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We have implemented and tested the method we have recently proposed [J. Phys.Chem. Lett. 10, 1537 (2019)] to treat dispersion interactions, which is derivedfrom a supramolecular wavefunction constrained to leave the diagonal of themany-body density matrix of each monomer unchanged. The correspondingvariational optimization leads to expressions for the dispersion coefficientsin terms of the ground-state pair densities of the isolated monomers only,which provides a framework to build new approximations without the need forpolarizabilities or virtual orbitals. The question we want to answer here ishow accurate this ``fixed diagonal matrices'' (FDM) method can be for isotropicand anisotropic $C_6$ dispersion coefficients when using monomer pair densitiesfrom different levels of theory, namely Hartree-Fock, MP2 and CCSD. Forclosed-shell systems, FDM with CCSD monomer pair densities yields the bestresults, with a mean average percent error for isotropic $C_6$ dispersioncoefficients of about 7\% and a maximum absolute error within 18\%. Theaccuracy for anisotropic dispersion coefficients with FDM on top of CCSD groundstates is found to be similar. The performance for open shell systems is lesssatisfactory, with CCSD pair densities not always providing the best result. Inthe present implementation, the computational cost on top of the monomer'sground-state calculations is $\mathcal{O}(N^4)$.

Dispersion without many-body density distortion: Assessment on atoms and small molecules