The application of Density Functional Theory (DFT) using variable-field finite-cluster models to the description of electrode-chemisorbate systems is considered, with the particular objective of assessing the relationships between potential-dependent metal-adsorbate vibrational frequencies and the chemical nature of the surface bond. The validity of employing finite-cluster models in variable homogeneous fields to describe potential-dependent electrode-chemisorbate bonding is discussed, including the choice of bulk-phase adsorbate reference states for ionic systems. The bond length-dependent charge polarization, as reflected in the so-called static (mu(S)) and dynamic (mu(D)) dipole moments, plays a central role in determining the field (F)-dependence of the metal-adsorbate binding energies, E-b, and vibrational force constants, KM-A, respectively. A distinction between 'ionic' and 'dative covalent' surface bonding, based on whether the signs of mu(S) and mu(D) are the same or opposite, respectively, is demonstrated by means of DFT calculations for selected atomic and molecular adsorbates on Pt(111), and interpreted in terms of bond length-dependent charge polarization and orbital overlap. A basic consequence of these behavioral differences between mu(S) and mu(D) is to deny the occurrence of any uniform correlation between the E-b-F and KM-A-F behavior (i.e. between the potential-energy well depth and well 'stiffness', respectively). On the other hand, combined potential-dependent bond-energy and bond-frequency data should therefore be invaluable in ascertaining the nature of the surface coordination. A more uniform relationship, however, is observed between F-dependent force constants and equilibrium bond lengths. The applicability of these notions to the interpretation of Stark-tuning (i.e. frequency-potential) data for intramolecular as well as metal-adsorbate vibrations is also briefly discussed.