Cluster-Weighting in Bulk Phase Vibrational Circular Dichroism

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.

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.

Exploring the Influence of the Phosphorus-Heteroatom Substitution in Nicotine on Its Electronic and Vibrational Spectroscopic Properties

The influence of phosphorus substitution of nitrogen in heterocyclic compounds on the vibrational spectroscopy as well as frontier molecular orbitals are analyzed. Nicotine with two nitrogen atoms in its structure is taken as the sample system to be studied computationally. By replacing the nitrogen atom in one or both rings of this molecule with phosphorus, three nicotine derivatives are created. The vibrational circular dichroism and infrared spectra of these four molecules in their monomer state, as well as the assemblies up to trimers are determined. The aforementioned spectra are calculated using static quantum chemical calculations employing a cluster-weighted approach. The calculated gas phase spectra of nicotine are compared to their respective experimental spectra. It is observed that the nicotine derivatives with phosphorus in the methylpyrrolidine ring have considerably different gas phase and bulk phase vibrational circular dichroism spectra when compared to nicotine. The phosphorus substitution reduces the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital as well as altering the polarizability and reactivity of the investigated molecules.

Structures of DMSO clusters and quantum cluster equilibrium (QCE)

Dimethylsulfoxide (DMSO) clusters are crucial for understanding processes in liquid DMSO. Despite its importance, DMSO clusters have received negligible attention due to the complexity of their potential energy surfaces (PESs). In this work, we explored the PESs of the DMSO clusters from dimer to decamer, starting with classical molecular dynamics, followed by full optimizations at the PW6B95-D3/def2-TZVP level of theory. In addition, the binding energies, the binding enthalpy per DMSO, and the quantum theory of atoms in molecules (QTAIM) analysis of the most stable isomers are reported. Temperature effects on the stability of the isomers have also been assessed. After thoroughly exploring the PESs of the DMSO clusters, 159 configurations have been used to apply the quantum cluster equilibrium (QCE) theory to liquid DMSO. The quantum cluster equilibrium theory has been applied to determine the liquid properties of DMSO from DMSO clusters. Thus, using the QCE, the population of the liquid DMSO, its infrared spectrum, and some thermodynamic properties of the liquid DMSO are predicted. The QCE results show that the population of the liquid DMSO is mainly dominated by the DMSO dimer and decamer, with the contribution in trace of the DMSO monomer, trimer, tetramer, pentamer, and octamer. More interestingly, the predicted infrared spectrum of liquid DMSO is in qualitative agreement with the experiment.

Efficient Prediction of Mole Fraction Related Vibrational Frequency Shifts

While so far it has been possible to calculate vibrational spectra of mixtures at a particular composition, we present here a novel cluster approach for a fast and robust calculation of mole fraction dependent infrared and vibrational circular dichroism spectra at the example of acetonitrile/(R)-butan-2-ol mixtures. By assigning weights to a limited number of quantum chemically calculated clusters, vibrational spectra can be obtained at any desired composition by a weighted average of the single cluster spectra. In this way, peak positions carrying information about intermolecular interactions can be predicted. We show that mole fraction dependent peak shifts can be accurately modeled and, that experimentally recorded infrared spectra can be reproduced with high accuracy over the entire mixing range. Because only a very limited number of clusters is required, the presented approach is a valuable and computationally efficient tool to access mole fraction dependent spectra of mixtures on a routine basis.

Modelling solute-solvent interactions in VCD spectra analysis with the micro-solvation approach

Vibrational circular dichroism (VCD) spectroscopy has become an important part of the (stereo-)chemists' toolbox as a reliable method for the determination of absolute configurations. Being the chiroptical version of infrared spectroscopy, it has also been recognized as being very sensitive to conformational changes and intermolecular interactions. This sensitivity originates from the fact that the VCD spectra of individual conformers are often more different than their IR spectra, so that changes in conformational distributions or band positions and intensities become more pronounced. What is an advantage for studies focussing on intermolecular interactions can, however, quickly turn into a major obstacle during AC determinations: solute-solvent interactions can have a strong influence on spectral signatures and they must be accurately treated when simulating VCD and IR spectra. In this perspective, we showcase selected examples which exhibit particularly pronounced solvent effects. It is demonstrated that it is typically sufficient to model solute-solvent interactions by placing single solvent molecules near hydrogen bonding sites of the solute and subsequently use the optimized structures for spectra simulations. This micro-solvation approach works reasonably well for medium-sized, not too conformationally flexible molecules. We thus also discuss its limitations and outline the next steps that method development needs to take in order to further improve the workflows for VCD spectra predictions.

