Quantum Cluster Equilibrium Theory for Multicomponent Liquids.

In this work, we present a new theory to treat multicomponent liquids based on quantum-chemically calculated clusters. The starting point is the binary quantum cluster equilibrium theory, which is able to treat binary systems. The theory provides one equation with two unknowns. In order to obtain another linearly independent equation, the conservation of mass is used. However, increasing the number of components leads to more unknowns, and this requires linearly independent equations. We address this challenge by introducing a generalization of the conservation of arbitrary quantities accompanied by a comprehensive mathematical proof. Furthermore, a case study for the application of the new theory to ternary mixtures of chloroform, methanol, and water is presented. Calculated enthalpies of vaporization for the whole composition range are given, and the populations or weights of the different clusters are visualized.

The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium.

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius-Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor-harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes.

Hydrogen Bonding and Vaporization Thermodynamics in Hexafluoroisopropanol-Acetone and -Methanol Mixtures. A Joined Cluster Analysis and Molecular Dynamic Study.

Binary mixtures of hexafluoroisopropanol with either methanol or acetone are analyzed via classical molecular dynamics simulations and quantum cluster equilibrium calculations. In particular, their populations and thermodynamic properties are investigated with the binary quantum cluster equilibrium method, using our in-house code Peacemaker 2.8, upgraded with temperature-dependent parameters. A novel approach, where the final density from classical molecular dynamics, has been used to generate the necessary reference isobars. The hydrogen bond network in both type of mixtures at molar fraction of hexafluoroisopropanol of 0.2, 0.5, and 0.8 respectively is investigated via the molecular dynamics trajectories and the cluster results. In particular, the populations show that mixed clusters are preferred in both systems even at 0.2 molar fractions of hexafluoroisopropanol. Enthalpies and entropies of vaporization are calculated for the neat and mixed systems and found to be in good agreement with experimental values.

Calculation of improved enthalpy and entropy of vaporization by a modified partition function in quantum cluster equilibrium theory.

In this work, we present an altered partition function that leads to an improved calculation of the enthalpy and entropy of vaporization in the framework of quantum cluster equilibrium theory. The changes are based on a previously suggested modification [S. Grimme, Chem. Eur. J. 18, 9955-9964 (2012)] of the molecular entropy calculation in the gas phase. Here, the low energy vibrational frequencies in the vibrational partition function are treated as hindered rotations instead of vibrations. The new scheme is tested on a set of nine organic solvents for the calculation of the enthalpy and entropy of vaporization. The enthalpies and entropies of vaporization show improvements from 6.5 error to 3.3 kJ mol-1 deviation to experiment and from 28.4 error to 13.5 J mol-1 K-1 deviation to experiment, respectively. The effect of the corrected partition function is visible in the different populations of clusters, which become physically more meaningful in that larger clusters are higher populated in the liquid phase and the gas phase is mainly populated by the monomers. Furthermore, the corrected partition function also overcomes technical difficulties and leads to an increased stability of the calculations in regard to the size of the cluster set.

Understanding the Complex Surface Interplay for Extraction: A Molecular Dynamics Study.

By means of classical molecular dynamics simulation the interfacial properties of methanol and n-dodecane, which are two potential candidate solvents for use in non-aqueous liquid-liquid extraction, were assessed. The question of how the interface changes depending on the concentration of extractant (tri-n-butyl phosphate) and salt (LiCl) is addressed. Two different models to represent systems were used to evaluate how LiCl and tri-n-butyl phosphate affect mutual miscibility, and how the last-named behaves depending on the chemical environment. Tri-n-butyl phosphate increases the mutual solubility of the solvents, whereas LiCl counteracts it. The extractant was found to be mostly adsorbed on the interface between the solvents, and therefore the structural features of the adsorption were investigated. Adsorption of tri-n-butyl phosphate changes depending on its concentration and the presence of LiCl. It exhibits a preferential orientation in which the butyl chains point at the n-dodecane phase and the phosphate group points at the methanol phase. For high concentrations of tri-n-butyl phosphate, its molecular orientation is preserved by diffusion of the excess molecules into both the methanol and n-dodecane phases. However, LiCl hinders the diffusion into the methanol phase, and thus increases the concentration of tri-n-butyl phosphate at the interface and forces a rearrangement with subsequent loss of orientation.

Predicting Mole-Fraction-Dependent Dissociation for Weak Acids.

