Multireference electronic structure methods

An important open problem in computational chemistry is predicting the energy and properties of open-shell species, intermediates that are formed during bond-breaking processes, excited states, and spin states of transition metal compounds.

Our group has developed new multireference theories based on the driven similarity renormalization group (DSRG). The strategy followed by the DSRG is to map all the electrons in a molecule to a small set of valence electrons that experience “renormalized” effective interaction. The DSRG effectively removes the orbitals responsible for weak (dynamical) correlation, greatly simplifying the problem of solving the Schrödinger equation. We have developed the DSRG in many directions, including low-cost methods for large molecule, high-accuracy methods, excited state methods, and have recently started to combine the DSRG with embedding schemes. Check out the publications page to learn more.

Our group also develops new methods to treat the strong (static) correlation. Traditional quantum chemistry methods typically assume some form of structure for the wave function. Methods built on this premise are computationally efficient, but are not sufficiently flexible to accurately compute near-degenerate electronic states. We have focused in particular on using selected configuration interaction (sCI), an approach that reduces the cost of computations by exploiting the sparsity of the wave function. This line of work led to the development of the adaptive CI (ACI) and projector CI methods.

Want to read more?
Check out our review on multireference theories. Our work on the DSRG started with this paper and is reviewed in this article.

Our work on selected CI can be found here. We have also combined the ACI with the DSRG to study the ground state of polyacenes.

Quantum computing and machine learning

Quantum computers perform computations using the principles of quantum mechanics. For example, while a classical computer can process a certain amount of bits (0s and 1s) at a time, a quantum computer can perform operations on a superposition of all possible configurations of bits. This feature gives quantum computers a great advantage in many applications, including the simulation of quantum mechanics. Our group has recently started to work on new quantum computing algorithms. We are part and lead a multi-investigator effort to create quantum algorithms for solving challenging electron correlation problems. As part of this project we have studied trial states based on unitary coupled cluster theory for quantum computing. We have also proposed a Quantum Krylov algorithm for strongly correlated electrons based on real-time evolution of the wave function.

We are also interested in exploring ways to employ machine learning techniques to create better quantum algorithms. This is work is just starting.

Our Quantum Krylov approach builds a basis of many-body states by performing a real-time dynamics.

X-ray spectroscopy and dynamics of core excitations

X-ray spectroscopy offers a powerful and unique approach to probe the local environment and electronic structure in an element-specific way. We are developing several approaches to compute core-excited states probed in X-ray absorption spectroscopies. Our initial work focused on developing an orthogonality-constrained DFT (OC-DFT) scheme for core-excited states, which we combined with relativistic Hamiltonians. We have also developed methods to analyze core-excited states. We are now exploring multireference wave function methods to compute core-excited states that employ a combination of the DSRG and ACI.

Another area that we have explored is simulating the dynamics of electrons following a core excitations. We have recently developed a time-dependent version of the adaptive CI and applied to study charge migration in core ionized states.