A 45-year-old prediction about the formation of triatomic molecules has been confirmed for the first time, creating molecules that scale in neat geometric ratios, and that might theoretically go on forever.
The existence of scalable three-atom molecules was predicted by Vitaly Efimov in 1970, as part of his work to predict the behaviour and energy states of molecules with more than two particles. His work showed mathematically that in three-particle systems, bound states can exist even when no two particles are attracted strongly enough to form a pair.
Efimov predicted that forces between any two particles in a three-particle system would “give rise to a series of levels” that could shape either molecules or the nuclei of certain atoms. Each of these levels would have different energy, and when applied to molecules, this should translate to different sizes.
In 2006, signs were found of the first Efimov state molecule, followed three years later by a second level. However, it is only now that the third level has been observed, allowing confirmation of one of Efimov's key predictions – that the energy levels would scale geometrically.
In Physical Review Letters, Professor Cheng Chin of the University of Chicago announced the discovery of three Efimov states, which are probably just the beginning of an infinite chain. The molecules used had two caesium atoms and a single lithium atom, cooled to one five-millionth of a degree of absolute zero (-273.15°C).
The molecules' “sizes are measured to be 17, 86 and 415 nano-meters, respectively,” Chin said. Each is 4.9 times as large as the previous one, confirming Efimov's geometric scaling prediction, and close to the predicted value of 4.88.
Credit: Cheng Chin group, University of Chicago. Relative sizes of the three triatom molecules produced to confirm the theory of geometric scaling.
The sequence should theoretically continue to the size of the universe, although the larger the molecule, the harder it will be to produce. The first Efimov state molecule was made of three caesium atoms. However, Chins says, "The difficulty is that based on what we understand of Efimov's theory, the scaling factor is predicted to be 22.7 for the caesium system, which is a very large number." Required temperatures are approximately proportional to the inverse square of the size.
Modeling suggests that molecules where one atom is much lighter than the others should have a smaller scaling factor and therefore be produceable in successive states in relative warmth. The caesium isotope used was 22 times as heavy as the lithium. The difference helped with size and temperature, but also made the molecules harder to work with. Lead author Dr. Shih-Kuang Tung described the challenge of working with such different atoms as like dangling a monkey and two elephants on strings and making them interact.
The interactions were controlled using Feshbach resonance, where two types of motion are coupled, which is a technique used on other very cold systems. Tung says this was, “A really important tool for us. We needed to tune the Feshbach resonances very carefully in order to generate these Efimov molecules.”
where two types of motion are coupled, a technique used on other very cold systems.