Many-body exchange-overlap interactions in rare gases and water

Generalized-gradient approximations (GGAs) of density-functional theory can suffer from substantial many-body errors in molecular systems interacting through weak non-covalent forces. Here, the errors of a range of GGAs for the 3-body energies of trimers of rare gases and water are investigated. The patterns of 3-body errors are similar for all the systems, and are related to the form of the exchange-enhancement factor FX(x) at large reduced gradient x, which also governs 2-body exchange-overlap errors. However, it is shown that the 3-body and 2-body errors depend in opposite ways on FX(x), so that they tend to cancel in molecular aggregates. Embedding arguments are used to achieve a partial separation of contributions to 3-body error from polarization, non-local correlation, and exchange, and it emerges that exchange is a major contributor. The practical importance of beyond-2-body errors is illustrated by the energetics of the water hexamer. An analysis of exchange-energy distributions is used to elucidate why 2-body and 3-body errors of GGAs depend in opposite ways on FX(x). The relevance of the present analysis to a range of other molecular systems is noted.