Solute-solvent System Research Articles

Development of three-dimensional site-site Smoluchowski-Vlasov equation and application to electrolyte solutions

Site-site Smoluchowski-Vlasov (SSSV) equation enables us to directly calculate van Hove time correlation function, which describes diffusion process in molecular liquids. Recently, the theory had been extended to treat solute-solvent system by Iida and Sato [J. Chem. Phys. 137, 034506 (2012)]. Because the original framework of SSSV equation is based on conventional pair correlation function, time evolution of system is expressed in terms of one-dimensional solvation structure. Here, we propose a new SSSV equation to calculate time evolution of solvation structure in three-dimensional space. The proposed theory was applied to analyze diffusion processes in 1M NaCl aqueous solution and in lithium ion battery electrolyte solution. The results demonstrate that these processes are properly described with the theory, and the computed van Hove functions are in good agreement with those in previous works.

Vibrational energy relaxation of the amide I mode of N-methylacetamide in D₂O studied through Born-Oppenheimer molecular dynamics.

The vibrational relaxation of the amide I mode of deuterated N-methylacetamide in D2O solution is studied through nonequilibrium simulations using the semiempirical Born-Oppenheimer molecular dynamics (SEBOMD) approach to describe the whole solute-solvent system. Relaxation pathways and lifetimes are determined using the instantaneous normal mode (INM) analysis. The relaxation of the amide I mode is characterized by three different time scales; most of the excess energy (80%) is redistributed through intramolecular vibrational energy redistribution processes, with a smaller contribution (20%) of intermolecular energy flowing into the solvent. The amide II mode is found to contribute modestly (7%) to the relaxation mechanism. The amide I mode and the total vibrational energy decay curves obtained using SEBOMD and INM are in satisfactory agreement with the experimental measurements.

Heterogeneous Hydration of p53/MDM2 Complex.

Water-mediated interactions play critical roles in biomolecular recognition processes. Explicit solvent molecular dynamics (MD) simulations and the variational implicit-solvent model (VISM) are used to study those hydration properties during binding for the biologically important p53/MDM2 complex. Unlike simple model solutes, in such a realistic and heterogeneous solute–solvent system with both geometrical and chemical complexity, the local water distribution sensitively depends on nearby amino acid properties and the geometric shape of the protein. We show that the VISM can accurately describe the locations of high and low density solvation shells identified by the MD simulations and can explain them by a local coupling balance of solvent–solute interaction potentials and curvature. In particular, capillary transitions between local dry and wet hydration states in the binding pocket are captured for interdomain distance between 4 to 6 Å, right at the onset of binding. The underlying physical connection between geometry and polarity is illustrated and quantified. Our study offers a microscopic and physical insight into the heterogeneous hydration behavior of the biologically highly relevant p53/MDM2 system and demonstrates the fundamental importance of hydrophobic effects for biological binding processes. We hope our study can help to establish new design rules for drugs and medical substances.

Solvent dependence of Stokes shift for organic solute–solvent systems: A comparative study by spectroscopy and reference interaction-site model–self-consistent-field theory

The Stokes shift magnitudes for coumarin 153 (C153) in 13 organic solvents with various polarities have been determined by means of steady-state spectroscopy and reference interaction-site model-self-consistent-field (RISM-SCF) theory. RISM-SCF calculations have reproduced experimental results fairly well, including individual solvent characteristics. It is empirically known that in some solvents, larger Stokes shift magnitudes are detected than anticipated on the basis of the solvent relative permittivity, ɛr. In practice, 1,4-dioxane (ɛr = 2.21) provides almost identical Stokes shift magnitudes to that of tetrahydrofuran (THF, ɛr = 7.58), for C153 and other typical organic solutes. In this work, RISM-SCF theory has been used to estimate the energetics of C153-solvent systems involved in the absorption and fluorescence processes. The Stokes shift magnitudes estimated by RISM-SCF theory are ∼5 kJ mol(-1) (400 cm(-1)) less than those determined by spectroscopy; however, the results obtained are still adequate for dipole moment comparisons, in a qualitative sense. We have also calculated the solute-solvent site-site radial distributions by this theory. It is shown that solvation structures with respect to the C-O-C framework, which is common to dioxane and THF, in the near vicinity (∼0.4 nm) of specific solute sites can largely account for their similar Stokes shift magnitudes. In previous works, such solute-solvent short-range interactions have been explained in terms of the higher-order multipole moments of the solvents. Our present study shows that along with the short-range interactions that contribute most significantly to the energetics, long-range electrostatic interactions are also important. Such long-range interactions are effective up to 2 nm from the solute site, as in the case of a typical polar solvent, acetonitrile.

