New theory promises faster, more accurate predictions of chemical reaction energetics

Researchers at the University of Illinois Urbana-Champaign have developed a new theoretical framework that could dramatically reduce the cost and complexity of predicting chemical reaction energetics without sacrificing accuracy. Led by chemical and biomolecular engineering professor Alexander V. Mironenko, the team introduces a method that may one day replace the current computational models used in quantum chemistry.

At the core of the research is a concept called the independent atom reference state in the density functional theory (DFT) framework, which offers a new way to compute the energy required for breaking chemical bonds – a calculation that is critical to understanding and designing chemical reactions and catalysts promoting them for production of plastics, gasoline additives, or dyes. Traditional models that employ the independent electron reference state require solving complicated equations to describe interactions of electrons in molecules, an inherently difficult and computationally expensive task. In contrast, the new method allows for considerable simplifications of mathematical expressions, providing a more elegant and computationally affordable alternative.

“Methods for predicting chemical reactivity of molecules and materials are based on quantum mechanics, the branch of science that is able to realistically describe the behavior of electrons on very tiny scales,” Mironenko said. “Conventional quantum methods are very expensive because molecules and materials typically contain a lot of electrons, and it is very difficult to keep track of them and their interactions.”

To illustrate the challenge, Mironenko compares it to shaking a bag of crushed candies: trying to track the motion of each powder particle (representing electrons) is nearly impossible. Yet tracking how electrons behave is central to quantum calculations.

To make the description of electron behavior more manageable, scientists commonly employ a reference state known as the independent electron approximation, which assumes electrons move independently. This reference state is easier to compute, but the oversimplification often leads to inaccuracies and requires complex, difficult-to-compute corrections. To deal with excessive computational costs, some of the physics is often sacrificed, which Mironenko said is a drawback of many existing empirical approximate quantum methods.

“If you think about really complicated mathematical formulas, it is common to remove – sometimes even arbitrarily – some parts of the formula which are thought to take too much time to compute and introduce some more approximate expressions to make chemical reactivity calculations more affordable,” he said. “But a rule of thumb is, the more physics in the model, the more predictive this model is. The less physics we have – for example, if we remove some key equations and add some parameters – then the model becomes less predictive.”

Mironenko points to a class of modern AI tools as a timely example of this.

“Neural networks are an AI technology behind face and speech recognition, which can also be used for calculations of chemical reaction energetics,” he said. “Despite their huge popularity, neural networks are commonly not mathematically based on quantum mechanical equations. Consequently, their predictive ability often suffers and their development and parameterization may require a large number of expensive quantum calculations.”

Mironenko’s team shifted perspective and introduced a new reference state called the independent atom approximation. Instead of focusing on electrons, they used atoms as the fundamental units for their model. In the candy analogy, this means tracking whole pieces of candy rather than powder particles – a much more manageable approach.

“In comparison with independent electrons, this is a much more realistic approximation and correcting it is mathematically simple,” he said. “Equivalently, quantum calculations involving the independent atom reference state require less processing power and are much more affordable.”

The team validated their model using well-known molecules such as O₂ (oxygen), N₂ (nitrogen), F₂ (fluorine) and others, comparing their predictions to established highly accurate and expensive methods. Their model reproduced bond lengths and energy curves with great accuracy, not only matching quantum methods currently in use but also performing better in certain cases – especially when atoms are far apart, a scenario where many models fail.

This work builds on Mironenko’s earlier research, including a 2023 study that investigated certain prototypical systems known as hydrogen clusters. Their new framework expands the scope to more complex molecules commonly encountered in chemical engineering.

“This is career-defining work,” Mironenko said. “If each subsequent developmental step proves as successful as our initial efforts, we may be on the verge of a revolution in quantum mechanical calculations.”

The research was supported by the National Science Foundation under award number CHE-2154781. Graduate student Lanie Leung, with help from graduate student Jiqing Zhuang, played the key role in implementing the theoretical model in a computer code and validating it.

In addition to his appointment in chemical and biomolecular engineering, Mironenko is affiliated with the Chemistry department in the College of Liberal Arts & Sciences at Illinois.

Editor’s Notes:

To reach Alex Mironenko, alexmir@illinois.edu

The paper, Self-Consistent Equations for Nonempirical Tight Binding Theory, is available online. DOI: 10.1063/5.0276043