Featured Lendület Researcher: Edit Mátyus
Although quantum electrodynamics is considered a well-established theory in physics, in chemistry – in the world of atoms and molecules – it still raises a number of unresolved questions. Edit Mátyus, Doctor of the Hungarian Academy of Sciences, Professor in the Department of Physical Chemistry at Eötvös Loránd University, and head of the Molecular Quantum Electrodynamics Research Group, and her colleagues are attempting to answer these questions with the support of the Momentum Programme.
In their research, Mátyus and her research group apply the methods and approaches of relativistic quantum electrodynamics (QED) to molecular systems. According to the research group leader, although physicists believe that the theory reached its peak in the middle of the last century and has since become well established, it can still be useful in studying a number of unsolved problems in the field of atomic and molecular systems. “I am a chemist, and I am really interested in atoms and molecules. I have come to realise that although QED is considered a fully developed theory in physical terms, we cannot currently apply it to the molecular domain,” said Mátyus. “At the same time, we are seeing more and more relativistic “effects” in molecular experiments. Currently, we can make statements and perform calculations about atoms and molecules using a non-relativistic approach within the framework of Schrödinger’s equation, but we do not know how to go beyond this non-relativistic approach.”
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Mátyus EditPhoto: ttk.elte.hu
According to the researcher, the field of quantum chemistry has accumulated a vast body of knowledge, and its methods are routinely used by experimental and theoretical research groups around the world. Until recently, however, most quantum chemists have maintained that, even if there are relativistic or even QED effects in this field, their significance is generally negligible. However, more and more experimental results are emerging that refute this belief,
as they show that these effects do indeed play an important role in understanding the behaviour of molecules.
In the case of compounds of elements in the lower rows of the periodic table, there is now a consensus that relativistic effects must be taken into account in order to interpret their behaviour.
Is there a wave equation beyond the Schrödinger equation?
“If I had to sum up the most important question investigated by our Momentum research group, it would be: ‘Is there a wave equation beyond the Schrödinger equation?’”, said Mátyus. “We are looking for an equation (approximate and systematically improvable) that is compatible with the physics of the 1950s and can also be used for atomic and molecular systems, building on the tools of quantum chemistry.”
The researcher first encountered this problem, which falls within the scope of relativistic quantum mechanics and relativistic quantum chemistry, more than a decade and a half ago, and has been searching ever since for an equation that is as robust as the Schrödinger equation and can be used to develop (approximate) computer algorithms to answer various chemical questions. “There was a time when I began to think that such an equation might not exist, but in the last few years we have found evidence that it might exist after all, so now we have some leads that my research group and I can follow,” the chemist continued. “Our research is based on relativistic QED, but it is important to us that our results and the methodology we have developed remain compatible with applied quantum chemistry. Ultimately, we are developing equations and computer algorithms that will provide results comparable to experimental (initially spectroscopic) results.”
This will be the basis for validating the results: if the calculated results match the experimental results within a predetermined margin of error, then it can be reasonably assumed that their theories accurately describe the physical mechanisms underlying the phenomenon and can also be used to model more complex chemical systems. The research group aims to ensure that t
heir calculations are not only valid for a specific material system, but also form a comprehensive theory
that applies to all elements and compounds in the entire periodic table. Another important consideration is that the developed framework should be easily computerised, as modern physical chemistry research is inconceivable without algorithms that can be run on computers. Thus, every theory is expected to effectively aid numerical calculations.
The spectroscopic experiments that will be used to test the theoretical developments will not be carried out by the research group. These are very specialised experiments that are considered completely novel worldwide. “One of the most exciting areas of precision spectroscopy is when spectrometers are synchronised with atomic clocks. But today, it is also possible to manipulate the quantum state of molecules using modern quantum technology methods,” said Mátyus. “Here, we are not talking about a multitude of particles, but literally the quantum state of a single molecule. These states are examined using spectrometers synchronised with atomic clocks. There are also methods that measure mass so accurately that they can even show the binding energy of individual electrons. These experiments are not as expensive as the equipment at CERN, but there are only a few places in the world where they can be carried out.”
No one has been able to do this so far
Even though it is now possible to conduct such high-precision experiments, it is pointless if we cannot support their results with theories. According to the research group leader, there are very few research groups in the world that are capable of applying relativistic quantum electrodynamics (in some formalism and with certain approximations) to the bound states of atoms and molecules. The Momentum group is aiming to go even further.
“Our goal is to develop methods for calculating QED corrections to correlated relativistic energy.
No one has been able to do this so far, but at least we can now see what kind of theoretical framework we can start from,” said Mátyus. “All of this is necessary in order to interpret the aforementioned cutting-edge experiments. At the same time, it advances the development of the fundamental theory of molecular matter and will provide a solution to a problem that has remained open for decades: how can we systematically go beyond Schrödinger-based, non-relativistic wave mechanics in quantum-chemical applications? In the course of the Momentum project, we aim to develop this line of research and reach at least the simplest atomic-molecular applications, for which precision experiments are already under way. As a result of our research, we will make relativistic quantum electrodynamics accessible for quantum chemistry calculations; at the same time, through applying this old yet still underexplored theory, we also hope to gain a better understanding of its possible errors and limitations.”
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