Density Functional Theory (DFT) is utilized to compute field-dependent binding energies and intramolecular vibrational frequencies for carbon monoxide and nitric oxide chemisorbed on five hexagonal Pt-group metal surfaces, Pt, Ir, Pd, Rh, and Ru. The results are compared with corresponding binding geometries and vibrational frequencies obtained chiefly from infrared spectroscopy in electrochemical and ultrahigh vacuum environments in order to elucidate the broad-based quantum-chemical factors responsible for the observed metal- and potential-dependent surface bonding in these benchmark diatomic chemisorbate systems. The surfaces are modeled chiefly as 13-atom metal clusters in a variable external field, enabling examination of potential-dependent CO and NO bonding at low coverages in atop and threefold-hollow geometries. The calculated trends in the CO binding-site preferences are in accordance with spectral data: Pt and Rh switch from atop to multifold coordination at negative fields, whereas Ir and Ru exhibit uniformly atop, and Pd hollow-site binding, throughout the experimentally accessible interfacial fields. These trends are analyzed with reference to metal d-band parameters by decomposing the field-dependent DFT binding energies into steric (electrostatic plus Pauli) repulsion, and donation and back-donation orbital components. The increasing tendency towards multifold CO coordination seen at more negative fields is due primarily to enhanced back-donation. The decreasing propensity for atop vs multifold CO binding seen in moving from the lower-left to the upper-right Periodic corner of the Pt-group elements is due to the combined effects of weaker donation, stronger back-donation, and weaker steric repulsion. The uniformly hollow-site binding seen for NO arises from markedly stronger back-donation and weaker donation than for CO. The metal-dependent zero-field DFT vibrational frequencies are in uniformly good agreement with experiment; a semiquantitative concordance is found between the DFT and experimental frequency-field ("Stark-tuning") slopes. Decomposition of the DFT bond frequencies shows that the redshifts observed upon chemisorption are due to donation as well as back-donation interactions; the metal-dependent trends, however, are due to a combination of several factors. While the observed positive Stark-tuning slopes are due predominantly to field-dependent back-donation, their observed sensitivity to the binding site and metal again reflect the interplay of several interaction components.