cases, it was verified that interference is the dominant effect for the one-electron bonds. The GPF-EP results clearly indicate that molecules exhibiting (2c1e) bonds should not be considered as special systems, since one- and two-electron bonds result from quantum interference and therefore there is no conceptual difference between them. Moreover, these results show that quantum interference provides a way to unify the chemical bond concept.