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02/18/2026 16:24

Machine Learning Helps Solve Central Problem of Quantum Chemistry

Marietta Fuhrmann-Koch Kommunikation und Marketing
Universität Heidelberg

By applying new methods of machine learning in quantum chemistry research, Heidelberg University scientists have made significant strides in computational chemistry. They achieved a major breakthrough towards solving a decades-old dilemma in quantum chemistry – the precise and stable calculation of molecular energies and electron densities with a so-called orbital-free approach, which uses considerably less computational power and therefore permits calculations for very large molecules.

Press Release
Heidelberg, 18 February 2026

Machine Learning Helps Solve Central Problem of Quantum Chemistry
Orbital-free approach enables precise, stable, and physically meaningful calculation of molecular energies and electron densities

By applying new methods of machine learning in quantum chemistry research, Heidelberg University scientists have made significant strides in computational chemistry. They achieved a major breakthrough towards solving a decades-old dilemma in quantum chemistry – the precise and stable calculation of molecular energies and electron densities with a so-called orbital-free approach, which uses considerably less computational power and therefore permits calculations for very large molecules. Within the STRUCTURES Cluster of Excellence, two research teams at the Interdisciplinary Center for Scientific Computing (IWR) have refined a computing process long held to be unreliable such that it delivers precise results and reliably establishes a physically meaningful solution.

How electrons are distributed in a molecule determines its chemical properties – from its stability and reactivity to its biological effect. Reliably calculating this electron distribution and the resulting energy is one of the central functions of quantum chemistry. These calculations form the basis of many applications in which molecules must be specifically understood and designed, such as for new drugs, better batteries, materials for energy conversion or more efficient catalysts. Yet such calculations are computationally intensive and quickly become very elaborate. The larger the molecule becomes or the more variants need checking the sooner established computing processes reach their limits. The “Quantum Chemistry without Orbitals” project is positioned here at the interface of chemistry, physics, and AI research.

In quantum chemistry, molecules are frequently described using density functional theory, which allows for the fundamental prediction of chemical molecular properties without having to calculate the quantum mechanical wave function. The electron density is used as the main quantity instead – a simplification that finally makes computations practicable. This orbital-free approach promises especially efficient calculations but until now was considered barely useful, since small deviations in the electron density led to unstable or “non-physical” results. With the aid of machine learning, the Heidelberg method finally solves this precision and stability problem for many different organic molecules.

The new process called STRUCTURES25 is based on a specifically developed neural network that learns the relationship between electron density and energy directly from precise reference calculations, capturing the chemical environment of each individual atom in a mathematically detailed representation. A unique training concept was pivotal: the model was trained not only with converged electron densities but also with many variants surrounding the correct solution – generated by targeted, controlled changes in the underlying reference calculations. This computing process is therefore able to reliably find a physically meaningful solution for molecular energies and electron densities even in case of small deviations. It remains stable without “getting lost” in the calculation, the Heidelberg researchers emphasize.

In tests on a large and diverse collection of organic molecules, STRUCTURES25 achieved a precision that can compete with established reference calculations, for the first time demonstrating a stable convergence using an orbital-free approach. The performance of the method was demonstrated not only on small examples but on considerably larger “drug-like” molecules as well. Initial runtime comparisons prove that the computing process can scale better with growing molecule size and hence increase the speed of the calculation. Calculations formerly considered too elaborate are now within reach.

“Orbital-free density functional theory long held the promise of faster calculation – but not at the expense of the physics, please,” states Prof. Dr Fred Hamprecht, who leads the “Scientific Artificial Intelligence” research group at the IWR. “With STRUCTURES25, we demonstrate for the first time that computing can include both: chemically precise energies and a stable, practical optimization of the electron density.” Prof. Dr Andreas Dreuw, head of the “Theoretical and Computational Chemistry” research group at the IWR, adds: “Optimization is no longer unstable, and hence a major step forward for considerably faster predictions with high precision. Now simulations are within reach that classic processes could barely touch, such as when many configurations or very large molecules need investigating.”

Underpinning the work was the close interdisciplinary cooperation of the research groups within the Cluster of Excellence “STRUCTURES: A Unifying Approach to Emergent Phenomena in the Physical World, Mathematics, and Complex Data” at Heidelberg University. Here researchers from various disciplines study how structures emerge, how they can be detected in large datasets, and the benefits they offer science and technology. In addition to the support provided by the Cluster of Excellence, funding also came from the Wildcard program of the Carl-Zeiss-Stiftung, which supports especially innovative and particularly bold projects. The research results were published in the “Journal of the American Chemical Society”.

Caption:
Can quantum chemistry function without orbitals? In fact, machine learning has, for the first time, enabled a stable convergence of orbital-free density functional theory, thereby opening up the potential for considerably faster predictions with high accuracy. The figure schematically illustrates the transition from a wave function-based description (ψ) to an orbital-free representation in which the energy (E) is calculated from the electron density (ρ). All graphical elements – except for the arrows and pictogram – are based on actual computational results.
Design: Virginia Lenk

Contact:
Heidelberg University
Communications and Marketing
Press Office, phone +49 6221 54-2311
presse@rektorat.uni-heidelberg.de

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Contact for scientific information:

Prof. Dr Fred Hamprecht
Interdisciplinary Center for Scientific Computing
Phone +49 6221 54-14833
fred.hamprecht@iwr.uni-heidelberg.de

Prof. Dr Andreas Dreuw
Interdisciplinary Center for Scientific Computing
Phone +49 6221 54-14735
dreuw@uni-heidelberg.de

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Original publication:

R. Remme, T. Kaczun, T. Ebert, C.A. Gehrig, D. Geng, G. Gerhartz, M.K. Ickler, M.V. Klockow, P. Lippmann, J.S. Schmidt, S. Wagner, A. Dreuw, F.A. Hamprecht: Stable and Accurate Orbital-Free Density Functional Theory Powered by Machine Learning. Journal of the American Chemical Society 2025 147 (32), 28851-28859, DOI: 10.1021/jacs.5c06219

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More information:

https://structures.uni-heidelberg.de – STRUCTURES Cluster of Excellence
https://www.iwr.uni-heidelberg.de/en – Interdisciplinary Center for Scientific Computing

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Can quantum chemistry function without orbitals? Detailed image description in the text.
Source: Design: Virginia Lenk
Copyright: Heidelberg University / IWR

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Criteria of this press release:
Journalists
Chemistry, Information technology, Physics / astronomy
transregional, national
Research results
English

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