Frozen-density embedding-based many-body expansions

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.