Numerical results for the electron-electron counterbalance density in a series of molecules are reported. A compact density-dependent expression for the electron-electron counterbalance density in symmetric systems is used in the discussion of the importance of the exchange and correlation effects in electron-pair distributions. In addition, the behavior of the electron-electron counterbalance density in the dissociation process of the H-2 molecule is analyzed in the light of the occurrence of strong nondynamical correlation effects. Finally, the advanced density-dependent expressions allow a direct comparison with the charge concentration index and the electron-electron coalescence density, thus revealing the decisive role of exchange and correlation effects in describing the chemical bonding in molecules.