Hydrogen transfer reactions in viscous media — Potential and free energy surfaces in solvent–solute coordinates and their kinetic implications

Two-dimensional potential energy and free energy surfaces are obtained using quantum mechanical and molecular dynamics calculations for four hydrogen transfer reactions in n-hexane solvent: the methyl–methane, n-propyl–n-propane, n-pentyl–n-pentane, and t-butyl–isobutane systems. The resultant surfaces have similar landscapes despite the fact the equilibrated solvent cavities for these systems are notably different in size and shape. The kinetic implications of these landscapes are discussed. The Arrhenius and tunneling kinetics of hydrogen transfer in nonpolar hydrocarbon solute–solvent systems are not expected to show any significant viscosity dependence.

Needle-Shaped Crystals: Causality and Solvent Selection Guidance Based on Periodic Bond Chains

Needle-shaped crystals, typified by aspect ratios of (1:1:100–1000) are often the steady-state growth shapes in the crystallization of active pharmaceutical ingredients from solution. Crystals with such high aspect ratio shapes are troublesome in the subsequent processing steps required in the formation of a drug product. Therefore, the ability to design crystallizations that directly avoid the formation of needles is of significant interest. In this article, a causality for the formation of needles and guidance for solvent selection based on this causality are provided. The causality presented in this article was formed based on a spiral growth model and requires the presence of a single strongest periodic bond chain within the lattice that is parallel to the direction of elongation of the crystal. The article provides a method for predicting the formation of a needle for a given solute–solvent system based on this causality. Furthermore, three case studies are provided that demonstrate good agreement between experimentally obtained and predicted shapes. As a result, generalized guidance for solvent selection based on the objective of avoiding needles is provided.

A maximum entropy thermodynamics of small systems

We present a maximum entropy approach to analyze the state space of a small system in contact with a large bath, e.g., a solvated macromolecular system. For the solute, the fluctuations around the mean values of observables are not negligible and the probability distribution P(r) of the state space depends on the intricate details of the interaction of the solute with the solvent. Here, we employ a superstatistical approach: P(r) is expressed as a marginal distribution summed over the variation in β, the inverse temperature of the solute. The joint distribution P(β, r) is estimated by maximizing its entropy. We also calculate the first order system-size corrections to the canonical ensemble description of the state space. We test the development on a simple harmonic oscillator interacting with two baths with very different chemical identities, viz., (a) Lennard-Jones particles and (b) water molecules. In both cases, our method captures the state space of the oscillator sufficiently well. Future directions and connections with traditional statistical mechanics are discussed.

Ultrafast intermolecular vibrational excitation transfer from solute to solvent: Observation of intermediate states

Ultrafast two-dimensional infrared (2DIR) and IR pump–probe (PP) spectroscopy was used to study the intermolecular vibrational energy transfer process from the excited state of asymmetric stretching vibration of HN3 to the overtone band of C–O stretching vibration of solvent methanol. A series of time-resolved 2DIR spectra indicate an intermolecular vibrational excitation transfer between the two modes, since the corresponding cross peaks appear at longer waiting times (>20ps). However, detailed analyses of temperature-dependent FTIR, dispersed IR PP, and 2DIR spectra showed that the vibrational relaxation of the azido stretch mode and its energy transfer to solvent methanol C–O stretch overtone mode involve not only heat dissipation directly to the solvent bath modes but also production of transient intermediate states. The present experimental work demonstrates that ultrafast nonlinear IR spectroscopy is quite useful to shed light into the complicated vibrational relaxation dynamics of H-bonded solute–solvent systems.

