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Little Interactions Mean a Lot

Noncovalent bonds are weaklings compared to familiar chemical reactions, but they add up to strongly influence the shape and behavior of molecules.

Roald Hoffmann

2014-03PerspectiveF1p95.jpgClick to Enlarge ImageI used to like my energies big. Strong chemical bonds and large energetic reactions are dramatic and easy to observe and understand. They make fire burn and drive much of industrial chemistry. But a lot of the world around us and inside us works on more subtle atomic and molecular interactions that operate on energy scales 10 or 100 times smaller.

Consider the following phenomenon: You dip a paintbrush into water, or watch Esther Williams jump into a pool—as she often did with staged abandon, wonderfully coiffed, when I grew up and first went to the movies. (If Esther Williams means little to you, substitute the singer Rihanna.) When the paintbrush or Esther emerge from the water, their hairs, to put it colloquially, are stuck together. The first instinctive reaction is to say that the hair clumps up and that the brush acquires its point because they are wet. But hold on: Look at the brush while it is in the water—the hairs remain apart, and you can’t get wetter than that!

So, it’s not wetness that makes the hairs clump. Rather, it’s the small hydrogen bonding forces between water molecules, which are greater in number when as many water molecules as possible are near each other. The macroscopic manifestation of this bonding is called surface tension: It’s why water droplets form in clouds, and it’s what allows whirligig beetles to scoot on the surface of ponds. It’s what C. V. Boys calls “the skin of the water” in his wonderful 1911 book Soap Bubbles: Their Colors and Forces which Mold Them, which Ben Widom brought to my attention. The energy of hair plus water is lower when the hairs clump together; the small hydrogen bonding forces that bring water molecules together carry along the hair strands with them.

Such weak, or noncovalent, bonds are ubiquitous, and their prevalence gives them a power that belies their modest nature. In water, they influence the global geology and climate of the Earth. In organic molecules, they regulate how proteins fold and hold together DNA’s double helix. Despite my partiality for big energies, the power of accumulated small energies have prompted me to question my prejudices.

The Cumulating Logic of the Small

What is big from one perspective is small from another, and energy can be measured in a variety of ways. By “big energies,” I mean those equal or greater than about 1 electron volt per molecule, which is equal to 23.1 kilocalories per mole, or 96.5 kilojoules per mole. A photon of yellow light has an energy of about 2.1 electron volts.

In theoretical chemistry, I was looking for molecules that in one bonding arrangement could be at least 1 electron volt per molecule more stable than in an alternative configuration, or that would require an activation energy (the barrier to a reaction taking place) that is at least 1 electron volt lower than a competing reaction, thus proceeding much more expeditiously. I knew that the strength of the hydrogen bonds that hold together the base pairs of the DNA in my body are, per pair of atoms involved, at least an order of magnitude smaller than 1 electron volt. So are the “dispersion” forces (more on these in a moment) that make the molecules around me—be they acetaminophen or ethanol—solids and liquids rather than gases.

Quantum mechanics, through accurate solution of Schrödinger’s wave equation for the energies of the matter waves, is needed to describe theoretically the reactants and products in a chemical reaction. I think the reason I favored the large gobs of energy was that my way of solving Schrödinger’s equation was … lousy. (I’m just a quantum mechanic—it comes with the chemistry.) I could only get approximate energies, plus or minus an electron volt of the solution. For energetic reactions that is good enough.

Yet I knew that energies much less than 1 electron volt could make a big difference in fundamental molecular processes, such as making functional proteins. Every molecule solves Schrödinger’s equation exactly, without worrying about it. Nature’s way of exercising decisive control is through the accumulation of many small differences. Once proteins of some complexity (containing more than 100 amino acids) became the toolkits for making and breaking bonds, then small differences in the folding and variations in the kit components (the amino acid sequence) create local environments (active sites) that are exquisitely tunable.

Through accumulation of small interactions, Nature creates an effective qualitative difference in the rate of cleavage of a carbon–carbon bond (C–C), the geometry of binding oxygen (O2), or the firing of a nerve signal. There is room in biology for large dollops of energy: Witness the two photons used in photosynthesis. But soon even that large influx of energy is partitioned in a cascade of many small reactions. This partitioning maximizes efficiency for the overall process, getting the energy of the photons into the energy courier of the cell, adenosine triphosphate (ATP).

Even if I was unable to calculate energies exactly, I’ve grown to appreciate the cumulating logic of the small. The wondrous world of the unromantic diminutive adding up to something big is increasingly important as the applications of nanotechnology and the potential for quantum computing unfold.

People Argue about Small Energies

In addition to the hydrogen bonding mentioned earlier, there are other small forces, like multipole interactions that convert an asymmetry of the way electrons are distributed in a molecule into forces between them. And dispersion forces, which are responsible for molecules and atoms condensing and eventually freezing. These are all essential, small, structure-determining factors called noncovalent interactions, to distinguish them from “real” chemical covalent (or ionic) bonds, which are 10 or more times stronger. For example, the covalent bonds that hold methane (CH4) together are achieved when each hydrogen atom shares an electron with the carbon atom; these bonds are much stronger than the hydrogen bonds that cause wet hair to stick together, and so it takes much more energy to break apart methane than strands of hair held together with bonds between water molecules.

There are volumes written on each noncovalent force, and yet people still disagree on their origins and even more vehemently on the relative contribution of the interactions mentioned above to the energy of the molecule as a whole. The energies involved in such interactions are characteristically small, tending to be less than 5 kilocalories per mole of atom pairs involved. I don’t want to lump them together; they are so interestingly different. But here I must, while saying just a few fuzzy words on two of them in particular.

Dispersion forces are also called van der Waals interactions. German American physicist Fritz London provided the quantum-mechanical view of these in 1930, so sometimes they are referred to as London dispersion forces. Their physical origin is in the correlated motions of the electrons in two interacting atoms or molecules: A fluctuation in the electron distribution in one induces a local asymmetry of electrons in the other. Carefully averaged over space and time, an attraction emerges that falls off as 1/R6, where R is the separation between the nuclei of the atoms involved.

Dispersion forces can be tiny, as is the case for two helium atoms, which is why helium cannot be frozen at ambient pressure, or large for big molecules, such as the alkanes in candle wax or aspirin. (The forces are related roughly to the number of “exposed” atoms capable of coming close to each other). However big they are, the 1/R6 falloff ensures that they are relevant only when atoms get close to each other. But not too close, because then they repel each other.

Prototypical hydrogen bonding, the noncovalent bond associated with wet hair and brushes, occurs when the hydrogen of a polar oxygen–hydrogen (O–H) or nitrogen–hydrogen (N–H) bond comes near an electron source, typically the lone pair of electrons of a nearby oxygen or nitrogen atom. The chemistry community sees these bonds most commonly as the result of an ionic attraction between the positively charged hydrogen (in the N–H or O–H bond) and the negatively charged electrons of the lone pair on a nearby N or O. (I don’t agree, but that is a story to be told elsewhere.)

Despite such disagreement on origins, there is no disagreement at all on the magnitude of the energy involved, generally less than 5 kilocalories per mole. Small again, but there are oh-so-many of them.

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