Structure and Properties of Supercritical Water: Experimental and Theoretical Characterizations

Water in the supercritical region of the phase diagram exhibits a markedly different structure and properties from that at ambient conditions, which is useful in controlling chemical reactions. Nonetheless, the experimental, as well as theoretical, characterization of the substance is not easy because the region is next to the critical point. This article reviews the experimental as well as theoretical studies on water in the supercritical region and its properties as a solvent for chemical reactions, as carried out by the authors and based on small-angle X-ray scattering and the statistical mechanics theory of molecular liquids, also known as reference interaction-site model (RISM) theory.

Evaluation of an Efficient 3D-RISM-SCF Implementation as a Tool for Computational Spectroscopy in Solution

The 3D-RISM-SCF solvent-model implementation of Gusarov et al. [ J. Phys. Chem. A 2006, 110, 6083-6090] in the Amsterdam density functional program has been improved and extended. In particular, an accurate yet efficient representation of the solute electrostatic potential is provided. The Coulomb-potential fitting of many DFT codes can be used advantageously in this context. The extra effort compared to a point-charge representation is small for a given SCF cycle and compensated by faster SCF convergence. This allows applications to large solutes, as demonstrated by evaluation of the solvatochromism of Reichardt's dye. In general, TDDFT applications to excitation energies in solution stand out and are highlighted. Applications to the ¹⁷O NMR chemical shifts of N-methylformamide in different solvents also demonstrate the distinct advantages of 3D-RISM over continuum solvents. Limitations are observed in this case for water solvent, where the solvent shielding is overestimated. This shortcoming applies also to the ¹⁷O gas-to-liquid shift of water, where we used localized molecular orbital analyses for a deeper understanding. For such cases of extremely strong solute-solvent interactions, couplings between solute and solvent orbitals induced by the magnetic perturbation are relevant. These clearly require a quantum-mechanical treatment of the most closely bound solvent molecules. Except for such extreme cases, 3D-RISM-SCF is very well suited to treat solvent effects on NMR parameters. More serious limitations pertain to the treatment of vibrational spectra, where the absence of the coupling between solute and solvent vibrational modes limits the accuracy of applications of 3D-RISM-SCF. The reported extended, efficient, and numerically accurate 3D-RISM-SCF implementation should provide a useful tool to study chemical and spectroscopic properties of molecules of appreciable size in a realistic solvent environment.

Quantum chemical study and isothermal titration calorimetry of β-cyclodextrin complexes with mianserin in aqueous solution

The structures, interaction energies and thermodynamics of the complex formation between mianserin (MIA) and β-cyclodextrin (β-CD) are investigated using computational methods and calorimetric measurements.

A closure relation to molecular theory of solvation for macromolecules

We propose a closure to the integral equations of molecular theory of solvation, particularly suitable for polar and charged macromolecules in electrolyte solution. This includes such systems as oligomeric polyelectrolytes at a finite concentration in aqueous and various non-aqueous solutions, as well as drug-like compounds in solution. The new closure by Kobryn, Gusarov, and Kovalenko (KGK closure) imposes the mean spherical approximation (MSA) almost everywhere in the solvation shell but levels out the density distribution function to zero (with the continuity at joint boundaries) inside the repulsive core and in the spatial regions of strong density depletion emerging due to molecular associative interactions. Similarly to MSA, the KGK closure reduces the problem to a linear equation for the direct correlation function which is predefined analytically on most of the solvation shells and has to be determined numerically on a relatively small (three-dimensional) domain of strong depletion, typically within the repulsive core. The KGK closure leads to the solvation free energy in the form of the Gaussian fluctuation (GF) functional. We first test the performance of the KGK closure coupled to the reference interaction site model (RISM) integral equations on the examples of Lennard-Jones liquids, polar and nonpolar molecular solvents, including water, and aqueous solutions of simple ions. The solvation structure, solvation chemical potential, and compressibility obtained from RISM with the KGK closure favorably compare to the results of the hypernetted chain (HNC) and Kovalenko-Hirata (KH) closures, including their combination with the GF solvation free energy. We then use the KGK closure coupled to RISM to obtain the solvation structure and thermodynamics of oligomeric polyelectrolytes and drug-like compounds at a finite concentration in electrolyte solution, for which no convergence is obtained with other closures. For comparison, we calculate their solvation structure from molecular dynamics (MD) simulations. We further couple the 3D-RISM integral equation with the 3D-version of the KGK closure, and solve it for molecular mixtures as well as oligomeric polyelectrolytes and drug-like molecules in electrolyte solutions.

