Part A; Statistical thermodynamic computer simulations of pure liquid water and of the hydration of model compounds ($CH_4$, $CH_3OH$, $CH_3NH_2$, $CH_3COOH$, $CH_3NH_3^+$, and $CH_3COO^-$) that are prototypes of the side-chain groups of proteins were carried out at $25\circ \!C$ under canonical ensemble conditions. The simulations employed a Monte Carlo method, with empirical pairwise potential functions derived from ab initio quantum mechanical calculations, to compute the free volume of a molecule. Thermodynamic properties and solute-solvent radial distribution functions are reported. These include, in particular, the molar excess entropies of the various solute and solvent water molecules in dilute aqueous solution, computed from the free volumes. The excess free energies of these molecules were calculated from the computed entropies. According to these calculations, the nonpolar solute molecule $CH_4$ induces somewhat stronger interactions among the solvent water molecules (structure-forming hydrophobic hydration) than does an $H_2O$ molecule in pure liquid water, whereas the other polar solute molecules induce weaker(structure-breaking) interactions. The excellent agreement between the experimental and computed molar excess entropy in pure liquid water demonstrates that the modified free-volume theory can be applied in calculations of the excess free energy of dense and rotationally hindered systems. In all of the dilute aqueous solutions considered here, the average molar excess free energies of the solvent water molecules are higher than that in pure liquid water. However, in considering the total excess free energies of these systems, a methane solution is less stable (i.e., has higher free energy) than pure liquid water, whereas the other solutions are more stable.
Part B; Monte Carlo method was used to examine the distributions of nonshort-circuited rings of hydrogen-bonded molecules in TIP4P water and methane solution at five temperatures tanging from -25 to $75\circ \!C$. Our interest was the distributions of water pentamers and hexamers in TIP4P water and methane solution. Therefore, the polygons larger than water hexamer were not considered. In counting the hydrogen-bonded rings, a energetic definition of the hydrogen bond was used. It was found that the ratio of water hexamers and pentamers ($R_6/R_5$) increased in according to decreasing temperature in both pure liquid water and methane solution; the decrease of temperature makes the forming of water hexmers easier than that of water pentamers. And also, at same temperature, the $R_6/R_5$'s value in methane solution was greater than that in pure liquid water. This implies that, in methane solution, water hexamers are formed more easily than water pentamers, in comparing with pure liquid water. On the other hand, at high temperature, the average numbers of water pentamers and hexamers are greater in pure liquid water than in methane solution, whereas reverse at low temperature. That is, at high temperature, a methane molecule induces the breaking of water pentamers and hexamers, whereas at low temperature, the forming of those water polygons.
단백질의 곁가지들의 전형적인 모델이 되는 분자들, 즉, $CH_4$, $CH_3OH$, $CH_3NH_2$, $CH_3NH_3^+$, $CH_3COOH$, $CH_3COO^-$ 들의 수화에 관한 연구결과, 비극성분자인 메탄은 용매인 물분자들간의 상호결합을 순수한 물에서보다 강하게 하고, 다른 비극성분자들은 그것을 약하게 함을 알았다. 또한 자유부피를 이용한계의 자유에너지를 계산해본 결과, 메탄수용액은 순수한 물보다 불안정한 반면, 다른 수용액들은 안정하다는 것을 알았다.
순수한 물과 메탄수용액에서의 물의 구조에 관한 연구결과, 메탄분자는 높은 온도에서는 오각수와 육각수를 깨뜨리지만 낮은 온도에서는 그것들을 형성시키는 역할을 함을 알았다. 또한 메탄수용액에서는 순수한 물에 비해 육각수가 오각수보다 더 쉽게 형성된다는 것을 알았다. 뿐만 아니라 순수한 물에서나 메탄수용액에서나 온도가 낮아짐에따라 오각수와 육각수는 모두 증가되지만 육각수가 오각수보다 많이 증가된다는 것을 알아냈으며 순수한 물보다 메탄수용액에서 그 결과가 현저하게 드러남을 알아냈다.