Making sense of motion on a quantum scale isn’t easy, but a new mathematical theory developed by scientists at Rice University and the University of Oxford could help — and could provide some insight into the motion. improvement of various computer, electrochemical and biological systems.
The theory developed by Rice theorist Peter Wolynes and Oxford theoretical chemist David Logan gives a simple prediction of the threshold at which large quantum systems change from orderly motion like clockwork to random, erratic motion like moving asteroids. in the early solar system. Using computer analysis of a model of photosynthesis, collaborators at the University of Illinois at Urbana-Champaign have shown that the theory can predict the nature of the movements of a chlorophyll molecule when it absorbs energy from sunlight.
The theory applies to any sufficiently complex quantum system and can provide insight into building better quantum computers. It could also, for example, help design the characteristics of next-generation solar cells or perhaps extend battery life.
The study is published this week in the Proceedings of the National Academy of Sciences.
Nothing is ever completely still at the molecular level, especially when quantum physics plays a role. A drop of water shining on a leaf may seem motionless, but inside, more than a sextillion molecules vibrate non-stop. Hydrogen and oxygen atoms and the subatomic particles they contain — nuclei and electrons — are constantly moving and interacting.
“Thinking about the motions of individual molecules on a quantum scale, there’s often this comparison to how we think about the solar system,” Wolynes said. “You learn that there are eight planets in our solar system, each with a well-defined orbit. But in fact, the orbits interact with each other. Nevertheless, the orbits are very predictable. You can go to a planetarium, and they’ll show you what the sky was like 2,000 years ago. Many movements of atoms in molecules are just as regular or clock-like.
When Wolynes and Logan first posed the question of predicting the regularity or randomness of quantum motion, they tested their calculations against observations of vibrational motions in individual molecules.
“You only need to know two things about a molecule to be able to analyze its quantum motion patterns,” Wolynes said. “First, you have to know the vibrational frequencies of its particles, that is, the frequencies at which the vibrations that are like the orbits occur, and, second, how those vibrations interact nonlinearly with each other. others. These anharmonic interactions mainly depend on the mass of atoms. For organic molecules, you can predict how well these vibrational orbits would interact with each other. »
Things get more complicated when the molecules also change their structure radically, for example as a result of a chemical reaction.
“As soon as we start looking at molecules that react chemically or rearrange their structure, we know that there is at least an element of unpredictability or randomness in the process because, even in classical terms, the reaction occurs or does not occur. “said Wolynes. “When we try to understand how chemical changes occur, there is this question: is the overall movement more like a clock or is it more irregular? »
Besides their uninterrupted vibrations, which occur without light, electrons can have quantum-level interactions that sometimes lead to a more dramatic twist.
“Because they are very light, electrons normally move thousands of times faster than the centers of atoms, the nuclei,” he said. “So although they are constantly in motion, the orbits of the electrons smoothly adjust to what the nuclei are doing. But once in a while, the nuclei come to a place where the electronic energies will be almost equal whether the excitation is on a molecule or on the surface. This is called a surface crossing. At this time, excitement has a chance to jump from one electronic level to another.
Predicting how the energy transfer that takes place during photosynthesis changes from orderly motion to randomness or dissipation would take a lot of time and effort by direct calculation.
“It’s great that we have a very simple formula that determines when this happens,” said Martin Gruebele, a chemist at the University of Illinois Urbana-Champaign and co-author of the study which is part of the joint Rice-Illinois study. Center for Adapting Flaws into Features (CAFF) funded by the National Science Foundation. “It’s something we just didn’t have before and figuring it out required very long calculations. »
The Logan-Wolynes theory opens a wide range of scientific research ranging from theoretical exploration of the fundamental principles of quantum mechanics to practical applications.
“The Logan-Wolynes theory worked pretty well in telling you roughly what energy input you would get from a change in the behavior of the quantum system,” Wolynes said. “But one of the interesting things that the large-scale calculations by (Chenghao co-author) Zhang and Gruebele found is that there are these exceptions that stand out from all the possible orbit patterns you might have. Sometimes there are a few laggards where simple movements persist for long periods of time and don’t seem to become random. One of the questions we will address in the future is to what extent this persistent regularity actually influences processes like photosynthesis.
“Another direction Rice is pursuing where this theory can help is the problem of making a quantum computer that behaves as synchronously as possible,” he said. “You don’t want your computers changing information randomly. The larger and more sophisticated you build a computer, the more likely you are to encounter some sort of randomization effects. »
Gruebele and his collaborators in Illinois also plan to use these ideas in other scientific contexts. “One of our goals, for example, is to design better human-built light-harvesting molecules, which could consist of carbon dots capable of transferring energy to their periphery where it can be harvested” , said Gruebele.
Wolynes is Rice’s Bullard-Welch Foundation Professor of Science and Professor of Chemistry, Biochemistry and Cell Biology, Physics and Astronomy and Materials Science and Nanoengineering and Co-Director of its Center for Theoretical Biological Physics (CTBP), which is funded by the National Science Foundation. Logan is Coulson Professor of Theoretical Chemistry at Oxford. Gruebele holds the James R. Eiszner Chair in Chemistry and Zhang is a graduate student in physics at the University of Illinois at Urbana-Champaign.
The James R. Eiszner Chair in Chemistry and the Illinois Department of Physics, Rice’s Bullard-Welch Chair (C-0016), and the National Science Foundation (PHY-2019745) supported the research.