Masaru Nakahara

Structural study of supercritical water. I. Nuclear magnetic resonance spectroscopy

The proton chemical shift of water is measured at temperatures up to 400°C and densities of 0.19, 0.29, 0.41, 0.49, and 0.60g/cm3. The magnetic susceptibility correction is made in order to express the chemical shift relative to an isolated water molecule in dilute gas. The chemical shift is related to the average number of hydrogen bonds in which a water molecule is involved. It is found that the hydrogen bonding persists at supercritical temperatures and that the average number of hydrogen bonds is more than one for a water molecule in the supercritical densities. The density and temperature dependence of the chemical shift at supercritical temperatures are analyzed on the basis of statistical thermodynamics. It is shown that the hydrogen bonding is spatially more inhomogeneous at lower densities.

Theory of solutions in the energetic representation. I. Formulation

The energetic representation of the molecular configuration in a dilute solution is introduced to express the solvent distribution around the solute over a one-dimensional coordinate specifying the solute–solvent interaction energy. In this representation, the correspondence is shown to be one-to-one between the set of solute–solvent interaction potentials and the set of solvent distribution functions around the solute. On the basis of the one-to-one correspondence, the Percus–Yevick and hypernetted-chain integral equations are formulated over the energetic coordinate through the method of functional expansion. It is then found that the Percus–Yevick, hypernetted-chain, and superposition approximations in the energetic representation determine the solvent distribution functions correctly to first-order with respect to the solute–solvent interaction potential and to the solvent density. The expressions for the chemical potential of the solute are also presented in closed form under these approximations and...

Theory of solutions in the energy representation. II. Functional for the chemical potential

An approximate functional for the chemical potential of a solute in solution is presented in the energy representation. This functional is constructed by adopting the Percus–Yevick-like approximation in the unfavorable region of the solute–solvent interaction and the hypernetted-chain-like approximation in the favorable region. The chemical potential is then expressed in terms of energy distribution functions in the solution and pure solvent systems of interest, and is given exactly to second order with respect to the solvent density and to the solute–solvent interaction. In the practical implementation, computer simulations of the solution and pure solvent systems are performed to provide the energy distribution functions constituting the approximate functional for the chemical potential. It is demonstrated that the chemical potentials of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions.

Theory of solutions in the energy representation. III. Treatment of the molecular flexibility

The method of energy representation for evaluating the solvation free energy is extended to a solute molecule with structural flexibility. When the intramolecular structure of the solute molecule exhibits a strong response to the solute–solvent interaction, the approximate functional for the solvation free energy needs to be modified from the original form presented previously [J. Chem. Phys. 117, 3605 (2002); 118, 2446 (2003)]. In the modification of the functional, the solvation-induced change in the distribution function of the solute structure is taken into account with respect to the intramolecular energy of the solute. It is then demonstrated over a wide range of thermodynamic conditions that the modified form of functional provides an accurate and efficient route to the solvation free energy of a flexible solute molecule even when the structural distribution function of the solute in solution overlaps barely with that of the solute at isolation.

A quantum chemical approach to the free energy calculations in condensed systems: The QM/MM method combined with the theory of energy representation

A methodology has been proposed to compute the solvation free energy of a molecule described quantum chemically by means of quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER). The present approximate approach is quite simple to implement and requires much less computational cost as compared with the free energy perturbation or thermodynamic integration. Furthermore, the electron distribution can be treated faithfully as a quantum chemical object, and it is no longer needed to employ the artificial interaction site model, a reduced form of the realistic electron distribution, which is commonly used in the conventional solution theory. The point of the present approach is to employ the QM solute with electron density fixed at its average distribution in order to make the solute-solvent interaction pairwise. Then, the solvation free energy can be computed within the standard framework of the energy representation. The remaining minor contribution originating from the many-body effect inherent in the quantum mechanical description can be evaluated separately within a similar framework if necessary. As a test calculation, the method has been applied to a QM water solute solvated by MM water solvent in ambient and supercritical states. The results of the QM/MM-ER simulations have been in excellent agreement with the experimental values.

REVERSIBLE MOLECULAR DYNAMICS FOR RIGID BODIES AND HYBRID MONTE CARLO

A time-reversible molecular dynamics algorithm is presented for rigid bodies in the quarternion representation. The algorithm is developed on the basis of the Trotter factorization scheme, and its structure is similar to that of the velocity Verlet algorithm. When the rigid body is an asymmetric top, its computationally inconvenient Eulerian equation of motion is integrated by combining the computationally convenient solutions to the Eulerian equations of motion for two symmetric tops. It is shown that a larger time step is allowed in the time-reversible algorithm than in the Gear predictor–corrector algorithm. The efficiency of the hybrid Monte Carlo method for a molecular system is also examined using the time-reversible molecular dynamics algorithm in the quarternion representation.

