This work carries out the study of the Laplacian field function of the electron density L(r) = -del(2)rho(r) splitted in two contributions rho(r) = rho((p))(r) + rho((u))(r), which correspond to the effectively paired and effectively unpaired electron densities, respectively. The visualization of the concentration and depletion of these fields and their spatial localization show no contribution of the effectively unpaired electrons to the conventional bonding among two centers, but the field -del(2)rho((u))(r) provides an interesting structure. We also study the reliability of the information contained in the partitioning of this electron density field function for describing nonclassical bondings as the three-center two-electron ones.