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

Quantum cluster equilibrium theory applied to liquid ammonia

Through this paper, the authors propose using the quantum cluster equilibrium (QCE) theory to reinvestigate ammonia clusters in the liquid phase. The ammonia clusters from size monomer to hexadecamer were considered to simulate the liquid ammonia in this approach. The clusterset used to model the liquid ammonia is an ensemble of different structures of ammonia clusters. After studious research of the representative configurations of ammonia clusters through the cluster research program ABCluster, the configurations have been optimized at the MN15/6-31++G(d,p) level of theory. These optimizations lead to geometries and frequencies as inputs for the Peacemaker code. The QCE study of this molecular system permits us to get the liquid phase populations in a temperature range of 190-260 K, covering the temperatures from the melting point to the boiling point. The results show that the population of liquid ammonia comprises mainly the ammonia hexadecamer followed by pentadecamer, tetradecamer, and tridecamer. We noted that the small-sized ammonia clusters do not contribute to the population of liquid ammonia. In addition, the thermodynamic properties, such as heat of vaporization, heat capacity, entropy, enthalpy, and free energies, obtained by the QCE theory have been compared to the experiment given some relatively good agreements in the gas phase and show considerable discrepancies in liquid phase except the density. Finally, based on the predicted population, we calculated the infrared spectrum of liquid ammonia at 215 K temperature. It comes out that the calculated infrared spectrum qualitatively agrees with the experiment.

The effect of machine learning predicted anharmonic frequencies on thermodynamic properties of fluid hydrogen fluoride

Anharmonic effects play a crucial role in determining thermochemical properties of liquids and gases. For such extended phases, the inclusion of anharmonicity in reliable electronic structure methods is computationally extremely demanding, and hence, anharmonic effects are often lacking in thermochemical calculations. In this study, we apply the quantum cluster equilibrium method to transfer density functional theory calculations at the cluster level to the macroscopic, liquid, and gaseous phase of hydrogen fluoride. This allows us to include anharmonicity, either via vibrational self-consistent field calculations for smaller clusters or using a regression model for larger clusters. We obtain the structural composition of the fluid phases in terms of the population of different clusters as well as isobaric heat capacities as an example for thermodynamic properties. We study the role of anharmonicities for these analyses and observe that, in particular, the dominating structural motifs are rather sensitive to the anharmonicity in vibrational frequencies. The regression model proves to be a promising way to get access to anharmonic features, and the extension to more sophisticated machine-learning models is promising.

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.

Exploring the Influence of the Phosphorus-Heteroatom Substitution in Nicotine on Its Electronic and Vibrational Spectroscopic Properties

The influence of phosphorus substitution of nitrogen in heterocyclic compounds on the vibrational spectroscopy as well as frontier molecular orbitals are analyzed. Nicotine with two nitrogen atoms in its structure is taken as the sample system to be studied computationally. By replacing the nitrogen atom in one or both rings of this molecule with phosphorus, three nicotine derivatives are created. The vibrational circular dichroism and infrared spectra of these four molecules in their monomer state, as well as the assemblies up to trimers are determined. The aforementioned spectra are calculated using static quantum chemical calculations employing a cluster-weighted approach. The calculated gas phase spectra of nicotine are compared to their respective experimental spectra. It is observed that the nicotine derivatives with phosphorus in the methylpyrrolidine ring have considerably different gas phase and bulk phase vibrational circular dichroism spectra when compared to nicotine. The phosphorus substitution reduces the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital as well as altering the polarizability and reactivity of the investigated molecules.

Conformer Weighting and Differently Sized Cluster Weighting for Nicotine and Its Phosphorus Derivatives

Weighting methods applied to systems with many conformers have been broadly employed to calculate thermodynamic properties, structural characteristics, and populations. To better understand and test the sensitivity of conventional weighting methods, the conformational distributions of nicotine and its phosphorus-substituted derivatives are investigated. The weighting schemes used for this are all based on Boltzmann statistics. Classical Boltzmann factors based on the electronic energy and the Gibbs free energy are calculated at different quantum chemical levels of theory and compared to cluster weights obtained by the quantum cluster equilibrium method. Furthermore, the influence of the modified rigid-rotor-harmonic-oscillator (mRRHO) approximation on the cluster weights is investigated. The substitution of the nitrogen atom in the methylpyrrolidine ring by a phosphorus atom results in more monomer conformers and clusters being populated. The conformational distribution of the monomers remained stable at different levels of theory and weighting methods. However, going to dimers and trimers, we observe a significant influence of the level of theory, weighting method, and mRRHO cutoff on the populations of these clusters. We show that mRRHO cutoff values of 50 and 100 cm^-1 yield similar results, which is why 50 cm^-1 is recommended as a robust choice. Furthermore, we observe that the global minimum for ΔE₀ and ΔG varies in a few cases and that the global minimum is not always the dominantly occupied structure.

