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.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene.

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

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

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius-Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor-harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes.

Strong Ferromagnetic Exchange Coupling and Single-Molecule Magnetism in MoS43--Bridged Dilanthanide Complexes.

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C5Me5)2][(C5Me5)2Ln(µ-S)2Mo(µ-S)2Ln(C5Me5)2], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS43- bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4dz2 orbital of MoV to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89Y hyperfine coupling constants of A⊥ = 23 MHz and A|| = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd, 1-Tb, and 1-Dy. This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving GdIII observed to date, with JGd-Mo = +16.1(2) cm-1. Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy, an extracted thermal relaxation barrier of Ueff = 68 cm-1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Together, these results provide a potentially generalizable route to enhanced nd-4f magnetic exchange, revealing opportunities for the design of new nd-4f single-molecule magnets and bulk magnetic materials.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Predicting Mole-Fraction-Dependent Dissociation for Weak Acids.

We demonstrate for formic and acetic acid dissolved in water as examples that the binary quantum cluster equilibrium (bQCE) approach can predict acid strengths over the whole range of acid concentrations. The acid strength increases in a complex rather than a simple way with increasing mole fraction of the acid from 0 to 0.7, reflecting the complex interplay between the dissociated ions or conjugate bases available as compared to the acid and water molecules. Furthermore, our calculated ion concentrations meet the experimental maximum of the conductivity with excellent agreement for acetic acid and satisfactorily for the formic acid/water mixture. As only a limited number of simple quantum-chemical calculations are required for the prediction, bQCE is clearly a valuable approach to access these quantities also in non-aqueous solutions. It is a highly valuable asset for predicting ionization processes in highly concentrated solutions, which are relevant for biological and chemical systems, as well as technological processes.

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.

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.

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.

Floating orbital molecular dynamics simulations.

We introduce an alternative ab initio molecular dynamics simulation as a unification of Hartree-Fock molecular dynamics and the floating orbital approach. The general scheme of the floating orbital molecular dynamics method is presented. Moreover, a simple but sophisticated guess for the orbital centers is provided to reduce the number of electronic structure optimization steps at each molecular dynamics step. The conservation of total energy and angular momentum is investigated in order to validate the floating orbital molecular dynamics approach with and without application of the initial guess. Finally, a water monomer and a water dimer are simulated, and the influence of the orbital floating on certain properties like the dipole moment is investigated.

Koopmans' theorem for acidic protons.

The famous Brønsted acidity, which is relevant in many areas of experimental and synthetic chemistry, but also in biochemistry and other areas, is investigated from a new perspective. Nuclear electronic orbital methods, which explicitly account for the quantum character of selected protons, are applied. The resulting orbital energies of the proton wavefunction are interpreted and related to enthalpies of deprotonation and acid strength in analogy to the Koopmans' theorem for electrons. For a set of organic acids, we observe a correlation which indicates the validity of such a NEO-Koopmans' approach and opens up new opportunities for the computational investigation of more complex acidic systems.

H2 Open - Guest Editorial.

This special collection presents original research articles and reviews that are connected to the multifaceted and rich chemistry of water. These works serve as an illustration of how, despite its apparent simplicity and ubiquity, water continues to be at the center of scientific exploration from a wide range of perspectives and employing the toolbox of modern-day chemistry.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

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.

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.

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.

Molecular Orientation at the Squalene/Air Interface from Sum Frequency Generation Spectroscopy and Atomistic Modeling.

Human skin oils are significant scavengers of atmospheric oxidants in occupied indoor environments, and squalene is a major ozone-active constituent. Here, we present a combined spectroscopic and atomistic modeling approach to elucidate the conformational and orientational preferences of squalene at the air/oil interface and their implications for reactions with ozone. We find that squalene chains have a tendency to align with the surface normal, resulting in different concentrations of the various types of its double bonds and thus different reactivities. We also observe the presence of water at the surface of this hydrophobic compound. Both findings have possible implications for the design and outcomes of kinetic models describing this important aspect of indoor air chemistry.

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, xe. 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.

Predicting the Ionic Product of Water.

We present a first-principles calculation and mechanistic characterization of the ion product of liquid water (K W ), 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 K W 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.

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.