The exchange counterpart of the second-order polarisation corrections was derived and calculated separately for He 2 and Be 2 molecules for the first time by Chałasiński and Jeziorski. The presented expressions were obtained within the single-exchange approximation and featured the subdivision for exchange-induction and exchange-dispersion corrections. The authors utilised the Møller-Plesset decomposition of the Hamiltonian in order to apply the method to many-electron subsystems. Moreover, the multipole expansions of exchange-induction and exchange-dispersion energies were studied by Chałasiński et al. The exact form in terms of overlap integrals S of second-order exchange-induction and exchange-dispersion energies were presented much later by Schäffer and Jansen in Refs. 2 and 3 respectively. In their work, they followed the derivation by cofactors, similarly to Jeziorski et al. . Moreover, the quality of S 2 approximation for second-order exchangeinduction and exchange-dispersion corrections was studied for various molecular systems. It has been shown that in several non-covalently bonded systems, the exchange-induction is underestimated in the single-exchange approximation. In some ionic systems, it may even lead to the incorrect attractive character of the interaction energies at short intermolecular separations. Only recently have the third-order exchange corrections to the interaction energy, which are exact in the overlap expansion, been presented. Introduced by Waldrop and Patkowski in 2021 , these corrections follow a similar approach to previous unapproximated methods. The derivations were based on the cofactors of the overlap integrals matrix S. The exact formulae for the third-order exchange-induction and exchange-dispersion corrections were provided, along with benchmark tests obtained for a selection of chemical datasets for non-covalent interactions.