  An exchange-correction to the Fixed Diagonal Matrices (FDM) method is
introduced to improve accuracy when employing a single reference wavefunction.
Also, the performance of the Becke-Roussel exchange-hole for approximating the
pair density mediated integrals is explored. With the exchange-correction, the
FDM procedure yields dispersion coefficients for closed-shell atoms on par with
highly correlated methods when using 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. In general, the FDM method
fails in underestimating the dispersion coefficients of open-shell atoms and
ions.
