Quasi-chemical Theory Research Articles

The Importance of the Water Molecular Quadrupole for Estimating Interfacial Potential Shifts Acting on Ions Near the Liquid-Vapor Interface.

Interfacial electrostatic potential gradients arise from nonuniform charge distributions encountered crossing the interface. The charges involved can include the molecular charges predominantly bound to each neutral solvent molecule and distributions of ions (or electrons) free to move in the interfacial region. This paper focuses on the solvent contribution to the interfacial potential. Quasichemical theory (QCT) provides a physical framework for the analysis of near-local (chemical) and far-field contributions to ion solvation free energies. Here, we utilize QCT to analyze cavity net potentials that contribute to the single-ion real solvation free energy. In particular, we discuss the results of molecular dynamics simulations of water droplets large enough to exhibit bulklike behavior in the droplet interior. A multipolar analysis of the cavity potential illustrates the importance of the solvent molecular quadrupole due to the near-cancellation of the dipolar contributions from the cavity-liquid and liquid-vapor interfaces. The results reveal the physical origin of the previously observed strong classical model dependence of the cavity potential.

Quasi-chemical theory for anion hydration and specific ion effects: [formula omitted](aq) vs.[formula omitted](aq)

Anion hydration is complicated by H-bond between neighboring water molecules in addition to H-bond donation to the anion. This situation leads to competing structures and anharmonic vibrations for simple clusters like (H2O)nCl-. This study applies quasi-chemical theory to study anion hydration and exploits dynamics calculations on isolated clusters to account for anharmonicity. Comparing singly hydrated halide clusters, classic H-bond donation to the anion occurs for F- , while Cl- clusters exhibit flexible dipole-dominated interactions. The predicted Cl- – F- hydration free energy difference agrees with experiment, a significant theoretical step for addressing issues like Hofmeister ranking and selectivity in ion channels.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration.

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H2O) n - can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Structure, Dynamics, and Hydration Free Energy of Carbon Dioxide in Aqueous Solution: A Quantum Mechanical/Molecular Mechanics Molecular Dynamics Thermodynamic Integration (QM/MM MD TI) Simulation Study.

The solvation of carbon dioxide in solution represents a key step for the capture and fixation CO2 in nature, which may be further influenced by the formation of (bi)carbonate species and/or the formation of CO2 clusters in solution. The latter processes are strongly dependent on the exact environment of the liquid state (e.g., pH value, solvated ions, etc.) and may interfere with the experimental determination of structural, dynamical, and thermodynamic properties. In this work a hybrid quantum mechanical/molecular mechanical (QM/MM) simulation approach at correlated ab initio level of theory resolution-of-identity second-order Møller-Plesset Perturbation Theory (RI-MP2) has been applied in the framework of thermodynamic integration (TI) to study structure, dynamics, and the hydration free energy of a single carbon dioxide molecule in aqueous solution. A detailed analysis of the individual QM/MM potential energy contributions demonstrate that the overall potential remains highly consistent over the entire sampling phase and that no artificial contributions are influencing the determination of the hydration free energy. The latter value of 0.01 ± 0.92 kcal/mol was found in very good agreement with the values of 0.06 and 0.24 kcal/mol obtained via quasi-chemical theory and experimental measurements, respectively. In order to obtain detailed information about the C- and O C-water interaction, conically restricted regions with respect to the main axis of the CO2 molecule have been employed in structural analysis. The presented data not only provide detailed information about the hydration properties of CO2 but act as a critical validation of the simulation technique, which will be beneficial in the study of nonaqueous solvents such as pure and aqueous NH3 solutions, which have been suggested as potential candidates to capture CO2 from anthropogenic sources.

Re-examining the tetraphenyl-arsonium/tetraphenyl-borate (TATB) hypothesis for single-ion solvation free energies

