The chemical structure of the ground state of C2 has been the subject of intense debate after the suggestion that the molecule could exhibit a "fourth" covalent bond. In this paper, we investigate this problem explicitly avoiding all the points of conflict from the previous papers to show that there is no quadruple bond in C2. The generalized product function energy partitioning (GPF-EP) method has been applied to calculate the interference energy (IE) that accounts for the formation of covalent bonds for each bond of the molecule. The IE analysis shows that for the standard σ and π bonds interference exhibits the expected behavior, while for the "fourth" bond interference is a destabilizing factor. To make sure this could not be attributed to a new kind of bond, we performed an equivalent analysis for the (3)Σ(-) excited state of C3 molecule in which similar "bonding" occurs between the two ending carbon atoms. We also show that the difference in force constants of C2 and acetylene can be rationalized in terms of the amount of charge density in the internuclear region by looking at the changes in the overlaps between orbitals along the bond axis.

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.

The formation of one-electron bonds follows the same mechanism as the regular covalent bonds. It is the same phenomenon, quantum interference, that rules the stabilization of systems containing such bonds and there is no distinction between one- and two-electron bonds from the conceptual point of view. The difference in the BDEs of the one- and two electron bonds has no relation with bond order. One-electron bonds are not “half-bonds”.

The analysis of the chemical bond in a variety of systems exhibiting distinct bonding patterns was performed using the Generalized Product Function Energy Partitioning (GPF‐EP) approach in order to verify the role played by quantum interference. Diatomic and polyatomic molecules, with single, double and triple bonds, with different degrees of polarity, linear or branched, cyclic or not, conjugated and aromatics, have been considered. In all cases the conclusion was exactly the same: for each bond of the molecule the energy partitioning results showed that the main contribution to the depth of the potential wells comes from the interference term. From the quantum interference perspective the minimum requirement for a chemical bond to be formed is one electron and two interfering one‐electron states belonging to different atoms. As a consequence, all chemical bonds are covalent in the sense that it takes a one‐electron state of each atom to form the bond, irrespective of its polarity.

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