We have investigated the contribution of molecular environment to the exchange reactions in the DNA molecule taking into account different geometries of the reaction centers in oxidized and reduced states. We have observed the influence of the ionization potential of the donor and the acceptor on the free energy of the hole transfer reaction in the solvated DNA molecule: A decrease of the free energy occurs if IPA >= IPD and an increase if IPA <= IPD. The corresponding decrease of the potential barrier by 0.244 eV for hole migration from (G-C) to (A-T) and increase for migration from (G-C) to (G-C)(n) in solvent have been determined. The prevalence of oxidation of the redox states in the molecule center in comparison to the molecule sides due to the nonuniform charge distribution along the phosphate backbone was found to be stronger for the non-neutralized backbone than for the neutralized case. The influence of the single counterion on the electrostatic interactions within the solute DNA molecule has been found to be smoothly spread over a long distance similar to 7-8 base pairs. Therefore, each counterion contributes to the oxidation potential of the 7-8 nearest nucleosides and any irregularity due to phosphate neutralization would not significantly modify the potential profile for the hole migration through the DNA molecule.