Researchers at the University of Chicago, led by Laura Gagliardi, Richard and Kathy Leventhal Professor in the Department of Chemistry and the Pritzker School of Molecular Engineering, have developed a new computational framework aimed at resolving a long-standing problem in materials science: how to accurately describe electrons in materials that fall between traditional chemical and physical models. The work brings together concepts from quantum chemistry and solid-state physics to better capture electronic behavior in complex materials.
At the heart of the challenge is the way electrons are treated in simulations. Physicists typically describe electrons in solids as delocalized waves spread across repeating lattices, while chemists focus on localized electrons tied to specific bonds or molecular fragments. Many advanced materials, including organic semiconductors, metal–organic frameworks, and strongly correlated oxides, do not conform neatly to either picture. In these systems, electrons may remain largely associated with repeating fragments while still interacting across the entire material.
Laura Gagliardi from University of Chicago stated,
“For decades, chemists and physicists have used very different lenses to look at materials. What we’ve done now is create a rigorous way to bring those perspectives together”.
The research team addressed this gap by extending a method known as the Localized Active Space approach to periodic solids. Originally developed for large molecules, this method allows computationally demanding quantum calculations to focus on chemically important regions while treating the rest of the system more efficiently. By adapting the approach to infinite, repeating structures, the researchers created a hybrid framework that preserves local electron correlation while still accounting for long-range electronic motion.
This balance is essential for materials where local interactions strongly influence global properties. Accurately modeling electrons at the fragment level without losing the overall band structure has been a persistent difficulty in electronic structure theory. The new framework allows electrons to be treated as localized within fragments while still allowing them to move between those fragments across the crystal lattice.
To test the method, the researchers applied it to a one-dimensional hydrogen chain, a deceptively simple system that has exposed weaknesses in many commonly used computational techniques. Standard density functional theory approaches often predict metallic behavior for this system, while more accurate treatments show that electron correlations lead to insulating behavior. The localized active space method correctly captured this insulating nature by resolving how electrons localize within individual hydrogen units while maintaining interactions along the chain.
The framework was also used to simulate a model p–n junction, a fundamental structure in solar cells and semiconductor devices. In this case, the method revealed how charge carriers separate and move across the junction when the system is excited. This type of charge transport depends on both local electronic structure and long-range electrostatic effects, making it difficult to capture with conventional approaches.
Although the current study focuses on demonstrating the method’s accuracy and consistency, the researchers view it as a foundation for further development. More advanced quantum techniques can be incorporated into the framework to improve precision and expand the range of materials that can be studied. Over time, this could allow researchers to predict electronic properties with fewer approximations, reducing the need for empirical adjustments.
Rather than replacing existing computational tools, the approach provides a bridge between them. By unifying molecular-level and material-level descriptions within a single framework, the method offers a way to study systems that have traditionally been difficult to model. For engineers and materials scientists, this represents progress toward simulations that more closely reflect the true quantum nature of functional materials.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
