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Complete geometry optimizations using a density functional theory (DFT) with the combined Becke3 and LYP functional potentials (B3-LYP) and the conventional ab initio Hartree-Fock (HF) method with the 6-31G(d,p) basis set were carried out for the fundamental tautomeric forms of nucleic acid bases (cytosine, thymine, guanine and adenine) and their derivatives methylated at the N1 (pyrimidines) or N9 (purines) positions. At the HF geometries, the dipole moments, electronic densities and molecular electrostatic potentials (MEPs) were computed using the HF,MP2(fc) , DFT(B3-LYP), DFT(B3-LYP) methods and DFT with inclusion of Becke nonlocal, gradient-corrected exchange energy terms (DFT(NLE) method) with the numerical DNP basis set. The same properties were also computed using the DFT(B3-LYP) method for the corresponding optimized geometries of the molecules. The charges that reproduce the MEP maps from the ab initio (HF, MP2) and DFT calculations were fitted and compared. The ground state molecular parameters (rotational constants, dipole moments) of the methylated bases are compared with the molecular parameters calculated at the same level for the nonmethylated DNA bases and with available experimental data. The results show that the DFT calculations reproduce well the MP2 results for the MEPs, the ESP charges and the dipole moments of the DNA bases and their N-methylated derivatives.