Theoretical study for partial molar volume of amino acids in aqueous solution: Implication of ideal fluctuation volume

A Kirkwood–Buff equation for the partial molar volumes of polyatomic molecules in solutions is derived based on the reference interaction site model (RISM) theory of molecular liquids. The partial molar volume of the twenty amino acids in aqueous solution at infinite dilution are calculated using the equation, and the results are discussed in comparison with the experimental data. The results indicate that ionizations of the C- and N-terminus groups give negative contributions to the volume ranging from $\text{−3.2\hspace{0.05em}}{\mathrm{cm}}^{\mathrm{3}}\mathrm{/mol}$ to $\text{−9.7\hspace{0.05em}}{\mathrm{cm}}^{\mathrm{3}}\mathrm{/mol}$ depending on the amino acid. Ionization of the dissociable residues also give negative contribution which ranges from $\text{−3.0\hspace{0.05em}}{\mathrm{cm}}^{\mathrm{3}}\mathrm{/mol}$ to $\text{−6.0\hspace{0.05em}}{\mathrm{cm}}^{\mathrm{3}}\mathrm{/mol}.$ On the other hand, contribution of the fractional charges on atoms to the volume is not necessarily negative, but rather slightly positive with few exceptions. It is clarified that contribution from an atom group to the volume is largely dependent on the situation where the group is placed. Therefore, it is concluded that the conventional way of determining the partial molar volume from group contributions is not reliable. The theoretical results for the partial molar volume exhibit a systematic deviation from corresponding experimental data, which increases nearly proportionally with increasing temperature and with the number of atoms in the amino acids. In order to account for the deviation, a concept of the “ideal fluctuation volume” is proposed, which is the ideal gas contribution to the volume, originating from the intramolecular fluctuation of solute.