Application of the Quantum Cluster Equilibrium (QCE) Model for the Liquid Phase of Primary Alcohols Using B3LYP and B3LYP-D DFT Methods

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.

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.

Structures of DMSO clusters and quantum cluster equilibrium (QCE)

Dimethylsulfoxide (DMSO) clusters are crucial for understanding processes in liquid DMSO. Despite its importance, DMSO clusters have received negligible attention due to the complexity of their potential energy surfaces (PESs). In this work, we explored the PESs of the DMSO clusters from dimer to decamer, starting with classical molecular dynamics, followed by full optimizations at the PW6B95-D3/def2-TZVP level of theory. In addition, the binding energies, the binding enthalpy per DMSO, and the quantum theory of atoms in molecules (QTAIM) analysis of the most stable isomers are reported. Temperature effects on the stability of the isomers have also been assessed. After thoroughly exploring the PESs of the DMSO clusters, 159 configurations have been used to apply the quantum cluster equilibrium (QCE) theory to liquid DMSO. The quantum cluster equilibrium theory has been applied to determine the liquid properties of DMSO from DMSO clusters. Thus, using the QCE, the population of the liquid DMSO, its infrared spectrum, and some thermodynamic properties of the liquid DMSO are predicted. The QCE results show that the population of the liquid DMSO is mainly dominated by the DMSO dimer and decamer, with the contribution in trace of the DMSO monomer, trimer, tetramer, pentamer, and octamer. More interestingly, the predicted infrared spectrum of liquid DMSO is in qualitative agreement with the experiment.

Cluster Analysis in Liquids: A Novel Tool in TRAVIS

We present a novel cluster analysis implemented in our open-source software TRAVIS and its application to realistic and complex chemical systems. The underlying algorithm is exclusively based on atom distances. Using a two-dimensional model system, we first introduce different cluster analysis functions and their application to single snapshots and trajectories including periodicity and temporal propagation. Using molecular dynamics simulations of pure water with varying system size, we show that our cluster analysis is size-independent. Furthermore, we observe a similar clustering behavior of pure water in classical and ab initio molecular dynamics simulations, showing that our cluster analysis is universal. In order to emphasize the application to more complex systems and mixtures, we additionally apply the cluster analysis to ab initio molecular dynamics simulations of the [C₂C₁Im][OAc] ionic liquid and its mixture with water. Using that, we show that our cluster analysis is able to analyze the clustering of the individual components in a mixture as well as the clustering of the ionic liquid with water.

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.

Thermodynamically Stable Cationic Dimers in Carboxyl-Functionalized Ionic Liquids: The Paradoxical Case of "Anti-Electrostatic" Hydrogen Bonding

We show that carboxyl-functionalized ionic liquids (ILs) form doubly hydrogen-bonded cationic dimers (c⁺=c⁺) despite the repulsive forces between ions of like charge and competing hydrogen bonds between cation and anion (c⁺–a⁻). This structural motif as known for formic acid, the archetype of double hydrogen bridges, is present in the solid state of the IL 1−(carboxymethyl)pyridinium bis(trifluoromethylsulfonyl)imide [HOOC−CH₂−py][NTf₂]. By means of quantum chemical calculations, we explored different hydrogen-bonded isomers of neutral (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻)₂, single-charged (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻), and double-charged (HOOC– (CH₂)_n−py⁺)₂ complexes for demonstrating the paradoxical case of “anti-electrostatic” hydrogen bonding (AEHB) between ions of like charge. For the pure doubly hydrogen-bonded cationic dimers (HOOC– (CH₂)_n−py⁺)₂, we report robust kinetic stability for n = 1–4. At n = 5, hydrogen bonding and dispersion fully compensate for the repulsive Coulomb forces between the cations, allowing for the quantification of the two equivalent hydrogen bonds and dispersion interaction in the order of 58.5 and 11 kJmol⁻¹, respectively. For n = 6–8, we calculated negative free energies for temperatures below 47, 80, and 114 K, respectively. Quantum cluster equilibrium (QCE) theory predicts the equilibria between cationic monomers and dimers by considering the intermolecular interaction between the species, leading to thermodynamic stability at even higher temperatures. We rationalize the H-bond characteristics of the cationic dimers by the natural bond orbital (NBO) approach, emphasizing the strong correlation between NBO-based and spectroscopic descriptors, such as NMR chemical shifts and vibrational frequencies.