Uncertainty quantification of phase transition quantities from cluster weighting calculations

In this work, we investigate how uncertainties in experimental input data influence the results of quantum cluster equilibrium calculations. In particular, we focus on the calculation of vaporization enthalpies and entropies of seven organic liquids, compare two computational approaches for their calculation and investigate how these properties are affected by changes in the experimental input data. It is observed that the vaporization enthalpies and entropies show a smooth dependence on changes in the reference density and boiling point. The reference density is found to have only a small influence on the vaporization thermodynamics, whereas the boiling point has a large influence on the vaporization enthalpy but only a small influence on the vaporization entropy. Furthermore we employed the Gauss--Hermite estimator in order to quantify the uncertainty in the thermodynamic functions that stems from inaccuracies in the experimental reference data at the example of the vaporization enthalpy of (\textit{R})-butan-2-ol. We quantify the uncertainty as 30.95~$\cdot$10$^{-3}$~kJ~mol$^{-1}$. Additionally we compare the convergence behaviour and computational effort of the Gauss--Hermite estimator with the Monte Carlo approach and show the superiority of the former. By this, we present how uncertainty quantification can be applied to examples from theoretical chemistry.

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.

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.

Size of the hydrogen bond network in liquid methanol: a quantum cluster equilibrium model with extensive structure search

Studies have debated what is a favorable cluster size in liquid methanol. Applications of the quantum cluster equilibrium (QCE) model on a limited set of cluster structures have demonstrated the dominance of cyclic hexamers in liquid methanol. In this study, we examined the aforementioned question by integrating our implementation of QCE with a molecular-dynamics-based structural searching scheme. QCE simulations were performed using a database comprising extensively searched stable conformers of (MeOH)n for n = 2-14, which were optimized by B3LYP/6-31+G(d,p) with and without the dispersion correction. Our analysis indicated that an octamer structure can contribute significantly to cluster probability. By reoptimizing selected conformers with high probability at the MP2 level, we found that the aforementioned octamer became the dominant species due to favorable vibrational free energy, which was attributed to modes of intermolecular vibration.

Pseudohalogen Chemistry in Ionic Liquids with Non-innocent Cations and Anions

Within the second funding period of the SPP 1708 "Material Synthesis near Room Temperature",which started in 2017, we were able to synthesize novel anionic species utilizing Ionic Liquids (ILs) both, as reaction media and reactant. ILs, bearing the decomposable and non-innocent methyl carbonate anion [CO3 Me]- , served as starting material and enabled facile access to pseudohalide salts by reaction with Me3 Si-X (X=CN, N3 , OCN, SCN). Starting with the synthesized Room temperature Ionic Liquid (RT-IL) [nBu3 MeN][B(OMe)3 (CN)], we were able to crystallize the double salt [nBu3 MeN]2 [B(OMe)3 (CN)](CN). Furthermore, we studied the reaction of [WCC]SCN and [WCC]CN (WCC=weakly coordinating cation) with their corresponding protic acids HX (X=SCN, CN), which resulted in formation of [H(NCS)2 ]- and the temperature labile solvate anions [CN(HCN)n ]- (n=2, 3). In addition, the highly labile anionic HCN solvates were obtained from [PPN]X ([PPN]=μ-nitridobis(triphenylphosphonium), X=N3 , OCN, SCN and OCP) and HCN. Crystals of [PPN][X(HCN)3 ] (X=N3 , OCN) and [PPN][SCN(HCN)2 ] were obtained when the crystallization was carried out at low temperatures. Interestingly, reaction of [PPN]OCP with HCN was noticed, which led to the formation of [P(CN)2 ]- , crystallizing as HCN disolvate [PPN][P(CN⋅HCN)2 ]. Furthermore, we were able to isolate the novel cyanido(halido) silicate dianions of the type [SiCl0.78 (CN)5.22 ]2- and [SiF(CN)5 ]2- and the hexa-substituted [Si(CN)6 ]2- by temperature controlled halide/cyanide exchange reactions. By facile neutralization reactions with the non-innocent cation of [Et3 HN]2 [Si(CN)6 ] with MOH (M=Li, K), Li2 [Si(CN)6 ] ⋅ 2 H2 O and K2 [Si(CN)6 ] were obtained, which form three dimensional coordination polymers. From salt metathesis processes of M2 [Si(CN)6 ] with different imidazolium bromides, we were able to isolate new imidazolium salts and the ionic liquid [BMIm]2 [Si(CN)6 ]. When reacting [Mes(nBu)Im]2 [Si(CN)6 ] with an excess of the strong Lewis acid B(C6 F5 )3 , the voluminous adduct anion {Si[CN⋅B(C6 F5 )3 ]6 }2- was obtained.

Activity coefficients of binary methanol alcohol mixtures from cluster weighting

The hydrogen bond network of different small alcohols is investigated via cluster analysis. Methanol/alcohol mixtures are studied with increasing chain length and branching of the molecule. Those changes can play an important role in different fields, including solvent and metal extraction. The extended tight binding method GFN2-xTB allows the evaluation and geometry optimization of thousands of clusters built via a genetic algorithm. Interaction energies and geometries are evaluated and discussed for the neat systems. Thermodynamic properties, such as vaporization enthalpies and activity coefficients, are calculated with the binary quantum cluster equilibrium (bQCE) approach using our in-house code peacemaker 2.8. Combined distribution functions of the distances against the angles of the hydrogen bonds are evaluated for neat and mixed clusters and weighted by the equilibrium populations achieved from bQCE calculations.

Isolating the role of hydrogen bonding in hydroxyl-functionalized ionic liquids by means of vaporization enthalpies, infrared spectroscopy and molecular dynamics simulations

Hydrogen bonding in hydroxyl-functionalized ionic liquids (right) prevents favourable dispersion interaction between cation and anion (left). We analyze this subtle balance of interactions by combining calorimetry, IR spectroscopy and MD simulations.

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.