Eva Perlt

Coupled Cluster in Condensed Phase. Part I: Static Quantum Chemical Calculations of Hydrogen Fluoride Clusters

A multiscale approach with roots in electronic structure calculations relies on the good description of intermolecular forces. In this study we lay the foundations for a condensed phase treatment based on the electronic structure of hydrogen fluoride on a very high level of theory. This investigation comprises cluster calculations in a static quantum chemical approach employing density functional theory, second order Møller-Plesset perturbation theory (MP2) and the coupled cluster singles, doubles with perturbative triples method in combination with several basis sets as well as at the complete basis set limit. The clusters we considered are up to 12 monomer units large and consist of ring and chain structures. We find a good agreement of the intramolecular distance obtained from the MP2 approach and the largest basis set. The binding energy of the hydrogen fluoride dimer calculated from coupled cluster at the basis set limit agrees excellently with experiment, whereas the calculated frequencies at all levels agree reasonably well with different experimental values. Large cooperative effects are observed for the ring structures as compared to the chain clusters. The energy per monomer unit indicates the most stable structures to be the ring clusters.

Coupled Cluster in Condensed Phase. Part II: Liquid Hydrogen Fluoride from Quantum Cluster Equilibrium Theory.

Treating the bulk phase with high-level ab initio methods, such as coupled cluster, is a nontrivial task because of the computational costs of these electronic structure methods. In this part of our hydrogen fluoride study we make use of the quantum cluster equilibrium method, which employs electronic structure input of small clusters and combines it with simple statistical mechanics in order to describe condensed phase phenomena. If no parameter adjustment is applied, then the lower quantum chemical methods, such as density functional theory in conjunction with the generalized gradient approximation, provide wrong results in accordance with the description of the strength of the interaction in the clusters. While density functional theory describes the liquid phase too dense due to overbinding of the clusters, the coupled cluster method and the perturbation theory at the complete basis set limit agree well with experimental observations. If we allow the two parameters in the quantum cluster equilibrium method to vary, then these are able to compensate the overbinding, thereby leading to very good agreement with experiment. Correlated methods in combination with small basis sets giving rise to too weakly bound clusters cannot reach this accuracy even if the parameters are flexible. Only at the complete basis set limit, the performance of the correlated methods is again excellent.

Importance of Structural Motifs in Liquid Hydrogen Fluoride

The investigation of liquid phases by means of accurate electronic structure methods is a demanding task due to the high computational effort. We applied second-order Møller-Plesset perturbation theory and high-level quantum chemical calculations using the coupled-cluster method with single, double and perturbative triple excitations in combination with Dunnings correlation-consistent basis sets up to quintuple ζ quality. Based on these calculations, we extrapolated the correlation energy to the basis set limit in order to improve the results even further. For comparison to the correlated electronic structure methods, density functional calculations employing different functionals are presented as well. The investigated species are a cyclic pentamer as well as a set of branched structures. The quantum cluster equilibrium method is employed for the investigation of the liquid-phase structure of hydrogen fluoride. The pentamer is found to be present to a high extent and in the case of the MP2/QZVP data, its presence improves the results significantly. Accounting for branched structures slightly improves results, so that they are found to be present but not to dominate in liquid hydrogen fluoride. Concerning both the interaction energy and the result of the quantum cluster equilibrium calculation the basis set has a major influence, whereas the difference between Møller-Plesset perturbation theory and coupled-cluster calculations is less pronounced.

What can clusters tell us about the bulk?: Peacemaker: Extended quantum cluster equilibrium calculations

Abstract The quantum cluster equilibrium theory and its implementation into the freely available Peacemaker program are described in this paper. The important equations of the quantum cluster equilibrium with a constant mean field potential and an excluded volume are derived. The scheme of the consecutive iterations to obtain both natural variables (volume and particle number) is presented, as well. Further, we describe the implemented method to solve the polynomials arising in each iteration. Additionally, we deal with the question: Which kinds of particles are important for a physically meaningful description of a system. In order to arrive at a systematic classification of these particles, we discuss the important term of a cluster motif. We propose how to determine whether a particle is important for the investigated system and describe the implementation of this method into Peacemaker . Finally, in a case study the thermodynamic properties computed with Peacemaker and the corresponding experimental data are compared with each other.

