Anharmonic effects in the quantum cluster equilibrium method

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.

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.

Hydrogen bond networks of dimethylsulfoxide (DMSO) pentamer

Understanding of clusters of dimethylsulfoxide (DMSO) is important in several applications in Chemistry. Despite its importance, very few studies of DMSO clusters, (DMSO)_n, have been reported in comparison to systems such as water clusters or methanol clusters. In order to provide further understanding of DMSO clusters, we investigated the structures and non-covalent interactions of the (DMSO)_n, n=5. Therefore, the potential energy surface (PES) of the DMSO pentamer has been examined using classical molecular dynamics. The structures generated using classical molecular dynamics are further optimized at the PW6B95D3/aug-cc-pVDZ level of theory. To comprehend the non-covalent bondings in the DMSO pentamer, we carried out a quantum theory of atoms in molecule (QTAIM) analysis. In addition, the effects of temperature on the structural stability is investigated between 20 and 500K. It comes out that seven different kind of non-covalent bondings can be found in DMSO pentamers.

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.

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.

Anharmonicity of Vibrational Modes in Hydrogen Chloride-Water Mixtures

A thorough analysis of molecular vibrations in the binary system hydrogen chloride/water is presented considering a set of small mixed and pure clusters. In addition to the conventional normal-mode analysis based on the diagonalization of the Hessian, anharmonic frequencies were obtained from the perturbative VPT2 and PT2-VSCF method using hybrid density functional theory. For all normal modes, potential energy curves were modeled by displacing the atoms from the minimum geometry along the normal mode vectors. Three model potentials, a harmonic potential, a Morse potential, and a fourth order polynomial, were applied to fit these curves. From these data, it was possible not only to characterize distinct vibrations as mainly harmonic, anharmonic, or involving higher order terms but also to extract force constants, k, and anharmonicity constants, x_e. By investigating all different types of intramolecular vibrations including covalent stretching or bending vibrations and intermolecular vibrations such as librations, we could demonstrate that while vibrational frequencies can be obtained applying scaling factors to harmonic results, useful anharmonicity constants cannot be predicted in such a way and the usage of more elaborate vibrational methods is necessary. For each particular type of molecular vibration, we could however determine a relationship between the wavenumber or wavenumber shift and the anharmonicity constant, which allows us to estimate mode dependent anharmonicity constants for larger clusters in the future.