Strong Electron Correlation
As with any complicated mathematical problem, our understanding of electronic structure is based on first approximating with a simple problem, which we can solve exactly, and adding small corrections to account for the deviations from the simple model. The established methods of quantum chemistry are based on a picture of noninteracting electrons. For a large portion of chemistry, non-interacting electrons are a good starting point. Indeed any system which is qualitatively described by one molecular-orbital diagram will be well described by Density Functional Theory or Coupled Cluster Theory. Systems which require many molecular orbital diagrams for a correct qualitative description are not well treated by the popular methods. DMRG and Slater determinant Monte Carlo describe these systems well, but are generally too expensive.
Our approach is to to break the problem into an easy problem we can solve, and small corrections for the deviations. No one model will solve every chemical problem, so we are working on many to account for different situations. Our starting point is exactly solvable (or integrable) models, such as Richardson-Gaudin, Heisenberg, Hubbard, etc.