We demonstrate for formic and acetic acid dissolved in water as examples that the binary quantum cluster equilibrium (bQCE) approach can predict acid strengths over the whole range of acid concentrations. The acid strength increases in a complex rather than a simple way with increasing mole fraction of the acid from 0 to 0.7, reflecting the complex interplay between the dissociated ions or conjugate bases available as compared to the acid and water molecules. Furthermore, our calculated ion concentrations meet the experimental maximum of the conductivity with excellent agreement for acetic acid and satisfactorily for the formic acid/water mixture. As only a limited number of simple quantum-chemical calculations are required for the prediction, bQCE is clearly a valuable approach to access these quantities also in non-aqueous solutions. It is a highly valuable asset for predicting ionization processes in highly concentrated solutions, which are relevant for biological and chemical systems, as well as technological processes.

Thermodynamics and proton activities of protic ionic liquids with quantum cluster equilibrium theory.

We applied the binary Quantum Cluster Equilibrium (bQCE) method to a number of alkylammonium-based protic ionic liquids in order to predict boiling points, vaporization enthalpies, and proton activities. The theory combines statistical thermodynamics of van-der-Waals-type clusters with ab initio quantum chemistry and yields the partition functions (and associated thermodynamic potentials) of binary mixtures over a wide range of thermodynamic phase points. Unlike conventional cluster approaches that are limited to the prediction of thermodynamic properties, dissociation reactions can be effortlessly included into the bQCE formalism, giving access to ionicities, as well. The method is open to quantum chemical methods at any level of theory, but combination with low-cost composite density functional theory methods and the proposed systematic approach to generate cluster sets provides a computationally inexpensive and mostly parameter-free way to predict such properties at good-to-excellent accuracy. Boiling points can be predicted within an accuracy of 50 K, reaching excellent accuracy for ethylammonium nitrate. Vaporization enthalpies are predicted within an accuracy of 20 kJ mol-1 and can be systematically interpreted on a molecular level. We present the first theoretical approach to predict proton activities in protic ionic liquids, with results fitting well into the experimentally observed correlation. Furthermore, enthalpies of vaporization were measured experimentally for some alkylammonium nitrates and an excellent linear correlation with vaporization enthalpies of their respective parent amines is observed.

How to Harvest Grotthuss Diffusion in Protic Ionic Liquid Electrolyte Systems.

Hydrogen is often regarded as fuel of the future, and there is an increasing demand for the development of anhydrous proton-conducting electrolytes to enable fuel-cell operation at elevated temperatures exceeding 120 °C. Much attention has been directed at protic ionic liquids as promising candidates, but in the search for highly conductive systems the possibility of designing Grotthuss diffusion-enabled protic ionic liquids has been widely overlooked. Herein, the mechanics of proton-transfer mechanism in the equimolar mixture of N-methylimidazole and acetic acid was explored using ab initio molecular dynamics simulations. The ionicity of the system is approximated with good agreement to experiments. This system consists mostly of neutral species but exhibits a high ionic conductivity through Grotthuss-like proton conduction. Chains of acetic-acid molecules and other species participating in the proton-transfer mechanisms resembling Grotthuss diffusion could be directly observed. Furthermore, based on these findings, a series of static quantum chemical calculations was conducted to investigate the effect of substituting the anion and cation with different functional groups. We predict whether a given combination of cation and anion will be a true ionic liquid or a molecular mixture and propose some systems as candidates for Grotthuss diffusion-enabled protic ionic liquids.

Predicting miscibility of binary liquids from small cluster QCE calculations.

The quantum cluster equilibrium method is applied to model binary systems of molecular solvents. We minimize the computational effort as well as the experimental input and present the results obtained for the completely miscible acetonitrile/acetone, benzene/acetone, and water/acetone systems, as well as for the hardly miscible water/benzene system. Only clusters of sizes up to n = 3 are applied and these are optimized employing the low-cost functional PBEh-3c. The thermodynamic functions of the pure liquids are in reasonable agreement with experiments. For both non-water containing binary systems, the Gibbs energy of mixing can be reproduced with an accuracy of ≈0.25 kJ/mol. Water containing systems are not sufficiently described by small clusters. The empirical mean-field parameter amf and exclusion volume scaling parameter bxv which depend on the experimental input are approximated by linear interpolation between their neat liquids' reference values. This makes the approach independent from the experimental data of the binary system. Despite the roughness of the approximation as well as the small size of the cluster sets, the approach is able to correctly predict the mixing behavior of all acetone systems. The benzene/water system is correctly predicted to be non-miscible at most mole fractions. A small range at high benzene concentrations (x> 0.8) is falsely predicted to be miscible.