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The realism of molecular modelling studies of peptides depends on the model of the electrostatic forces, and thus on the quality of the wave function used to derive the atomic charges or multipoles. To establish this dependence, we have studied the electrostatic properties of N-acetylalanine Wmethylamide (CH3CONHCHCH3CONHCH3) calculated from a distributed multipole representation of both SCF and correlated wave functions with a range of respectable basis sets. The electron correlation is included in the wave function at second-order Maller-Plesset theory using a 'direct" method which calculates the relaxed electron density. To predict the electrostatic potential on the water-accessible surface of the peptide to within a few kJ mol-' requires a correlated wave function and a large basis set of double-zeta plus polarization quality or better. For a given basis set, the SCF wave function overestimates the electrostatic potential by around 15%, the inclusion of electron correlation producing a consistent change in the electron density. Changing the basis set, within a given ab initio method, also produces significant differences in the electrostatic potential around the peptide and in its electrostatic interaction with water. However, it is observed that the electrostatic potential for this peptide correlates strongly with the total dipole moment of the charge density, as the direction of the dipole moment is almost independent of basis set within each ab initio method. Upon correlating the wave function there is a small, almost constant, change in the direction of the dipole moment of 3.5O * 0.1O. Thus, the electrostatic potential calculated from smaller (split valence) basis sets can be scaled to give good agreement with more accurate calculations.