Researchers in the United States and China have published results for ultra-cold potassium rubidium dimers, showing for the first time how quantum effects cause deviations from the quantum statistical model, one of the canonical theories of physical chemistry.

Chemical reactions are basically highly complex quantum transformations from one set of electronic orbitals to another, but the equations required to model reactions on that basis usually go beyond what we can solve. Chemists therefore rely on several approximations to determine the reaction path.

When atoms or molecules react, the products can be made in a variety of translational, rotational, vibrational, and energetic quantum states. Which state is created depends on how the energy in the states of the reactants affects the transient intermediate complexes that form for a fraction of a second. These intermediate complexes can have hundreds of different quantum states, many of which lead to the same product state. A common assumption in reaction dynamics is that every intermediate quantum state is equally likely. The more intermediate quantum states lead to a certain product state, the more likely the product state becomes.

In their latest study, Kang-Kuen Ni from Harvard University and colleagues cooled potassium rubidium dimers (KRb) in an optical trap to their quantum ground states – close to absolute zero. When two KRb dimers collide, they can react to form a separate potassium (K)2) and rubidium (Rb2) Molecules. This reaction is exothermic and can take place spontaneously even at 500 nK. The researchers mapped the statistical distribution of the 57 possible quantum states of the products, correlated products from the same reaction, and examined where the results deviated from statistical predictions.

An image with two charts, the left is a 3D bar chart with some of the bars on the back of the chart sticking out over all the others, while the right is a 2D chart of lighter and darker boxes with numbers overlaid

The researchers found that a state in which the products have a very high angular momentum was strongly suppressed. They believe that this is because with so much energy flowing into the rotations of the products, there is not enough translational kinetic energy for the molecules to escape their potential well and break apart. The reaction could therefore never be completed. Apart from this extreme example, product states in which the product dimers have high – and very similar – angular momentum were preferred over the statistical model. The reasons for this remain uncertain, however, as the team was unable to run a full quantum simulation to predict the results.

This is next on their list. The researchers now plan to investigate a simpler system in which an atom reacts with a molecule. “In this case, an accurate calculation is easier,” says Ni. “If we could achieve the same level of detail in a system in which the theory is understandable, we could see whether the experiment and theory match.”

Ultra-cold chemist Matthew Frye of Durham University in the UK believes the work is a significant step. “It’s a wonderful experiment that Kang-Kuen created, and the simultaneous detection of the two product states is remarkable,” he says. “It allows us to peel off more layers of onion in the chemical reaction and remove layers of averaging. It’s really a state-to-state thing now.”

“Your ordinary chemist in the lab, where most things are in the solid or liquid phase, probably won’t run into it that often,” says Frye. “But in things like atmospheric chemistry and space chemistry, those theories could be very important.”

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