Researchers at Brown University have produced the first direct experimental evidence that the textbook triple-bond structure breaks down in heavy elements, where the rules of Einstein’s relativity take over.

Atoms form bonds by sharing electrons, the negatively charged particles that orbit atomic nuclei. Each atom shares one electron to form a bonding pair, and the strong negative charge of that pair attracts the two positively charged nuclei, holding them together. Some elements share more than one electron pair, forming double or triple bonds.

The textbook picture of a triple bond involves two different types of bonds: one sigma bond and two pi bonds. The sigma bond is a strong, “head-on” bond that occurs along an imaginary horizontal axis between nuclei, while the two pi bonds are somewhat weaker, “side-by-side” bonds that wrap around the sigma bond.

When Electrons Approach the Speed of Light

That picture works for lighter elements, but toward the bottom of the periodic table, where atomic nuclei get heavier, things get messy. The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, a regime where the rules of Einstein’s theory of relativity become important.

In that relativistic regime, an electron’s spin — the magnetic moment that points either up or down — and the electron’s orbit are no longer independent of each other, a state known as spin-orbit coupling. That coupling changes the rules for how electrons interact, disrupting the strict separation between sigma and pi bonds.

“The boundary between a sigma bond and a pi bond is now sort of smeared. We still have three bonds, but we don’t really strictly have a sigma or a pi anymore,” said Lai-Sheng Wang, a chemistry professor at Brown University.

Testing the Theory with Bismuth

To find evidence for this bonding hybridization, Wang and his team, led by Brown Ph.D. students Deniz Kahraman and Jie Hui, formed molecules made from bismuth and carbon. Bismuth is a heavy element, sitting right next to lead on the periodic table, where relativistic effects should be significant. After cooling the molecules to near absolute zero, the team analyzed them using photoelectron spectroscopy, a technique that uses a laser to knock individual electrons out of their positions in the molecule. The distance each electron flies tells researchers how strongly it was bound.

The resulting photoelectron spectrum showed that the carbon-bismuth bonds did not fit the traditional triple-bond picture of one sigma and two pi bonds. Instead, the structure looked more like one pi bond and two hybrid sigma-pi bonds.

Wang says the experimental verification of this relativistic structure may spur a rewriting of chemistry textbooks, especially as heavy elements — bismuth in particular — draw more research interest. Bismuth could serve as an alternative to toxic lead in next-generation solar cells, and it has also drawn interest in research related to quantum materials and quantum computing.

“Maybe this will become the new textbook idea as we are dealing with more heavy elements,” Wang said.

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Journal: Science
Article Title: Relativistic collapse of the classical triple bond in the CBi− molecular ion
DOI: 10.1126/science.aei1285
Funding: U.S. National Science Foundation (CHE-2403841); U.S. Department of Energy (DE-SC0008501)