The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium

Kirchner, Barbara; Ingenmey, Johannes; Domaros, Michael von; Perlt, Eva

doi:10.3390/molecules27041286

Cited by 6 publications

(8 citation statements)

References 60 publications

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“…As can be seen in the case of the NN monomers at all levels of theory, all parameter values are the same independent of the method. This is not always the case; counter-examples can be found in ref 48. Moreover, the values are smaller than those for the NP, PN, and PP systems with the order of PP > NP = PN > NN.…”

Section: Methods and Computational Detailsmentioning

confidence: 91%

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

et al. 2022

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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 ΔE 0 and ΔG varies in a few cases and that the global minimum is not always the dominantly occupied structure.

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Section: Methods and Computational Detailsmentioning

confidence: 91%

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

et al. 2022

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“…For direct comparisons with many previous chemical applications in the NBO/NRT literature [52,53], we employed the familiar B3LYP/6-311++G** level of hybrid density functional theory for all geometry optimizations and energy evaluations of the present work. As shown elsewhere [54,55], realistic treatment of thermodynamic properties requires balanced treatment of energetic (primarily electronic) and entropic (primarily vibrational) contributions to free energy. All species were fully optimized and checked for vibrational stability with standard options of the Gaussian-16 program [56].…”

Section: Methodsmentioning

confidence: 95%

“…The inherent chirality of the coordination pattern about each O atom of higher-coordinated water clusters of Figures 2 and 3 indicates that reduced symmetry (net chirality) is a high-probability feature of equilibrium water cluster distributions in any phase involving their participation. Note that although H-bonds are considered weak noncovalent attractions, the cumulative energy release from larger cluster formation (viz., ∆E ≈ 170 kcal/mol for the 8,8,0 W 16 cluster) can readily exceed that necessary to dissociate a strong covalent bond, as in the ion pair clusters involved in self-dissociation (pH) of liquid water [54,55]. The per-monomer free energies of formation shown in Figures 2 and 3 remain slightly positive under standard-state conditions, but the windowpane clusters are expected to gain increased stability relative to the ice-like clusters of the near-ambient regime as pressure increases.…”

Section: Sequential Aufbau Of 2- 3- 4-coordinate Windowpane Water Clu...mentioning

confidence: 99%

High-Density “Windowpane” Coordination Patterns of Water Clusters and Their NBO/NRT Characterization

Weinhold¹

2022

Molecules

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Cluster mixture models for liquid water at higher pressures suggest the need for water clusters of higher coordination and density than those commonly based on tetrahedral H-bonding motifs. We show here how proton-ordered water clusters of increased coordination and density can assemble from a starting cyclic tetramer or twisted bicyclic (Möbius-like) heptamer to form extended Aufbau sequences of stable two-, three-, and four-coordinate “windowpane” motifs. Such windowpane clusters exhibit sharply reduced (~90°) bond angles that differ appreciably from the tetrahedral angles of idealized crystalline ice Ih. Computed free energy and natural resonance theory (NRT) bond orders provide quantitative descriptors for the relative stabilities of clusters and strengths of individual coordinative linkages. The unity and consistency of NRT description is demonstrated to extend from familiar supra-integer bonds of the molecular regime to the near-zero bond orders of the weakest linkages in the present H-bond clusters. Our results serve to confirm that H-bonding exemplifies resonance–covalent (fractional) bonding in the sub-integer range and to further discount the dichotomous conceptions of “electrostatics” for intermolecular bonding vs. “covalency” for intramolecular bonding that still pervade much of freshman-level pedagogy and force-field methodology.

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“…14 In the paper on the ionic product of water, Kirchner et al found that using BYLP, PBE0, and PBEh0 functionals at ambient temperature and including the counterpoise gCP and D3 dispersion corrections, entropy is underestimated by the QCE calculations. 49 The calculated value of heat capacity Cp of liquid ammonia done by Weinhold shows an error of about 30% compared to the experiment in liquid phase. 33 The heat capacity values at and also in computing the frequencies.…”

Section: Thermodynamic Propertiesmentioning

confidence: 93%

Quantum cluster equilibrium theory applied to liquid ammonia

Maya,

Malloum,

Fifen

et al. 2024

J Comput Chem

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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.

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The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium

Cited by 6 publications

References 60 publications

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

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

High-Density “Windowpane” Coordination Patterns of Water Clusters and Their NBO/NRT Characterization

Quantum cluster equilibrium theory applied to liquid ammonia

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