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F. Billes, H. Mikosch:
"Protonation and Solvation of Pyrazine, A Theoretical Study";
Structural Chemistry, 3 (1992), 5; 307 - 319.

Some properties of neutral, once, and twice-protonated pyrazines and their supermolecules with two water molecules were calculated at CNDO level as functions of solvent polarity. The solvents were assumed to be homogeneous continua in which the solute molecules induce electric charges. Atomic net charges, binding energies, force constants, vibrational frequencies, and potential energy distributions were calculated by applying the CNDO optimized geometries of the isolated molecules as references. Pyrazine force constants were scaled to the pyrazine fundamental frequencies. These scaling factors were transferred to the other molecules. For supermolecules the additional scaling factors were chosen based on the chemical similarity of the coordinates.
The symmetries of the monocations are reflected in the charge distribution and in the values of the force constants. With increasing molecular charge and increasing solvent polarity the fundamental shifts become more larger and more negative. The calculated frequencies were assigned to normal modes. The influence of the solvent polarity on the binding energies is very interesting: For isolated species that of the neutral molecules is the lowest and that of the bication is the highest, and with increasing polarity all binding energies increase, but the higher the charge, the quicker the increase and the order reverses.
The calculated values for the pyrazine parts of the supermolecules are mostly close to those of the corresponding results of the nonhydrated species with the same charge. The results for the substituents are close to the corresponding free species. The interactions are expressed most frequently in the hydrogen bonds. These are investigated in detail. The NH bond lengths are underestimated as a consequence of the CNDO approximation. For water substitution NH stretching force constants and frequencies are low, and the coupled OH stretching force constants and frequencies are large. For the hydroxoniumion substitutent the situation is opposite: In the case of two hydroxonium ion substituents, the two stretching coordinates are mixed in the corresponding normal modes.

http://dx.doi.org/10.1007/BF00678555