Binary systems from quantum cluster equilibrium theory.

An extension of the quantum cluster equilibrium theory to treat binary mixtures is introduced in this work. The necessary equations are derived and a possible implementation is presented. In addition an alternative sampling procedure using widely available experimental data for the quantum cluster equilibrium approach is suggested and tested. An illustrative example, namely, the binary mixture of water and dimethyl sulfoxide, is given to demonstrate the new approach. A basic cluster set is introduced containing the relevant cluster motifs. The populations computed by the quantum cluster equilibrium approach are compared to the experimental data. Furthermore, the excess Gibbs free energy is computed and compared to experiments as well.

A one-parameter quantum cluster equilibrium approach.

The established quantum cluster equilibrium approach is further developed in this work. The equations are reformulated to result in a one-parameter expression, i.e., with one of two empirical parameters eliminated. Instead of a parametrized constant mean field interaction we present two further approaches using temperature dependent mean field functions. The suggested functions are assessed by means of two test systems, namely hydrogen fluoride and water which are investigated concerning their liquid phase properties as well as the phenomenon of evaporation. The obtained thermodynamic data are compared with each other for the different mean field functions including the conventional approach as well as to experimental data.

Predicting the Ionic Product of Water

We present a first-principles calculation and mechanistic characterization of the ion product of liquid water (KW), based on Quantum Cluster Equilibrium (QCE) theory with a variety of ab initio and density functional methods. The QCE method is based on T-dependent Boltzmann weighting of different-sized clusters and consequently enables the observation of thermodynamically less favored and therefore low populated species such as hydronium and hydroxide ions in water. We find that common quantum chemical methods achieve semi-quantitative accuracy in predicting KW and its T-dependence. Dominant ion-pair water clusters of the QCE equilibrium distribution are found to exhibit stable 2-coordinate buttress-type motifs, all with maximally Grotthus-ordered H-bond patterns that successfully prevent recombination of hydronium and hydroxide ions at 3-coordinate bridgehead sites. We employ standard quantum chemistry techniques to describe kinetic and mechanistic aspects of ion-pair formation, and we obtain NBO-based bonding indices to characterize other electronic, structural, spectroscopic, and reactive properties of cluster-mediated ionic dissociation.

Thermodynamics and proton activities of protic ionic liquids with quantum cluster equilibrium theory

We applied the binary Quantum Cluster Equilibrium (bQCE) method to a number of alkylammonium-based protic ionic liquids in order to predict boiling points, vaporization enthalpies, and proton activities. The theory combines statistical thermodynamics of van-der-Waals-type clusters with ab initio quantum chemistry and yields the partition functions (and associated thermodynamic potentials) of binary mixtures over a wide range of thermodynamic phase points. Unlike conventional cluster approaches that are limited to the prediction of thermodynamic properties, dissociation reactions can be effortlessly included into the bQCE formalism, giving access to ionicities, as well. The method is open to quantum chemical methods at any level of theory, but combination with low-cost composite density functional theory methods and the proposed systematic approach to generate cluster sets provides a computationally inexpensive and mostly parameter-free way to predict such properties at good-to-excellent accuracy. Boiling points can be predicted within an accuracy of 50 K, reaching excellent accuracy for ethylammonium nitrate. Vaporization enthalpies are predicted within an accuracy of 20 kJ mol-1 and can be systematically interpreted on a molecular level. We present the first theoretical approach to predict proton activities in protic ionic liquids, with results fitting well into the experimentally observed correlation. Furthermore, enthalpies of vaporization were measured experimentally for some alkylammonium nitrates and an excellent linear correlation with vaporization enthalpies of their respective parent amines is observed.

Quantum Cluster Equilibrium

The Quantum Cluster Equilibrium model which has been developed within the past two decades is presented. It constitutes an alternative for the investigation of fluid phases and phase transitions. In that contribution, a conceptual overview is given. It is explained, how a limited number of molecular clusters is employed for the description of the liquid phase and the computation of thermodynamic properties. Herein, high-level electronic structure methods may be transferred to macroscopic phases via statistical mechanics. The suggested method is employed so that liquid water may be treated at the coupled-cluster level including single, double and perturbative triple excitations.

Finding the best density functional approximation to describe interaction energies and structures of ionic liquids in molecular dynamics studies

Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.