A bond-by-bond partitioning of the electron energy within the p(2 x 2)-CO/Pd(111) and p(2 x 2)-NO/Pd(111) chemisorption systems has been used to demonstrate a preference for CO and NO chemisorption in hollow sites. The changes in bonding within the adsorbate and within the surface that accompany formation of the chemisorption bond are quantified using Hamilton population analysis: a partitioning of the electron energy among the atoms and bonds. In this way, the preference for CO and NO chemisorption in hollow sites is seen to result from the inability of the increased reduction in bonding within both the adsorbate and surface to counter the increase in surface-adsorbate bonding with increasing adsorbate coordination. By comparison with CO chemisorption, the chemisorption of NO is characterized by stronger surface-adsorbate bonding on all sites; principally the result of increased mixing between the NO(2pi) orbitals and the surface d band. Increased mixing between the NO(2pi) orbitals and the surface d band, in turn, results in increased back-donation to the NO(2pi) orbitals on all sites and, correspondingly, a greater degree of bond weakening within NO on all sites. The increase in 2pi-d mixing on chemisorbing NO does not, however, result in increased Pd-Pd bond weakening. Instead, increased 2pi-d mixing on chemisorbing NO serves to depopulate a greater number of those surface states contributing to d-d antibonding interactions within Pd-Pd bonds about chemisorbed NO. In this way, the analysis of CO and NO chemisorption presented provides new insight into the mechanism by which chemisorbed CO and NO perturb the electronic structure of the surface and, potentially, influence the chemisorption of neighboring adsorbates at higher coverages. Detailed analysis of the adsorbate orbital contributions to Pd-CO and Pd-NO bonding also reveals that both the adsorbate sigma and pi orbitals mix primarily with the surface s and p bands. Within the context of the molecular orbital picture of CO and NO chemisorption presented, interaction of the adsorbate orbitals with the d band acts only to perturb the more substantial interaction between the adsorbate orbitals and the surface s and p bands. In this way, the molecular orbital picture of CO and NO chemisorption presented serves to validate the d-band model of chemisorption devised previously by Hammer et al.