Dispersion with fixed diagonal matrices: Exchange energy correction and an assessment of the Becke–Roussel exchange hole

An exchange-correction to the fixed diagonal matrices (FDM) method is introduced to improve accuracy when employing a single reference wavefunction. In addition, the performance of the Becke-Roussel exchange-hole in approximating the pair density-mediated integrals was explored. With the exchange-correction, the FDM procedure yields dispersion coefficients for closed-shell atoms on par with highly correlated methods when using only Hartree-Fock or Kohn-Sham pair density. Conversely, the Becke-Roussel exchange-hole results in an overestimation of the dispersion coefficients for closed-shell atoms; however, the performance of the Becke-Roussel model can be improved by scaling the multipole moment integrals by a fixed amount. For both the exchange-correction and the Becke-Roussel model, the FDM method continues to fail for open-shell atoms and ions by consistently underestimating the dispersion coefficients.