The chemical bond: The biggest chemical paradigm, or the greatest chemical uncertainty?

The chemical bond is the bedrock of chemistry, the central idea behind our understanding of molecules and reactivity; some may even consider it the biggest chemical paradigm. Every question and every answer in every chemical experiment makes sense only in terms of the existence of chemical bonds. Most lines drawn in chemistry schemes denote bonds; all chemical reactions involve breaking and making bonds; and for the most part, our chemical thinking patterns work under the assumption that the chemical bond is there. This is true for organic, inorganic, physical, analytical, biological, theoretical, or any other branch of chemistry. Moreover, if we do not deal with bonds in a research laboratory, we may say that it is not a chemical laboratory.

Fig. 1 The Laplacian of the electronic density, and a molecular orbital of a novel ring system based on dative bonds. These are some of the possible descriptors of the putative chemical bond.

There are strong bonds and weak bonds; we have covalent bonds, ionic bonds, and non-covalent bonds; we have hydrogen bonds, halogen bonds, coordinative bonds, dative bonds, four-electrons-three-center bonds, collective bonds, London interactions, hydrophobic bonds, σ-hole interactions, charge-shift bonds, and even pancake bonds for the food-oriented chemist. And the list is growing by the day. The amount of inter- or intramolecular interactions can easily fill a deck of cards.

And yet, we have a big issue. One that might take the podium as “the hard problem in chemistry”. Simply put, the challenge is how to define the chemical bond.¹ There are good definitions, but they are not complete.^2,3 They suffer from false positives and false negatives, leaving out interactions that every chemist would include, and leaving in cases that should not be considered as bonds.

The first and broadest definition of the bond is as an attractive force between atoms. Basically, if we stretch the distance between two atoms and the energy of the system rises, then there is a chemical bond. This is extremely comprehensive, covering any possible type of interaction. We may say that it is too comprehensive. Consider the case of a nanocrystal, such as a tiny diamond where all neighbor carbons are bonded in a large arrangement of covalent bonds. If we stretch the distance between carbon atoms positioned at opposite corners of the structure, separated by nanometers (a huge distance on molecular scales), the geometry will be distorted, and the energy will go up. Does this mean that there is a real chemical bond between any pair of atoms in the crystal? Every chemist will say this is nonsense, since there are no meaningful chemical bonds beyond a single digit number of angstroms, not even non-covalent interactions. Moreover, this definition is not explanatory, as it tells us that there may be a bond, but it does not tell us what a bond is.⁴

Another rather obvious definition that actually describes the bond is the structural definition. It says that the chemical bond occurs if there is a build-up of electronic density. In other words, if the electrons prefer to be arranged and localized right between atoms, then there is a bond. This can truly be observed, at least in terms of quantum mechanics, since there is a Hermitian operator for the density. Indeed, certain microscopic techniques can detect this electron concentration where we expect to see a bond. This is a big plus for the structural definition, as it depicts a physical entity. In this sense, it also answers the question of what a bond is, which the previous definition was lacking. It also matches the old Lewis model of electron pairs for covalent bonds, which is a nice touch for chemists. Indeed the structural definition is a good definition. Sadly, some very important chemical bonds, such as ionic and electrostatic interactions, do not exhibit any electronic density build-up, making this definition irrelevant for such cases. In essence, this is not a complete definition.

Beyond these, we can define a chemical bond according to molecular orbitals or valence bond structures. These give us mathematical (or, more accurately, computational) ways of finding and explaining bonds right up to their wavefunction roots. These are useful and elegant definitions, with a couple of caveats. First, similar to the structural definition, they do not have a simple description of van der Waals interactions. Moreover, there are no orbitals involved in ionic bonds. But more importantly, strictly speaking orbitals and valence bond structures are not quantum observables, and therefore we cannot say that they truly exist (another heavily discussed philosophical topic).

It might be possible to find other definitions for the chemical bond, which I bet will also be incomplete. How can all our chemical world be standing on such relatively “flimsy” definitions? Essentially, because they are working definitions, in the sense that they work for most intents and purposes. In this sense, they can be taken more as models or as a pattern⁴ than as definitions.

Similar to many other fuzzy concepts in chemistry,⁵ we might have to live with the fact that the bond cannot be fully defined, labelled, and categorized in a single, foolproof way, even if this is a key concept in chemistry. There are just too many types of bonds with significantly different natures, each one requiring different descriptions and partial definitions. Like the short blanket dilemma, if we try to cover all cases of one type of bond (such as the covalent one), we will leave too many other bonds uncovered (such as the ionic case). This sometimes leaves the recognition of “gray-area” bonds in the eye of the beholder. Personally, I enjoy describing the chemical bond under the IKIWISI principle (“I know it when I see it”).

(1)        Kozuch, S. Do We Know the Chemical Bond? A Case for the Ethical Teaching of Undefined Paradigms. Chem. Teach. Int. 2024, 6 (4), 445–462. https://doi.org/10.1515/cti-2024-0113.

(2)        Hendry, R. F. Two Conceptions of the Chemical Bond. Philos. Sci. 2008, 75 (5), 909–920. https://doi.org/10.1086/594534.

(3)        Weisberg, M. Challenges to the Structural Conception of Chemical Bonding. Philos. sci. 2008, 75 (5), 932–946. https://doi.org/10.1086/594536.

(4)        Seifert, V. A. The Chemical Bond Is a Real Pattern. Philos. sci. 2022, 1–47. https://doi.org/10.1017/psa.2022.17.

(5)        Gonthier, J. F.; Steinmann, S. N.; Wodrich, M. D.; Corminboeuf, C. Quantification of “Fuzzy” Chemical Concepts: A Computational Perspective. Chem. Soc. Rev. 2012, 41 (13), 4671. https://doi.org/10.1039/c2cs35037h.