Einstein Was Right Even in Chemistry: How the Structure of Triple Bonds Changes

A group of chemists from Brown University has dismantled one of the cornerstones taught in general chemistry courses: the structure of triple bonds in heavy elements. The study, published in the journal Science, demonstrates that when the atomic nucleus exceeds a certain mass, the effects of Einstein's relativity alter the electronic geometry of the bond, erasing the clear boundary between the two types of bonds predicted by classical theory.

The textbook model describes a triple bond as the sum of one sigma bond, frontal and robust, and two pi bonds, weaker and arranged laterally around the first. For light elements, this description has held for decades. The problem emerges when moving down to the bottom of the periodic table, where nuclear mass increases and the orbiting electrons reach speeds close to that of light.

At that regime, spin-orbit coupling comes into play, a phenomenon where the electron's spin and its orbital motion cease to behave as independent variables. Lai-Sheng Wang, a chemistry professor at Brown and corresponding author of the research, clarifies: the idea that relativity matters in heavy elements has been circulating since the 1970s, but up until now, direct experimental proof was lacking.

To obtain it, Wang and his group, led by PhD students Deniz Kahraman and Jie Hui, synthesized molecules composed of carbon and bismuth, a heavy element that occupies the box immediately preceding lead in the periodic table. After cooling them to temperatures near absolute zero, the researchers analyzed them with photoelectron spectroscopy, a technique that uses a laser to eject single electrons from the molecule and measure their bond strength based on the distance traveled.

The photoelectron spectrum redraws the structure of the triple bond.

The collected spectrum does not correspond to the classical signature of one sigma and two pi bonds. The observed structure resembles rather a pure pi bond alongside two sigma-pi hybrid bonds, a direct consequence of the merging of the two categories caused by spin-orbit coupling. Wang describes the situation as a "frosted" boundary between sigma and pi: the three bonds remain, but no longer adhere to the clear separation predicted by non-relativistic theory.

The experimental confirmation comes while bismuth gains attention far beyond academic chemistry. The element is being studied as a non-toxic alternative to lead in next-generation solar cells, as well as in quantum materials and quantum computing research. Wang does not rule out that the results may end up necessitating a revision of textbooks as the chemistry of heavy elements gains ground in applied research.