For most people, the weak, short-range attractions known as van der Waals forces are something chemistry teachers use to account for deviations from the ideal gas law. These forces, which consist of attractions between various kinds of dipoles, also come to the fore when we hear explanations of how geckos manage to climb smooth walls and even race across smooth ceilings.

More significant, however, may be the contribution of van der Waals forces to the behavior of complex molecules, particularly biomaterials such as proteins. Alas, van der Waals forces at the molecular scale are hard to measure, much harder than the van der Waals forces that influence the behavior of single atoms or macroscopic objects. Scientists interested in the intermediate, molecular scale typically make do with estimates based on theory, and these estimates have been used in simulations of biochemical events.

Are the simulations off? Could they be improved? Hard to say. But it may become easier to answer such questions now that researchers at Forschungszentrum Jülich’s Peter Grünberg Institute (PGI) have developed a method of measuring the attractive potential between differently sized organic molecules and a metal surface using an atomic force microscope.

“Using our method, we determined the van der Waals force for the first time for single molecules throughout a larger distance range,” said Christian Wagner, Ph.D., a PGI physicist.

Dr. Wagner is the first author of an article by PGI researchers that appeared November 26 in Nature Communications (“Non-additivity of molecule-surface van der Waals potentials from force measurements”). The article explains that the measurements taken by the researchers largely agree with theoretical predictions. For example, the measurements confirm that binding strength decreases with the cube of the distance—which explains the extremely small range of the interaction. The measurements also reveal that the bigger the molecule, the stronger its attraction to the surface. In reality, this effect is even stronger than simple models predict and also than would be intuitively assumed.

“The experiment allows testing the asymptotic vdW force law and its validity range,” wrote the authors. “We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules.”

“Usually, only the interaction of all those atoms involved is added together. But the van der Waals forces that we measured are 10% higher than this,” noted Dr. Wagner.

What is the reason for the superlinear increase? The van der Waals force, to put it simply, emerges due to the displacement of electrons in the shells of atoms and molecules, caused by quantum fluctuations, which leads to a weak electrical attraction. In the case of larger molecules, more atoms are involved as each of these molecules also comprises more atoms. And on top of this, each and every atom contributes more strongly.

“As large organic molecules often form electron clouds that stretch across the entire molecule, they offer electrons considerably more room to maneuver than a single atom,” explained the PGI researcher group’s leader, Ruslan Temirov, Ph.D. “This makes them easier to displace, which overproportionally increases the electrical attraction.”

For the measurements, the scientists affixed complex organic carbon compounds, which they had attached to a metal surface, to the tip of an atomic force microscope. They had secured this tip in turn to a vibration sensor so that the tip moved back and forth rapidly, a bit like a tiny tuning fork. When the molecules are removed from the surface, this vibrational frequency alters, allowing conclusions to be drawn in relation to the van der Waals forces, even when the tip is withdrawn a few molecule lengths (about 4 nanometres) from the surface.

The values determined are particularly interesting for simulation calculations using density functional theory, the development of which was honored with the Nobel Prize in 1998. The technique is the most commonly used method today for calculating the structural, electronic, and optical properties of molecules and solids. Despite its many advantages, it still has problems correctly predicting the van der Waals forces.

“This non-additivity is of general validity in molecules and thus relevant at the intersection of chemistry, physics, biology and materials science,” concluded the authors of the Nature Communications article. “As non-additive contributions (which can amount to several eV in biomolecules) cannot, by construction, be accounted for in state-of-the-art density functional calculations, we suggest further development in that direction.”

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