Attempts to establish an absolute single-ion hydration free energy scale have followed multiple strategies. Two central themes consist of (1) employing bulk pair thermodynamic data and an underlying interfacial-potential-free model to partition the hydration free energy into individual contributions [Marcus, Latimer, and tetraphenyl-arsonium/tetraphenyl-borate (TATB) methods] or (2) utilizing bulk thermodynamic and cluster data to estimate the free energy to insert a proton into water, including in principle an interfacial potential contribution [the cluster pair approximation (CPA)]. While the results for the hydration free energy of the proton agree remarkably well between the three approaches in the first category, the value differs from the CPA result by roughly +10 kcal/mol, implying a value for the effective electrochemical surface potential of water of -0.4 V. This paper provides a computational re-analysis of the TATB method for single-ion free energies using quasichemical theory. A previous study indicated a significant discrepancy between the free energies of hydration for the TA cation and the TB anion. We show that the main contribution to this large computed difference is an electrostatic artifact arising from modeling interactions in periodic boundaries. No attempt is made here to develop more accurate models for the local ion/solvent interactions that may lead to further small free energy differences between the TA and TB ions, but the results clarify the primary importance of interfacial potential effects for analysis of the various free energy scales. Results are also presented, related to the TATB assumption in the organic solvents dimethyl sulfoxide and 1,2-dichloroethane.

Influence of salt concentration on solubility and tie-line data for the system: Formic acid + n-butanol + water

ABSTRACTThe tie-line and solubility data, i.e. formic acid (FA) + n-butanol + water + NaCl, were resolved at T = 298.15 K and under ambient pressure. The Othmer–Tobias equation was applied in this study. The experimental data were correlated and all linear correlation coefficients were found to be approximately equal to 1. Both the Universal Quasi-chemical Theory (UNIQUAC) and Nonrandom Two Liquid Theory (NRTL) and NRTL models were employed in order to compare the experimental liquid–liquid equilibrium (LLE) and tie-line data. Consequently, the calculated and experimental data proved to be a good fit. Results show that adding salt to the system proved beneficial by increasing the separation of FA from water.

Erratum: "Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute" [J. Chem. Phys. 147, 124505 (2017)

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Equilibrium study for ternary mixtures of biodiesel

The liquid-liquid equilibrium (LLE) data for the ternary mixtures of methanol + fatty acid methyl ester (FAME) + palm oil and FAME + palm oil + glycerol at various temperatures from 35 to 55°C, the tie lines and binodial curves were also investigated and plotted in the equilibrium curve. The experimental results showed that the binodial curves of methanol + FAME + palm oil depended significantly with temperature while the binodial curves of FAME + palm oil + glycerol illustrated insignificant change with temperatures. The interaction parameters between liquid pair obtained for NRTL (Nonrandom Two-Liquid) and UNIQUAC (Universal Quasi-Chemical Theory) models from the experimental data were also investigated. It was found that the correlated parameters of UNIQUAC model for system of FAME + palm oil + glycerol, denoted as a13 and a31, were 580.42K and -123.69K, respectively, while those for system of methanol + FAME + palm oil, denoted as a42 and a24, were 71.48 K and 965.57K, respectively. The ternary LLE data reported here would be beneficial for engineers and scientists to use for prediction of yield and purity of biodiesel for the production. The UNIQUAC model agreed well with the experimental data of ternary mixtures of biodiesel.

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute.

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere to a Janus particle to a solute whose entire surface is available for association.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited.

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Utility of chemical computations in predicting solution free energies of metal ions

Here, we study quasi-chemical theory (QCT) for the free energies of divalent alkaline earth ions (Ba, Sr, Ca, Mg) in water, emphasizing that: (a) interactions between metal ions and proximal water molecules are as strong as traditional chemical effects; (b) QCT builds directly from accessible electronic structure calculations but rests on fully elaborated molecular statistical thermodynamics; (c) QCT offers choices of convenience in identifying coordination numbers for analysis. We investigate utilisation of direct QCT with inner-shell conditioning , alternative to the traditional conditioning motivated by a generalised van der Waals view. The alternative works well: deleterious non-Gaussian effects of van der Waals repulsive interactions are not serious, and the alternative conditioning improves the convenience of QCT calculations. Comparison between ab initio and force field molecular dynamics (AIMD and FFMD) with standard models suggests that FFMD likely exaggerates the anharmonicity in the thermal motion of inner-shell ion-water clusters. Together with the general encouraging support for the harmonic approximations implied by the conditioning, that observation helps explain the remarkable success of the cluster-based QCT solution free energies, which do not require assessment of all inner-shell occupancies by simulation.

Real single ion solvation free energies with quantum mechanical simulation.

