DFT Embedding: Many Pair Expansion

Density functional theory has become the workhorse of quantum mechanical simulations in chemistry and materials science. However, most local and semi-local density functionals suffer from delocalization errors and cannot describe strongly correlated systems or dispersion interactions very well. As a result, the applications of DFT rely heavily on picking functionals for specific problems and careful benchmarking. In order to alleviate this problem, we have developed a wavefunction-in-DFT embedding method called Many Pair Expansion (MPE). It is a new density functional hierarchy that systematically corrects any deficiency of an approximate functional to finally converge to the exact ground-state energy. The core idea is to partition the electron density into localized electron pairs and numerically compute the exact energy for the fragment densities built from these electron pairs. The exact energies of fragment densities are used to improve the approximate total DFT energy. We have implemented this method for lattice Hamiltonians such as 1D and 2D Hubbard, Peierls-Hubbard and PPP models and proved it is efficient in describing strong correlations and dispersion interactions. MPE is also extended to molecular systems and shown to provide promising results. We are now working on more thorough tests on MPE using different starting functionals and making a faster implementation. We also hope to use MPE as a tool to design better density functionals in the future.