The Effect of Molecular Structure and Environment on the Miscibility and Diffusivity in Polythiophene-Methanofullerene Bulk Heterojunctions: Theory and Modeling with the RISM Approach

Although better means to model the properties of bulk heterojunction molecular blends are much needed in the field of organic optoelectronics, only a small subset of methods based on molecular dynamics- and Monte Carlo-based approaches have been hitherto employed to guide or replace empirical characterization and testing. Here, we present the first use of the integral equation theory of molecular liquids in modelling the structural properties of blends of phenyl-C61-butyric acid methyl ester (PCBM) with poly(3-hexylthiophene) (P3HT) and a carboxylated poly(3-butylthiophene) (P3BT), respectively. For this, we use the Reference Interaction Site Model (RISM) with the Universal Force Field (UFF) to compute the microscopic structure of blends and obtain insight into the miscibility of its components. Input parameters for RISM, such as optimized molecular geometries and charge distribution of interaction sites, are derived by the Density Functional Theory (DFT) methods. We also run Molecular Dynamics (MD) simulation to compare the diffusivity of the PCBM in binary blends with P3HT and P3BT, respectively. A remarkably good agreement with available experimental data and results of alternative modelling/simulation is observed for PCBM in the P3HT system. We interpret this as a step in the validation of the use of our approach for organic photovoltaics and support of its results for new systems that do not have reference data for comparison or calibration. In particular, for the less-studied P3BT, our results show that expectations about its performance in binary blends with PCBM may be overestimated, as it does not demonstrate the required level of miscibility and short-range structural organization. In addition, the simulated mobility of PCBM in P3BT is somewhat higher than what is expected for polymer blends and falls into a range typical for fluids. The significance of our predictive multi-scale modelling lies in the insights it offers into nanoscale morphology and charge transport behaviour in multi-component organic semiconductor blends.

TOWARDS A MOLECULAR THEORY FOR THE VAN DER WAALS–MAXWELL DESCRIPTION OF FLUID PHASE TRANSITIONS

We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to first-principles microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals–Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids.

Compressibility oftert-Butyl Alcohol-Water Mixtures: The Rism Theory

The isothermal compressibility χTof binary mixtures of water and tert-butyl alcohol (TBA) is calculated using the reference interaction site model (RISM) integral equation theory. The calculations are performed over the whole concentration from x = 0 to 1 and a wide temperature from T = 283 to 313 K ranges employing the extended point charge model for water and optimized site–site potentials for TBA molecules. The results obtained are compared versus available experimental data. It is demonstrated that, despite an approximate character of the model potentials and closure relation applied, the theory is able to reproduce qualitatively all main features of the x- and T-dependencies of χTinherent in real experiment. Such features include the decrease of compressibility with increasing T in the low TBA concentration limit x → 0 (pure water), and the increase of χTwith rising T in the opposite regime x → 1 (pure alcohol); the presence of a concentration region where the function χT(x, T) does not depend much on T; as well as the existence of a minimum in χTwith respect to x at each given T. The question of how to achieve a quantitative agreement between the theoretical and experimental values by correcting the closure relation is also discussed.

Molecular dynamics investigation of dipeptide-transition metal salts in aqueous solutions

Molecular dynamics (MD) simulations of glycylglycine dipeptide with transition metal ions (Mn(2+), Fe(2+), Co(2+), Ni(2+), Cu(2+), and Zn(2+)) in aqueous solutions have been carried out to get an insight into the solvation structure, intermolecular interactions, and salt effects in these systems. The solvation structure and hydrogen bonding were described in terms of radial distribution function (RDF) and spatial distribution function (SDF). The dynamical properties of the solvation structure were also analyzed in terms of diffusion and residence times. The simulation results show the presence of a well-defined first hydration shell around the dipeptide, with water molecules forming hydrogen bonds to the polar groups of the dipeptide. This shell is, however, affected by the strong electric field of divalent metal ions, which at higher ion concentrations lead to the shift in the dipeptide-water RDFs. Higher salt concentrations lead also to increased residence times and slower diffusion rates. In general, smaller ions (Cu(2+), Zn(2+)) demonstrate stronger binding to dipeptide than the larger ones (Fe(2+), Mn(2+)). Simulations do not show any stronger association of peptide molecules indicating their dissolution in water. The above results may be of potential interest to future researchers on these molecular interactions.

