# The nature of three-body interactions in DFT: exchange and polarization effects

## TL;DR

This paper decomposes three-body nonadditive interaction energies in DFT into exchange and polarization parts, revealing limitations of current DFAs in capturing exchange effects, especially in dispersion-bonded systems, and proposing improved approaches.

## Contribution

It introduces a physically motivated decomposition of three-body interactions in DFT and evaluates the performance of various DFAs in capturing exchange effects.

## Key findings

- Semilocal, hybrid, and range-separated DFAs poorly account for nonadditive exchange in dispersion-bonded trimers.
- Range-separated hybrids perform well for hydrogen-bonded systems, within 20% of reference exchange energy.
- Hartree-Fock based monomer interactions in the Pauli Blockade scheme yield reliable results across systems.

## Abstract

We propose a physically motivated decomposition of DFT 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar$_2$-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems range-separated hybrids achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli Blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component although semilocal and global hybrid DFAs appear to imitate it in the short range.