Quantum cluster equilibrium model of N-methylformamide–water binary mixtures

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.

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.

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.

Discrete Modeling Approach for Cluster-Based Excess Gibbs-Energy of Molecular Liquids

The excess Gibbs-energy of a two-component liquid molecular mixture is modeled based on discrete clusters of molecules. These clusters preserve the three-dimensional geometric information about local molecule neighborhoods that inform the interaction energies of the clusters. In terms of a discrete Markov-chain, the clusters are used to hypothetically construct the mixture using sequential insertion steps. Each insertion step and, therefore, cluster is assigned a probability of occurring in an equilibrium system that is determined via the constrained minimization of the Helmholtz free energy. For this, informational Shannon entropy based on these probabilities is used synonymously with thermodynamic entropy. A first approach for coupling the model to real molecules is introduced in the form of a molecular sampling algorithm, which utilizes a force-field approach to determine the energetic interactions within a cluster. An exemplary application to four mixtures shows promising results regarding the description of a variety of excess Gibbs-energy curves, including the ability to distinguish between structural isomers.

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.

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.

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.

Cluster-Based Thermodynamics of Interacting Dice in a Lattice

In this paper, a model for two-component systems of six-sided dice in a simple cubic lattice is developed, based on a basic cluster approach previously proposed. The model represents a simplified picture of liquid mixtures of molecules with different interaction sites on their surfaces, where each interaction site can be assigned an individual energetic property to account for cooperative effects. Based on probabilities that characterize the sequential construction of the lattice using clusters, explicit expressions for the Shannon entropy, synonymously used as thermodynamic entropy, and the internal energy of the system are derived. The latter are used to formulate the Helmholtz free energy that is minimized to determine thermodynamic bulk properties of the system in equilibrium. The model is exemplarily applied to mixtures that contain distinct isomeric configurations of molecules, and the results are compared with the Monte-Carlo simulation results as a benchmark. The comparison shows that the model can be applied to distinguish between isomeric configurations, which suggests that it can be further developed towards an excess Gibbs-energy, respectively, activity coefficient model for chemical engineering applications.

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.

Assessing cluster models of solvation for the description of vibrational circular dichroism spectra: synergy between static and dynamic approaches

Solvation effects are essential for defining the shape of vibrational circular dichroism (VCD) spectra.

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.