A molecular theory of liquid interfaces

We propose a site site generalization of the Lovett-Mow-Buff-Wertheim integro-differential equation for the one-particle density distributions to polyatomic fluids. The method provides microscopic description of liquid interfaces of molecular fluids and solutions. It uses the inhomogeneous site-site direct correlation function of molecular fluid consistently constructed by nonlinear interpolation between the homogeneous ones. The site site correlations of the coexisting bulk phases are obtained from the reference interaction site model (RISM) integral equation with our closure approximation. For illustration, we calculated the structure of the planar liquid-vapor as well as liquid-liquid interfaces of n-hexane and methanol at ambient conditions.

Self-consistent combination of the three-dimensional RISM theory of molecular solvation with analytical gradients and the Amsterdam density functional package

The three-dimensional reference interaction site model with the closure relation by Kovalenko and Hirata (3D-RISM-KH) in combination with the density functional theory (DFT) method has been implemented in the Amsterdam density functional (ADF) software package. The analytical first derivatives of the free energy with respect to displacements of the solute nuclear coordinates have also been developed. This enables study of chemical reactions, including reaction coordinates and transition state search, with the molecular solvation described from the first principles. The method yields all of the features available by using other solvation approaches, for instance infrared spectra of solvated molecules. To evaluate the accuracy of the present method, test calculations have been carried out for a number of small molecules, including four glycine conformers, a set of small organic compounds, and carbon nanotubes of various lengths in aqueous solution. Our predictions for the solvation free energy agree well with other approaches as well as experiment. This new development makes it possible to calculate at modest computational cost the electronic properties and molecular solvation structure of a solute molecule in a given molecular liquid or mixture from the first principles.

Partial molar volume of proteins studied by the three-dimensional reference interaction site model theory

The three-dimensional reference interaction site model (3D-RISM) theory is applied to the analysis of hydration effects on the partial molar volume of proteins. For the native structure of some proteins, the partial molar volume is decomposed into geometric and hydration contributions using the 3D-RISM theory combined with the geometric volume calculation. The hydration contributions are correlated with the surface properties of the protein. The thermal volume, which is the volume of voids around the protein induced by the thermal fluctuation of water molecules, is directly proportional to the accessible surface area of the protein. The interaction volume, which is the contribution of electrostatic interactions between the protein and water molecules, is apparently governed by the charged atomic groups on the protein surface. The polar atomic groups do not make any contribution to the interaction volume. The volume differences between low- and high-pressure structures of lysozyme are also analyzed by the present method.

Locating missing water molecules in protein cavities by the three-dimensional reference interaction site model theory of molecular solvation

Water molecules confined in protein cavities are of great importance in understanding the protein structure and functions. However, it is a nontrivial task to locate such water molecules in protein by the ordinary molecular simulation and modeling techniques as well as experimental methods. The present study proves that the three-dimensional reference interaction site model (3D-RISM) theory, a recently developed statistical-mechanical theory of molecular solvation, has an outstanding advantage in locating such water molecules. In this paper, we demonstrate that the 3D-RISM theory is able to reproduce the structure and the number of water molecules in cavities of hen egg-white lysozyme observed commonly in the X-ray structures of different resolutions and conditions. Furthermore, we show that the theory successfully identified a water molecule in a cavity, the existence of which has been ambiguous even from the X-ray results. In contrast, we confirmed that molecular dynamics simulation is helpless at present to find such water molecules because the results substantially depend on the initial coordinates of water molecules. Possible applications of the theory to problems in the fields of biochemistry and biophysics are also discussed.