Modeling of precipitation of ultra-fine particles by pressure reduction over CO2-expanded liquids

A mathematical model has been developed to describe the process of precipitation of ultrafine particles by pressure reduction over gas (CO2)-expanded liquids. A rapid pressure reduction over a CO2-expanded organic solution, from 30–70 to 1bar at 303K decreases the solution temperature by 30–80K in a very short span of time (0.5–1.5min), which generates a rapid, high, and uniform supersaturation of the dissolved solute in the solution and facilitates precipitation of ultrafine particles. The model developed in this work estimates the supersaturation attained, nucleation and growth rates obtained during the pressure reduction over CO2-expanded organic solutions, and the particle size distribution of the precipitated particles. Cholesterol has been chosen as a model solute to be precipitated, and acetone has been chosen as a solvent. A new method has been developed for prediction of equilibrium solubility of solute which is affected by a decrease in CO2 mole fraction as well as a simultaneous decrease in solution temperature during pressure reduction. This method combines the semi-empirical approach of using the partial molar volume fraction of solvent in a CO2-solvent binary mixture and solid–liquid equilibrium data for a solute–solvent system. Size distributions of the precipitated particles have been calculated assuming primary nucleation (homogeneous as well as heterogeneous nucleation) and diffusion-limited growth kinetics. The predicted mean average particle sizes are then compared with the size of cholesterol particles precipitated by pressure reduction of a CO2-expanded acetone solution of cholesterol. The particle sizes predicted assuming heterogeneous nucleation are found to be closer to the experimentally observed particle sizes, indicating that the heterogeneous nucleation could be the main mechanism of nucleation, which could occur at the gas–liquid interface of the CO2 bubbling out of CO2-expanded solution during pressure reduction.

Theoretical spectroscopy using molecular dynamics: theory and application to CH5+ and its isotopologues

Infrared spectroscopy is a powerful technique to unravel the structure and dynamics of molecular systems of ever increasing complexity. For isolated molecules in the gas phase theoretical approaches that directly rely on solving the Schrödinger equation, either approximately or quasi-exactly, are well established. A distinctly different approach to compute infrared spectra can be based on advanced molecular dynamics, itself being based on classical Newtonian dynamics, in conjunction with concurrent first principles electronic structure calculations. At variance with traditional methods, which are formulated in terms of the Schrödinger representation of quantum mechanics, the molecular dynamics approach stems from Heisenberg's representation and thus relies on computing thermal expectation values of time-correlation functions. Crucial in addition to generating the spectra themselves is their decomposition in terms of modes, which can be assigned to correlated atomic motion. This ab initio molecular dynamics route to compute infrared spectra, and its recent extension to quasiclassical techniques relying on approximate path integral dynamics, is covered in the review part of this Perspective. The usefulness of this unconventional approach, which can be generalized beyond infrared spectroscopy, is demonstrated in detail by applying the full machinery in computing and assigning the infrared spectra of protonated methane and its isotopologues. This particular molecule is often considered to be the most prominent member of the class of floppy or fluxional molecules. CH5(+) has been a longstanding challenge for theoretical infrared spectroscopy because it undergoes intricate large-amplitude motion, which is also reviewed. Molecular dynamics based infrared spectroscopy is general and can be applied to diverse systems such as molecular complexes in the gas phase, chromophores in biomolecular environments, and solute-solvent systems in the liquid phase.

Identification of nucleation rates in droplet-based microfluidic systems

Characterization of the rate of nucleation of crystals from solution continues to be of interest, both for investigations into fundamental molecular phenomena as well as for applications in the pharmaceuticals, biotechnology, and fine chemicals industries. Substantial experimental evidence indicates that nucleation in some solute-solvent systems does not agree with classical theory, especially at high supersaturations. An approach is proposed for computing bounds on the nucleation rate as a function of supersaturation that does not require an assumed analytical expression for the nucleation kinetics. The approach involves (1) a microfluidic platform that measures crystal nuclei formation in droplets, (2) the analytical solution of the Chemical Master equation for nucleation that takes finite-volume effects into account, and (3) a numerical algorithm that employs linear splines to construct upper and lower bounds on the nucleation rate from the experimental data produced by the microfluidic platform. The approach is demonstrated for mean induction times measured for the nucleation of paracetamol and glycine crystals in aqueous solution. The approach can be used to suggest dependencies for the development of new nucleation expressions and for providing kinetic information needed for the simulation of crystallizers that operate at high supersaturations, such as dual-impinging-jet and vortex-mixer crystallizers.

