Research

 

Time-independent DFT approaches for excited states

Time-dependent DFT is de facto the only DFT approach used to compute excited states. We are interested in exploring time-independent DFT methods that can be justified on the grounds of a variational approach to DFT.
Our first achievement has been the formulation of an orthogonality constrained DFT computational scheme. This method was derived formulating a variation functional for the excited state and imposing an adiabatic approximation to the exchange-correlation functional. At the same time we developed a SCF algorithm that can enforce orthogonality between the SCF solution and a given determinant.

dsrg_illustration4

Renormalization group methods for strongly correlated electrons

Electronic structure theories based on the renormalization group remain largely unexplored.  We have recently proposed the driven similarity renormalization group (DSRG) method, which is based on a field-theoretic formalism originally introduced independently by Wegner and by Głazek and Wilson.  In addition to formulating the DSRG using a single Slater determinant reference, we extended it to use a general complete-active-space reference using the Mukherjee–Kutzelnigg generalization of Wick’s theorem.

Adaptive electronic structure methods

Traditional quantum chemistry methods rely on rigidly structured approximate wave functions. Methods built on this premise are computationally efficient, but are not sufficiently flexible to accurately compute near-degenerate electronic states.  We are exploring new ways to create adaptive multireference theories using zeroth-order wave functions that are obtained via importance selection.

Relativistic effects

We are currently interested in approximate relativistic theories that permit to include scalar and spin-orbit effects easily into existing DFT and wave function methods.  We are currently implementing the exact two-component approach (X2C), in particular its one-electron variant.

Work in Progress

  • Adaptive equation-of-motion approaches.
  • Multireference methods based on the driven similarity renormalization group.
  • Time-independent DFT approaches for excited states.
  • One-electron exact two-component relativistic Hamiltonians