Structure and Dipole Moments of the Two Distinct Solvated Forms of p-Nitroaniline in Acetonitrile/CCl4 As Studied by Infrared Electroabsorption Spectroscopy

Structure and dipole moments of the two distinct solvated forms of p-nitroaniline (pNA) in acetonitrile/CCl4 have been studied by infrared electroabsorption spectroscopy. We measured a series of infrared electroabsorption spectra of pNA dissolved in an acetonitrile/CCl4 mixed solvent by altering the angle chi between the external electric field and the electric field vector of the incident infrared light. A singular value decomposition analysis has revealed that the observed infrared electroabsorption spectra are decomposed into two major components: the chi-dependent and chi-independent components. The decomposed spectral components as well as the infrared absorption spectrum are well explained in terms of two distinct solvated forms of pNA that exist in equilibrium in the mixed solvent. These solvated forms can be assigned to the 1:1 and 1:2 species, which have one and two acetonitrile molecule(s), respectively, associated with pNA. From a least-squares fitting analysis of the chi-dependent spectral component, it is shown that, for both the 1:1 and 1:2 species, a head-to-tail structure accounts well for the experimental results. On the other hand, the chi-independent component is likely to arise from the population change between the two solvated forms. This electric-field-induced population change of solvated forms may lead to the control of dielectric environments in solution by an external electric field.

A new method to determine electrostatic potential around a macromolecule in solution from molecular wave functions

The three-dimensional reference interaction site model integral equation theory (3D-RISM) combined with the ab initio molecular orbital method (3D-RISM-SCF) is applied to a solvated macromolecular system. The solvation structure around a solute molecule is obtained from the 3D-RISM integral equation under the electrostatic potential of the solute molecule, calculated by the ab initio molecular orbital theory. The electrostatic potential should be calculated on each grid point in the three-dimensional real space. Therefore, the calculation of the electrostatic potential is the most time consuming part in this method. In this article, we propose a new procedure to save the computational cost for calculating the electrostatic potential and the solvated fock matrix. The strategy of this procedure is to evaluate the electrostatic potential and the solvated fock matrix in different ways, depending on the distance between solute and solvent. Inside the repulsive cores of solute atoms, it is possible to avoid the calculation of electrostatic potential and solvated Fock matrix by assuming the potential to be infinity. In the region sufficiently far from solute, they are evaluated classically by putting the effective point charge on each atom. In the intermediate region, the electrostatic potential is evaluated directly by integrating the molecular orbitals of the solute molecule. The electronic structure and the energy gradient of Methionine-Enkephalin and solvation structure are estimated by using this procedure in aqueous solution, and are compared with the results from other procedures. The results are compared also with those from the continuum model.

Hydrophobic effects on partial molar volume

The hydrophobic effects on partial molar volume (PMV) are investigated as a PMV change in the transfer of a benzenelike nonpolar solute from the nonpolar solvent to water, using an integral equation theory of liquids. The volume change is divided into two effects. One is the "packing" effect in the transfer from the nonpolar solvent to hypothetical "nonpolar water" without hydrogen bonding networks. The other is the "iceberg" effect in the transfer from nonpolar water to water. The results indicate that the packing effect is negative and a half compensated by the positive iceberg effect. The packing effect is explained by the difference in the solvent compressibility. Further investigation shows that the sign and magnitude of the volume change depend on the solute size and the solvent compressibility. The finding gives a significant implication that the exposure of a hydrophobic residue caused by protein denaturation can either increase or decrease the PMV of protein depending on the size of the residue and the fluctuation of its surroundings.

Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.

Enthalpic homogeneous pair interaction coefficients of L-alpha-amino acids as a hydrophobicity parameter of amino acid side chains

Enthalpies of dilution of aqueous solutions of L-alpha-cysteine, L-alpha-histidine, L-alpha-asparagine, L-alpha-glutamine, L-alpha-arginine, L-alpha-tryptophan, and L-alpha-glutamic acid in water at a temperature of 298.15 K have been measured. The values of dilution enthaply were used to determine enthalpic homogeneous pair interaction coefficients which characterize the interactions between zwitterions of the examined L-alpha-amino acids in water. Approachable literature data of hydrophobic scales have been analyzed to obtain average values. The obtained values of enthalpic pair interaction coefficients have been put together with an average hydrophobic scale.