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

A comparative theoretical and experimental study on liquid-liquid equilibria of membrane forming polymeric solutions

The phase equilibria of two ternary system of Polyethersulfone (PES) - n-methyl pyrolidine (NMP) – distilled Tap water (H2O) and Polysulfone (PSf) – NMP - H2O has been investigated critically using both theoretical and experimental methods. The cloud point measurement technique was used for determination of experimental binodal curves. Gamma-gamma (γ-γ), gamma-phi (γ-φ), phi-gamma (φ-γ) and phi-phi (φ- φ) approaches were assessed using measured binodal data. Compressible regular solution (CRS), Nonrandom Two Liquids model (NRTL), Universal Quasi-Chemical theory (UNIQUAC) were used for activity coefficient (gamma) calculations and Gasem–Gao–Pan–Robinson modification to the PR EOS (PRGGPR) and Twu–Coon–Cunningham modification to the RK EOS (RKTCC) were used for fugacity coefficient (phi) calculations. The Othmer-Tobias and the Hand correlation equations were used to check the consistency of the obtained tie-line data, by which the distribution coefficients (D) and separation factors (S) were calculated. Description of LLE using CRS-UNIQUAC in a gamma-gamma approach, the RKTCC-RKTCC in a phi-phi approach, CRS-RKTCC in a gamma-phi approach and the RKTCC-UNIQUAC in a phi-gamma approach gives the best agreement and correlation to the experimental data. The overall performance of gamma-gamma approach using CRS-UNIQUAC model revealed an averaged Accumulative Absolute Relative Deviation (AARD) of 2.47%.

Ion-Specific Effects in Carboxylate Binding Sites.

Specific ion binding by carboxylates (-COO-) is a broadly important topic because -COO- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li+, Na+, K+, Cs+) and divalent (Zn2+, Ca2+) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.

Scaling Atomic Partial Charges of Carbonate Solvents for Lithium Ion Solvation and Diffusion.

Lithium-ion solvation and diffusion properties in ethylene carbonate (EC) and propylene carbonate (PC) were studied by molecular simulation, experiments, and electronic structure calculations. Studies carried out in water provide a reference for interpretation. Classical molecular dynamics simulation results are compared to ab initio molecular dynamics to assess nonpolarizable force field parameters for solvation structure of the carbonate solvents. Quasi-chemical theory (QCT) was adapted to take advantage of fourfold occupancy of the near-neighbor solvation structure observed in simulations and used to calculate solvation free energies. The computed free energy for transfer of Li+ to PC from water, based on electronic structure calculations with cluster-QCT, agrees with the experimental value. The simulation-based direct-QCT results with scaled partial charges agree with the electronic structure-based QCT values. The computed Li+/PF6- transference numbers of 0.35/0.65 (EC) and 0.31/0.69 (PC) agree well with NMR experimental values of 0.31/0.69 (EC) and 0.34/0.66 (PC) and similar values obtained here with impedance spectroscopy. These combined results demonstrate that solvent partial charges can be scaled in systems dominated by strong electrostatic interactions to achieve trends in ion solvation and transport properties that are comparable to ab initio and experimental results. Thus, the results support the use of scaled partial charges in simple, nonpolarizable force fields in future studies of these electrolyte solutions.

Structure and thermodynamics of a mixture of patchy and spherical colloids: A multi-body association theory with complete reference fluid information.

A mixture of solvent particles with short-range, directional interactions and solute particles with short-range, isotropic interactions that can bond multiple times is of fundamental interest in understanding liquids and colloidal mixtures. Because of multi-body correlations, predicting the structure and thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman [J. Chem. Phys. 139, 104904 (2013)] developed a theory wherein association effects due to interactions multiply the partition function for clustering of particles in a reference hard-sphere system. The multi-body effects are incorporated in the clustering process, which in their work was obtained in the absence of the bulk medium. The bulk solvent effects were then modeled approximately within a second order perturbation approach. However, their approach is inadequate at high densities and for large association strengths. Based on the idea that the clustering of solvent in a defined coordination volume around the solute is related to occupancy statistics in that defined coordination volume, we develop an approach to incorporate the complete information about hard-sphere clustering in a bulk solvent at the density of interest. The occupancy probabilities are obtained from enhanced sampling simulations but we also develop a concise parametric form to model these probabilities using the quasichemical theory of solutions. We show that incorporating the complete reference information results in an approach that can predict the bonding state and thermodynamics of the colloidal solute for a wide range of system conditions.