Unexpected molecular dynamics of ethanol in hydrogen-bonded binary mixtures, ethanol-octanol and ethanol-water

In view of getting a quantitative picture of the dynamics in mixtures of hydrogen-bonded liquids, in particular the ternary water-ethanol-octanol, we examine in this paper the dynamics of two binary systems: ethanol-water and ethanol-octanol. Our multiscale investigation includes quasi-elastic neutron scattering for the characterization of the dynamics at the molecular scale, completed by NMR at the mesoscopic scale and eventually compared with macroscopic viscosity properties. We highlight the decrease of diffusivity in pure alcohols when increasing the lengthscale and conjecture its relation with the two processes measured in dielectric spectroscopy. While the behaviour of ethanol-water is well understood, unexpected inversion of the slowest component between the micro and the mesoscale are evidenced in the ethanol-octanol mixture. This effect could be at the origin of the negative viscosity excess in the mixture of alcohols.

Temperature-Induced Change of Water Structure in Aqueous Solutions of Some Kosmotropic and Chaotropic Salts

The hydrogen bond structure of water was examined by comparing the temperature dependent OH-stretching bands of water and aqueous NaClO₄, KClO₄, Na₂SO₄, and K₂SO₄ solutions. Results called attention to the role of cations on top of the importance of anions determining the emerging structure of a multi-layered system consisting single water rings or multi-ring water-clusters.

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.

Chemical Equilibrium of Zinc Acetate Complexes in Ethanol Solution. A Theoretical Description through Thermodynamic Cycles

The Gibbs free energy of complexation between the Zn(II) species and acetate ligands, forming the [Zn(OAc)_n]^2-n complexes with n = 1, 2 in an ethanol solution, was assessed by two different theoretical protocols based on thermodynamic cycles. In both approaches, the solution phase Gibbs free energy of each reaction is computed by summing up contributions from gas phase thermochemistry calculations to solvation Gibbs free energies obtained in a hybrid fashion, i.e., each (neutral or electrically charged) solute was first solvated by explicit solvent molecules in order to capture relevant (micro) solute-solvent and/or solvent-solvent interactions and then, a continuum model calculation is performed in order to get the corresponding bulky solute-solvent contributions. For our first thermodynamic protocol, here denominated as variant 1, a set of x independent solvent molecules are used to screen each of the involved solutes, while the variant 2 strategy uses the fact that a set of solvent molecules may exist as aggregates (or molecular clusters) in the solvent macroscopic media, before the solvation process of solutes. Our selected quantum theoretical protocol was the M05-2X/6-31+G(d)/SMD level. We made a systematic exploration about the influence of several sources of errors, such as the solvent conformation, the number of solvent molecules used to screen each of the involved solutes, the coordination geometry of the metallic center before and after the complexation process, and the pertinence of using molecular geometries optimized in gas phase and in ethanol solution, for the computation of the Gibbs free energy variation regarding the two chemical reactions under study. We set an accuracy threshold equal or less than 4.0 kcal·mol^-1, with respect to the corresponding experimental records. The robustness of our thermodynamic strategies was then tested by computing the gas phase free energy contributions to the (solution phase) reaction free energies here assessed, using different density functional approximations, namely the M05-2X, BH&HLYP, PBE0, ωb97X-D and M06-2X functionals in conjunction with the larger 6-311+G(d,p) basis set.

Conformational and structural stability of the single molecule and hydrogen bonded clusters of para aminobenzoic acid in the gas and solution phases

The structures of α- and β-para aminobenzoic acid are deconstructed into their hydrogen bonding molecular structural building blocks, where they are analysed usingab initioquantum mechanical calculations of their conformation and cluster stability in solution.

Anharmonic effects in the quantum cluster equilibrium method

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

The vibrational spectrum of 1,4-dioxane in aqueous solution – theory and experiment

Frequency shifts in dioxane–water mixtures were studied using conductor-like screening and explicit solvation models, showing predominance of the latter one.

Structural properties of methanol–water binary mixtures within the quantum cluster equilibrium model

The Quantum Cluster Equilibrium (QCE) method computes cluster distributions and thermodynamic properties of binary methanol–water mixtures in agreement with experiments.