Predicting miscibility of binary liquids from small cluster QCE calculations

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.

Appropriate clusterset selection for the prediction of thermodynamic properties of liquid water with QCE theory

Evident in many physical and chemical phenomena, thermodynamics is the study of how energy is stored, transformed and transferred in a molecule or material. However, prediction of these properties with simulation techniques is a non-trivial task as several factors such as composition and intermolecular interactions come into play. While molecular dynamics and ab initio molecular dynamics are the most common techniques for the prediction of thermodynamic properties, there exists many shortcomings associated with their use. Therefore, in this work we instead apply QCE theory to predict the thermodynamic properties of liquid water. This theory assumes that a condensed phase system can be represented as a 'mixture' of varying sized clusters rather than as a continuum. As QCE theory relies on first-principle simulations and statistical thermodynamics to determine the thermodynamic behavior of a system, appropriate selection of clusters is a crucial step towards achieving accurate predictions. In this study, we use molecular dynamics and ab initio calculations to obtain initial configurations of 400 water clusters, Wn where n = 3 to 10 and contrast their stability using two different criteria. The role of entropy towards cluster stabilization is investigated by comparing the binding (ΔE_BIND/mol) and Gibbs free binding energy per molecule (ΔG_BIND/mol) of various Wn at 298.15 K. Initial clustersets are constructed by exploring two-, three-, four and five-combinations of clustersets using the minimum ΔG_BIND/mol structures of Wn. We also expand the ΔG_BIND/mol criteria for Wn of sizes 3 to 7 to include values larger than 0.0 kJ mol^-1 and smaller than 3.0 kJ mol^-1 as a means of improving thermodynamic predictions. 37 of the 459 resulting clustersets predicted the correct boiling point of water and its thermodynamic properties with an accuracy of 95%. A scaled population-weighted infrared spectrum was compared to experimental results to validate the composition of the top 5 clustersets. The predicted spectra showed an exact match within the low frequency range (<1000 cm^-1) with some discrepancy at the high frequency range (>3400 cm^-1). This work highlights that ΔG_BIND/mol is so far the best criteria to apply when determining an appropriate clusterset for QCE theory.

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.

Chlorine Dioxide: An Exception that Proves the Rules of Localized Chemical Bonding

We employ natural bond orbital (NBO) and natural resonance theory (NRT) tools to analyze the enigmatic properties of the C2v-symmetric isomer of chlorine dioxide radical (ClO2), whose many challenges to Pauling-type localized bonding concepts were recognized by Linus Pauling himself. Although spin-contamination is minimal in this species, ClO2 exhibits an unusually strong form of "different Lewis structures for different spins" bonding pattern, intrinsically outside the framework of "maximal pairing" concepts. We show how the novel spin-unpaired donor-acceptor interactions lead to weakened bonding in the supramolecular domain of polyradical (ClO2)n homoclusters and aqueous ClO2(H2O)n heteroclusters. Despite feeble binding energies and large inter-radical separations, the polyradical clusters are found to maintain coherent spin patterns in each cluster component, attesting to the quantal donor-acceptor nature of their interactions and the cooperative and anticooperative couplings that govern intra- and intermolecular spin distributions in such spin-clusters.

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.

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.

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.