Statistical Analyses of Hydrophobic Interactions: A Mini-Review

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. First, the inverse temperature phenomenology of hydrophobic interactions, i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Second, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, nontrivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.

COSMO-RSC: Second-Order Quasi-Chemical Theory Recovering Local Surface Correlation Effects.

The conductor-like screening model for realistic solvation (COSMO-RS) was introduced 20 years ago and meanwhile has become an important tool for the prediction of fluid phase equilibrium properties. Starting from quantum chemical information about the surface polarity of solutes and solvents, it solves the statistical thermodynamics of molecules in liquid phases by the very efficient approximation of independently pairwise interacting surfaces, which meanwhile was shown to be equivalent to Guggenheim's quasi-chemical theory. One of the basic limitations of COSMO-RS, as of any quasi-chemical model, is the neglect of neighbor information, i.e., of local correlations of surface types on the molecular surface. In this paper we present the completely novel concept of using the first-order COSMO-RS contact probabilities for the construction of local surface correlation functions. These are fed as an entropic correction for the pair interactions into a second COSMO-RS self-consistency loop, which yields new contact probabilities, enthalpies, free energies and activity coefficients recovering much of the originally lost neighbor effects. By a novel analytic correction for concentration dependent interactions, the resulting activity coefficients remain exactly Gibbs-Duhem consistent. The theory is demonstrated on the example of a lattice Monte Carlo fluid of dimerizing pseudomolecules. In this showcase the strong deviations of the lattice Monte Carlo fluid from quasi-chemical theory are almost perfectly reproduced by COSMO-RSC.

Correlation of interaction parameters in Wilson, NRTL and UNIQUAC models using theoretical methods

The activity coefficient models of Wilson, Nonrandom Two Liquid Theory (NRTL) and Universal Quasi-chemical Theory (UNIQUAC) are of the most applied chemical thermodynamic models in phase equilibria calculations and materials behavior prediction and/or correlation. The reliable and accurate evaluation and determination of interaction/adjustable parameters defined in these models, which are necessary for any future applications of models in binary and multicomponent systems, requires the knowledge on experimental data of binary systems. By using such experimental data and regression and fitting of data, in literature, these interaction parameters are obtained for a substantial number of systems. Here, a new theoretical methodology has been developed and examined for estimation of these parameters without the use of experimental data. The presented method equates the activity coefficients calculated by a Compressible Regular Solution Theory (CRS) to those calculated using the three aforementioned models and the interaction parameters are obtained by optimally solving the constructed system of equations. For CRS theory, the application of Sanchez and Lacombe Equation of State (LS-EoS), Constantinou and Gani Group Contribution Method and Hoftyzer and van Krevelen Group Contribution Method was considered while for models of Wilson, NRTL and UNIQUAC, the interaction parameters were searched by implementation of an evolutionary optimization technique. The obtained results are compared to those reported in literature and desirable agreement was found. The method is simple, fast, implementable in computer routines; straightforward and accurate and can be used to estimate these binary interaction parameters for systems of interest. Some phase calculations are also included to demonstrate the applicability of method.

Liquid–liquid equilibrium data and correlation for quaternary systems of acetic acid + water + methyl acetate + p-xylene at 313.2 K

The experimental liquid–liquid equilibrium (LLE) data of the quaternary (acetic acid+water+p-xylene+methyl acetate) system was investigated at 313.2K and atmospheric pressure. This research is aimed to examine the potential of the mixture of methyl acetate and p-xylene, which available as the remaining substances in terephthalic acid production, to be prospective extracting solvent for the acetic acid dehydration. LLE phase diagrams at different ratio of p-xylene to methyl acetate were presented for this quaternary system. The results showed that an enlargement of the LLE two-phase region occurred with increasing p-xylene to methyl acetate mass ratio in the initial solvent phase. The distribution coefficient and selectivity for the extraction of acetic acid were also obtained to evaluate the capability of solvent. LLE data were sufficiently correlated by Othmer-Tobias and Bachman equations. The experimental results were used to obtain binary interaction parameters as correlated by the non-random two liquid (NRTL) and universal quasi-chemical theory (UNIQUAC) equation models. The root mean square deviations (RMSD) values as low as 0.0119 and 0.0128 were calculated for NRTL and UNIQUAC, respectively; indicating excellent results for both models were suitable for the determination of LLE data of this quaternary system.