Scientists at the University of Heidelberg have made major advances in computational chemistry by applying new methods of machine learning to quantum chemistry research. They achieved a major breakthrough toward solving a decades-old dilemma in quantum chemistry. This is an accurate and stable calculation of molecular energies and electron densities through the so-called orbital-free approach. This approach uses significantly less computational power and thus allows calculations of very large molecules. Within the STRUCTURES Cluster of Excellence, two research teams at the Interdisciplinary Center for Scientific Computing (IWR) have improved computing processes that have long been known to be unreliable, ensuring that they deliver accurate results and establish physically meaningful solutions.
How electrons are distributed within a molecule determines its chemical properties, from its stability and reactivity to its biological effects. Reliably calculating this electron distribution and the resulting energy is one of the central functions of quantum chemistry. These calculations form the basis for many applications that require a specific understanding and design of molecules, including new drugs, better batteries, materials for energy conversion, and more efficient catalysts. However, such calculations are computationally intensive and quickly become very complex. The larger the molecule or the more variants that need to be checked, the faster established computing processes will reach their limits. The “Orbitless Quantum Chemistry” project is here at the intersection of chemistry, physics, and AI research.
In quantum chemistry, molecules are often described using density functional theory, which allows fundamental predictions of chemical molecular properties without calculating quantum mechanical wave functions. Instead, electron density is used as the main quantity. This finally allows the calculation to be performed. Although this orbital-free approach promises particularly efficient calculations, it was previously thought to be of little use because small deviations in the electron density lead to unstable or “unphysical” results. The Heidelberg method finally solves this accuracy and stability problem for a variety of organic molecules with the help of machine learning.
The new process, called STRUCTURES25, is based on a specially developed neural network that learns the relationship between electron density and energy directly from precise reference calculations, providing a detailed mathematical representation of the chemical environment of individual atoms. A unique training concept was crucial. The model was trained using a converged electron density as well as many variants surrounding the correct solution, generated by targeted and controlled changes in the underlying reference calculations. Therefore, this computational process can reliably find physically meaningful solutions for molecular energies and electron densities even with small deviations. The Heidelberg researchers stress that they do not “get lost” in their calculations and remain stable.
In tests against a large and diverse collection of organic molecules, STRUCTURES25 achieved accuracy competitive with established reference calculations and demonstrated for the first time stable convergence using a trajectory-free approach. The performance of this method was demonstrated not only in small examples but also in much larger “drug-like” molecules. Comparisons during initial runs prove that the computational speed increases as the computing process can scale better as the molecular size grows. Calculations that were previously considered too complex are now within reach.
“Orbital free density functional theory has long held promise for faster calculations, but we don’t want it to come at the expense of physics,” said Professor Fred Hamprecht, head of the Scientific Artificial Intelligence research group at IWR. “With STRUCTURES25, we demonstrate for the first time that computing can include both chemically accurate energy and stable and practical optimization of electron density.” Professor Andreas Drew, head of IWR’s Theoretical and Computational Chemistry research group, added: “This is a major step towards highly accurate and significantly faster predictions, as optimization is no longer unstable. Simulations that were largely untouched by traditional processes are now within reach, such as when many configurations or very large molecules need to be investigated.”
This research was supported by the close interdisciplinary collaboration of research groups within the Heidelberg University Cluster of Excellence “STRUCTURES: Unified Approaches to Emergent Phenomena in the Physical World, Mathematics and Complex Data”. Here, researchers from a variety of disciplines study how structures emerge, how they can be detected in large datasets, and the benefits they bring to science and technology. In addition to support from the Clusters of Excellence, funding was also provided by the Carl Zeiss Foundation’s Wildcard Program, which supports particularly innovative and particularly daring projects. The research results were published in the Journal of the American Chemical Society.
original publication
Roman Lemme, Tobias Cousin, Tim Ebert, Christoph A. Gehrig, Dominik Genn, Gerrit Gerharz, Mark K. Ickler, Manuel V. Klokow, Peter Lippmann, Johannes S. Schmidt, Simon Wagner, Andreas Drew, Fred A. Hamprecht. “Stable and accurate free orbital density functional theory using machine learning”; Journal of the American Chemical Society, Vol. 147, 2025-8-1
