Ab initio Hartree-Fock (HF) and density functional theory (DFT) calculations have been performed on various model structures containing up to 1019 atoms and derived from molecular dynamics simulations of the KcsA potassium channel. The electrostatic potential and K+ binding energies are computed and compared to those of Amber molecular mechanics force-field and semiempirical methods. Errors in molecular mechanics results are shown to be predominantly due to neglect of protein atom/protein atom polarization, whereas polarization of the protein by the K+ ion is a secondary effect. Polarization effects are largest for nearby atoms (3-5 Å) but cannot be neglected even for atoms separated by over 10 Å. Of the semiempirical methods, only the AM1 method gives reasonable results, whereas both PM3 and PM5 failed to describe the K+ binding energy correctly. Both the HF and DFT methods produce good estimations of K + binding energies, but the DFT results suggest abnormally large polarization effects leading to an almost complete loss of charge from the K+ ion.