Separation of lactic acid from fermentation broth by cross flow nanofiltration: Membrane characterization and transport modelling

A dynamic mathematical model was developed for a flat sheet cross flow nanofiltration membrane module for separation of lactic acid from fermentation broth. The model developed with extended Nernst-Planck approach included pH effects during Donnan exclusion of lactate ions through Henderson–Hasselbalch equation. The most relevant structural characteristics (pore radius, porosity to thickness ratio and membrane charge density) of the membranes were completely determined by comparison and convergence of the model-predicted and experimental data on flux and rejection using standard solute-solvent systems as well as actual fermentation broth. Thus the pore sizes of the investigated three nanofiltration membranes NF2, NF3 and NF20 were determined as 0.57nm, 0.55nm, and 0.54nm respectively. Through the modelling and experimental investigation the best membrane (NF2) that could retain and recycle more than 90% sugars while allowing more than 70% lactic acid to permeate could also be selected. Finally refined model could very well predict transport of lactic acid through nanofiltration membranes operated in flat-sheet cross flow module as evident in very small relative error (<0.1) and the value of overall correlation coefficient (R2) of greater than 0.980.

Two-dimensional measurements of the solvent structural relaxation dynamics in dipolar solvation

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214-223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.

The number-adaptive multiscale QM/MM molecular dynamics simulation: Application to liquid water

A new treatment is proposed for application to a solute–solvent system of adaptive multiscale QM/MM–MD method that enables the solvent molecules to flow across the boundary between the QM and MM regions by introducing the transition (T) one. In contrast to previous treatments, we define both the QM and T regions by using a number of solvent molecules around the solute, instead of the distance from it. For demonstration, we have applied it to pure water; it has shown that the present method can work effectively with a shorter computation time linearly-scaled by the number of QM calculations.

On a relationship between molecular polarizability and partial molar volume in water

We reveal a universal relationship between molecular polarizability (a single-molecule property) and partial molar volume in water that is an ensemble property characterizing solute-solvent systems. Since both of these quantities are of the key importance to describe solvation behavior of dissolved molecular species in aqueous solutions, the obtained relationship should have a high impact in chemistry, pharmaceutical, and life sciences as well as in environments. We demonstrated that the obtained relationship between the partial molar volume in water and the molecular polarizability has in general a non-homogeneous character. We performed a detailed analysis of this relationship on a set of ~200 organic molecules from various chemical classes and revealed its fine well-organized structure. We found that this structure strongly depends on the chemical nature of the solutes and can be rationalized in terms of specific solute-solvent interactions. Efficiency and universality of the proposed approach was demonstrated on an external test set containing several dozens of polyfunctional and druglike molecules.

A New Approach for Investigating the Molecular Recognition of Protein: Toward Structure-Based Drug Design Based on the 3D-RISM Theory.

A new approach to investigate a molecular recognition process of protein is presented based on the three-dimensional reference interaction site model (3D-RISM) theory, a statistical mechanics theory of molecular liquids. Numerical procedure for solving the conventional 3D-RISM equation consists of two steps. In step 1, we solve ordinary RISM (or 1D-RISM) equations for a solvent mixture including target ligands in order to obtain the density pair correlation functions (PCF) among molecules in the solution. Then, we solve the 3D-RISM equation for a solute-solvent system to find three-dimensional density distribution functions (3D-DDF) of solvent species around a protein, using PCF obtained in the first step. A key to the success of the method was to regard a target ligand as one of "solvent" species. However, the success is limited due to a difficulty of solving the 1D-RISM equation for a solvent mixture, including large ligand molecules. In the present paper, we propose a method which eases the limitation concerning solute size in the conventional method. In this approach, we solve a solute-solute 3D-RISM equations for a protein-ligand system in which both proteins and ligands are regarded as "solutes" at infinite dilution. The 3D- and 1D-RISM equations are solved for protein-solvent and ligand-solvent systems, respectively, in order to obtain the 3D- and 1D-DDF of solvent around the solutes, which are required for solving the solute-solute 3D-RISM equation. The method is applied to two practical and noteworthy examples concerning pharmaceutical design. One is an odorant binding protein in the Drosophila melanogaster , which binds an ethanol molecule. The other is phospholipase A2, which is known as a receptor of acetylsalicylic acid or aspirin. The result indicates that the method successfully reproduces the binding mode of the ligand molecules in the binding sites measured by the experiments.

