xTC: An efficient treatment of three-body interactions in transcorrelated methods

An efficient implementation for approximate inclusion of the three-body operator arising in transcorrelated methods via exclusion of explicit three-body components (xTC) is presented and tested against results in the "HEAT" benchmark set Tajti et al., J. Chem. Phys. 121, 011599 (2004). Using relatively modest basis sets and computationally simple methods, total, atomization, and formation energies within near-chemical accuracy from HEAT results were obtained. The xTC ansatz reduces the nominal scaling of the three-body part of transcorrelation by two orders of magnitude to O(N5) and can readily be used with almost any quantum chemical correlation method.