What happens when two reagents are mixed together? Does a reaction occur? If so, what are the major and minor products? How can we adjust the reaction mixture to increase the reaction rate and tune the product distribution? Why does a small change in the reaction mixture sometimes lead to very different products? The goal of our research is to develop mathematical models and computational methods for questions like these.

To answer questions like these, one must understand the relationship between a substance’s electronic structure and its chemical properties; this is the mandate of quantum chemistry. Within the broad purview of quantum chemistry, our research focuses on developing:

Accurate, affordable, and robust approaches to the electronic structure problem.

Reliable approaches for predicting chemical reaction mechanisms and the products of chemical reactions.

New concepts that elucidate chemical phenomena.

New machine-learning methods for predicting molecular properties and chemical reactivity.

These projects are united by our desire to predict the products and mechanisms of chemical reactions. They are also united by a common approach, wherein a chemical problem is carefully studied, converted to a mathematical problem, and then solved using state-of-the-art mathematical and computational techniques. Our research methodology, therefore, combines all three facets of modern theoretical chemistry:

Mathematical studies of the underlying physical principles

Development of new computational methods

Applications to relevant chemical systems

Because we are particularly interested in modeling the reactivity of large and complex systems, including large organic and inorganic molecules, biomolecules, and complex materials, we focus our efforts on developing tools and methods that are computationally inexpensive and conceptually facile.

Members of the Ayers group are encouraged to pursue their own ideas and to adapt these broad research themes to match their interests, use their abilities, and achieve their ambitions. If you have questions about our research, want to request a reprint, wish to collaborate, or are interested in joining the research group, contact Paul.