Ann Arbor Times

A research team at the University of Michigan has developed a new method to improve the accuracy of quantum chemistry simulations. Their work focuses on density functional theory (DFT), a widely used approach in materials science and chemistry that enables researchers to model systems with hundreds of atoms by calculating electron densities rather than tracking each individual electron.

One persistent challenge in DFT is determining the exchange-correlation (XC) functional, which describes how electrons interact according to quantum mechanics. Researchers typically use approximations for this functional because its exact form remains unknown.

“We know that there exists a universal functional—it doesn’t matter whether the electrons are in a molecular system, a piece of metal or a semiconductor. But we do not know what its form is,” said Vikram Gavini, professor of mechanical engineering at the University of Michigan and corresponding author of the study published in Science Advances.

To address this issue, the team used machine learning techniques to derive an XC functional based on data from quantum many-body calculations. These calculations are considered highly accurate but are computationally intensive and usually limited to small systems.

“Many-body theories give us the right answer for the right reason, but at an unreasonable computational cost. Our team has translated many-body results into a simpler, faster form that retains most of its accuracy,” said Paul Zimmerman, professor of chemistry at U-M, who led these calculations with Ph.D. student Jeffrey Hatch.

The researchers trained their model using data from five atoms—lithium, carbon, nitrogen, oxygen, neon—and two molecules: dihydrogen and lithium hydride. Attempts to add fluorine and water did not further improve results. The resulting XC functional performed better than expected for its level of complexity.

DFT methods are categorized by increasing levels of detail known as rungs on a ladder. The second-rung version used by Gavini’s team considers gradients in electron density rather than assuming uniformity. Despite only using second-rung information, their approach achieved accuracies typically seen at higher rungs that require more complex input.

“The use of an accurate XC functional is as diverse as chemistry itself, precisely because it is material agnostic. It’s equally relevant for researchers trying to find better battery materials to those discovering new drugs to those building quantum computers,” said Bikash Kanungo, assistant research scientist in mechanical engineering at U-M and first author on the study.

The team plans to test their method on solid materials next and explore ways to achieve even higher accuracy by incorporating information about individual electron orbitals—a step that would require additional computing resources.

Funding for this research was provided by the Department of Energy (grant no. DE-SC0022241) and additional support came from the Air Force Office of Scientific Research (grant no. FA9550-21-1-0302). Supercomputer time was supplied by facilities including the National Energy Research Scientific Computing Center and Oak Ridge National Laboratory.