Joint time-dependent density-functional theory for excited states of electronic systems in solution

We present a novel joint time-dependent density-functional theory for the description of solute-solvent systems in time-dependent external potentials. Starting with the exact quantum-mechanical action functional for both electrons and nuclei, we systematically eliminate solvent degrees of freedom and thus arrive at coarse-grained action functionals which retain the highly accurate \emph{ab initio} description for the solute and are, in principle, exact. This procedure allows us to examine approximations underlying popular embedding theories for excited states. Finally, we introduce a novel approximate action functional for the solute-water system and compute the solvato-chromic shift of the lowest singlet excited state of formaldehyde in aqueous solution, which is in good agreement with experimental findings.

Note on thin film equations for solutions and suspensions

This note discusses how one may further develop thin film evolution equations for solutions and suspensions. First, we review the time evolution equation of a film or drop of simple liquid under the sole influence of wettability and capillarity and its formulation as a gradient dynamics. Second, we introduce such a gradient dynamics for a film of suspension or solution and show that it is equivalent to thin film equations in the literature. Finally, the new formulation is used to discuss extensions towards solute molecules/particles with net attractive interactions, decomposing solute-solvent systems and a solute-dependent wettability.

Ab Initio Study of the Anomalous Solvatochromic Behavior of Large Betaines

The structure and spectroscopic properties of a diluted compound can be deeply affected by its interaction with the neighboring molecules of the solvent, and the associated solvatochromism is an effect that becomes more noticeable with the increase in both the dipole moment of the solute and the polarity of the medium. The correct description of the complex set of interactions that prevail in the solvation process remains a challenge for theoreticians not only when interpreting an observed behavior but also when considering the possible existence of novel properties in untested solute-solvent systems. On the basis of an ab initio study, we examine here how the presence of solvents of different polarities should affect the electronic properties of a family of molecules, formally related to Betaine-30 (aka Reichardt's dye), whose donor (D) and acceptor (A) groups are terminally connected to conjugated chains of different sizes. Because these molecules exhibit elevated ground-state dipole moment that should strongly interact with molecules of a polar solvent, a large hypsochromic shift is predicted for them. However, in a recent gas-phase study of these molecules, we have established the existence of an "inversion" in the spatial localization of their frontier orbitals when the size of the conjugated bridge connecting the D and A groups is progressively increased. This fact has led us to suggest that the increase in size of dissolved betaines should be accompanied by a large variation in their solvatochromic properties. In this work, we first use the self-consistent reaction field approach at the configuration interaction level to estimate the expected bathochromic shift in the absorption spectra (positive solvatochromism) in the largest members of the investigated betaine family when dissolved in different low polarity solvents and then discuss the conformational changes as a consequence of the solute--solvent interactions. We then use these results to interpret the observed solvatochromic properties of push--pull molecules of varying size and discuss the corresponding implications on their photochemical properties.

A new framework and a simpler method for the development of batch crystallization recipes

AbstractWe use a new generalized dimensionless model of a seeded batch crystallization process to compare results from four crystal growth rate/concentration trajectories: a numerically‐computed optimal trajectory, a constant growth rate trajectory, a trajectory proposed by Mullin and Nyvlt [Chem Eng Sci. 1971;26:369–377] that can be calculated without a kinetic model, and a linear concentration‐time trajectory. Because the model is generalized and dimensionless it is not specific to any particular solute–solvent system. We show that if seed properties are good, all trajectories achieve a good result, whereas if seed properties are poor all trajectories achieve a poor result. If seed properties are intermediate, the linear concentration trajectory performs much worse than the other trajectories. On the basis of this, we conclude: (1) Linear trajectories and natural cooling trajectories are poor and should be avoided. When evaluating the benefit derived from an optimization of a temperature/saturation concentration trajectory, the appropriate benchmark should be the Mullin‐Nyvlt trajectory, which typically performs much better than the linear trajectory and can be calculated knowing only the mass of seeds at the beginning of the batch. (2) Changing seed properties is more likely to improve batch crystallizer performance than optimizing the growth/saturation concentration trajectory. (3) For rapid process development, the most reasonable approach is to use the Mullin‐Nyvlt trajectory and seek to improve process performance by adjusting seed properties. © 2010 American Institute of Chemical Engineers AIChE J, 2011