Free-energy analysis of solubilization in micelle

A statistical-mechanical treatment of the solubilization in micelle is presented in combination with molecular simulation. The micellar solution is viewed as an inhomogeneous and partially finite, mixed solvent system, and the method of energy representation is employed to evaluate the free-energy change for insertion of a solute into the micelle inside with a realistic set of potential functions. Methane, benzene, and ethylbenzene are adopted as model hydrophobic solutes to analyze the solubilization in sodium dodecyl sulfate micelle. It is shown that these solutes are more favorably located within the micelle than in bulk water and that the affinity to the micelle inside is stronger for benzene and ethylbenzene than for methane. The micellar system is then divided into the hydrophobic core, the head-group region in contact with water, and the aqueous region outside the micelle to assess the relative importance of each region in the solubilization. In support of the pseudophase model, the aqueous region is found to be unimportant to determine the extent of solubilization. The contribution from the hydrophobic-core region is shown to be dominant for benzene and ethylbenzene, while an appreciable contribution from the head-group region is observed for methane. The methodology presented is not restricted to the binding of a molecule to micelle, and will be useful in treating the binding to such nanoscale structures as protein and membrane.

Free-energy analysis of the molecular binding into lipid membrane with the method of energy representation

A statistical-mechanical treatment of the molecular binding into lipid membrane is presented in combination with molecular simulation. The membrane solution is viewed as an inhomogeneous, mixed solvent system, and the free energy of solvation of a solute in membrane is computed with a realistic set of potential functions by the method of energy representation. Carbon monoxide, carbon dioxide, benzene, and ethylbenzene are adopted as model solutes to analyze the binding into 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) membrane. It is shown that the membrane inside is more favorable than bulk water and that the solute distribution is diffuse throughout the membrane inside. The membrane-water partition coefficient is then constructed with the help of the Kirkwood-Buff theory from the solvation free energy obtained separately in the hydrophobic, glycerol, headgroup, and aqueous regions. To discuss the role of repulsive and attractive interactions, the solvation free energy is partitioned into the DMPC and water contributions and the effect of water to stabilize the benzene and ethylbenzene solutes within the membrane is pointed out.

Structural study of supercritical water. II. Computer simulations

The proton chemical shift of supercritical water is analyzed by computer simulations with emphasis on its relationship to the number of hydrogen bonds per water molecule and the dipole moment of a water molecule. The chemical shift is shown to be proportional to the number of hydrogen bonds, and the dipole moment of a water molecule at supercritical states is estimated within the simple point charge (SPC)-like and TIP4P-like frameworks of the water intermolecular potential model. The dipole moment can then be used to construct an effective potential model suitable for simulating supercritical water. The radial and orientational correlations in supercritical water are examined using the effective potential model.

A new high-temperature multinuclear-magnetic-resonance probe and the self-diffusion of light and heavy water in sub- and supercritical conditions

A high-resolution nuclear-magnetic-resonance probe (500 MHz for 1H) has been developed for multinuclear pulsed-field-gradient spin-echo diffusion measurements at high temperatures up to 400 degrees C. The convection effect on the self-diffusion measurement is minimized by achieving the homogeneous temperature distributions of +/-1 and +/-2 degrees C, respectively, at 250 and 400 degrees C. The high temperature homogeneity is attained by using the solid-state heating system composed of a ceramic (AlN) with high thermal conductivity comparable with that of metal aluminium. The self-diffusion coefficients D for light (1H2O) and heavy (2H2O) water are distinguishably measured at subcritical temperatures of 30-350 degrees C with intervals of 10-25 degrees C on the liquid-vapor coexisting curve and at a supercritical temperature of 400 degrees C as a function of water density between 0.071 and 0.251 gcm3. The D value obtained for 1H2O is 10%-20% smaller than those previously reported because of the absence of the convection effect. At 400 degrees C, the D value for 1H2O is increased by a factor of 3.7 as the water density is reduced from 0.251 to 0.071 gcm3. The isotope ratio D(1H2O)D(2H2O) decreases from 1.23 to approximately 1.0 as the temperature increases from 30 to 400 degrees C. The linear hydrodynamic relationship between the self-diffusion coefficient divided by the temperature and the inverse viscosity does not hold. The effective hydrodynamic radius of water is not constant but increases with the temperature elevation in subcritical water.