A one-parameter quantum cluster equilibrium approach

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.

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.

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.

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.

Hydrogen bonding between hydrides of the upper-right part of the periodic table

One of the most important electrostatic interactions between molecules is most definitely the hydrogen bond. Understanding the basis of this interaction may offer us the insight needed to understand its effect on the macroscopic scale. Hydrogen bonding is for example the reason for anomalous properties in compounds like water and naturally life as we know it. The strength of the bond depends on numerous factors, among them the electronegativity of participating atoms. In this work we calculated the strength of hydrogen bonds between hydrides of the upper-right part of the periodic table (C, N, O, F, P, S, Cl, As, Se, Br) using quantum-chemical methods. The aim was to determine what influences the strength of strong and weak hydrogen bonds in simple hydrides. Various relationships were checked. A relation between the strength of the bond and the electronegativity of the participating atoms was found. We also observed a correlation between the strength of hydrogen bonds and the inter-atomic distances, along with the dependence on the charge transfer on the atom of the donor. We also report characteristic geometries of different dimers.

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.

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.