University of Montreal

Electronic structure theory group

Matthias Ernzerhof


Research Interests

Electronic structure theory


Theory of molecular electronic devices

Molecular electronics poses a new challenge to electronic structure theory which cannot be tackled with the conventional repertoire of methods. A typical molecular electronic device (MED) consists of a molecule that is connected to two macroscopic metal contacts. A voltage is applied to the contacts, introducing a difference in chemical potentials between them. This imbalance between the chemical potentials means that the system is in a non-equilibrium state. An electron current will start to flow from the contact of high to the contact of low chemical potential. To describe a stationary non-equilibrium state it is desirable to have non-equilibrium density functional theory (DFT). Thus, we work on the development of a non-equilibrium DFT that allows us to employ the experience gained with approximations in the ground-state domain.

In the process of studying the inner workings of MEDs, we also implemented existing methods such as the non-equilibrium Green’s function DFT approach. We used this tool extensively to study MEDs that are of experimental interest. 

Another aspect of our research concerns structure-conductance relationships. Chemists have a very good intuition about how a certain functionalization of a molecule changes its properties. Many powerful concepts, such as the Woodward-Hoffman rules, are available for the prediction of molecular properties. These rules inspired us to start developing a similar set of rules relating molecular structure to electron transport.


Density Functional Theory

Among the numerous approaches to model the properties of atoms, molecules, and solids, the Kohn-Sham (KS) density functional method emerged as one of the most useful tools. The KS method reduces the many-electron problem to a self-consistent one-electron form. This is possible because the Hohenberg-Kohn and Kohn-Sham theorems allow us to express the exchange and correlation energy of the electrons as a functional of the electron density calculated from the KS orbitals. The KS method is a purely mathematical scheme and it is formally exact for the electronic ground state. Its success relies solely on our ability to find accurate approximations to . Because of the enormous progress made in recent years in constructing functionals, the KS method is now perhaps the most frequently used method in computational chemistry and materials science. However, despite its many successes, there are various areas where the existing functionals yield less than satisfactory results and where DFT could benefit from further functional improvements. Using new ideas, such as the correlation factor ansatz, we develop improved approximations for the exchange-correlation energy.