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

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 ΔE₀ and ΔG varies in a few cases and that the global minimum is not always the dominantly occupied structure.

Vibrational Circular Dichroism from DFT Molecular Dynamics: The AWV Method

The paper illustrates the Activity Weighted Velocities (AWV) methodology to compute Vibrational Circular Dichroism (VCD) anharmonic spectra from Density Functional Theory (DFT) molecular dynamics. AWV calculates the spectra by the Fourier Transform of the time correlation functions of velocities, weighted by specific observables: the Atomic Polar Tensors (APTs) and the Atomic Axial Tensors (AATs). Indeed, AWV shows to correctly reproduce the experimental spectra for systems in the gas and liquid phases, both in the case of weakly and strongly interacting systems. The comparison with the experimental spectra is striking especially in the fingerprint region, as demonstrated by the three benchmark systems discussed: (1S)-Fenchone in the gas phase, (S)-(−)-Propylene oxide in the liquid phase, and (R)-(−)-2-butanol in the liquid phase. The time evolution of APTs and AATs can be adequately described by a linear combination of the tensors of a small set of appropriate reference structures, strongly reducing the computational cost without compromising accuracy. Additionally, AWV allows the partition of the spectral signal in its molecular components without any expensive postprocessing and any localization of the charge density or the wave function.

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.

Chemistry Dissolved in Ionic Liquids. A Theoretical Perspective

The theoretical treatment of ionic liquids must focus now on more realistic models while at the same time keeping an accurate methodology when following recent ionic liquids research trends or allowing predictability to come to the foreground. In this Perspective, we summarize in three cases of advanced ionic liquid research what methodological progress has been made and point out difficulties that need to be overcome. As particular examples to discuss we choose reactions, chirality, and radicals in ionic liquids. All these topics have in common that an explicit or accurate treatment of the electronic structure and/or intermolecular interactions is required (accurate methodology), while at the same time system size and complexity as well as simulation time (realistic model) play an important role and must be covered as well.

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.

Hydrogen Bonding and Vaporization Thermodynamics in Hexafluoroisopropanol-Acetone and -Methanol Mixtures. A Joined Cluster Analysis and Molecular Dynamic Study

Binary mixtures of hexafluoroisopropanol with either methanol or acetone are analyzed via classical molecular dynamics simulations and quantum cluster equilibrium calculations. In particular, their populations and thermodynamic properties are investigated with the binary quantum cluster equilibrium method, using our in‐house code peacemaker 2.8, upgraded with temperature‐dependent parameters. A novel approach, where the final density from classical molecular dynamics, has been used to generate the necessary reference isobars. The hydrogen bond network in both type of mixtures at molar fraction of hexafluoroisopropanol of 0.2, 0.5, and 0.8 respectively is investigated via the molecular dynamics trajectories and the cluster results. In particular, the populations show that mixed clusters are preferred in both systems even at 0.2 molar fractions of hexafluoroisopropanol. Enthalpies and entropies of vaporization are calculated for the neat and mixed systems and found to be in good agreement with experimental values.

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.

The important role of non-covalent interactions for the vibrational circular dichroism of lactic acid in aqueous solution

We present a computational study of vibrational circular dichroism (VCD) in solutions of (S)-lactic acid, relying on ab initio molecular dynamics (AIMD) and full solvation with bulk water. We discuss the effect of the hydrogen bond network on the aggregation behaviour of the acid: while aggregates of the solute represent conditions encountered in a weakly interacting solvent, the presence of water drastically interferes with the clusters - more strongly than originally anticipated. For both scenarios we computed the VCD spectra by means of nuclear velocity perturbation theory (NVPT). The comparison with experimental data allows us to establish a VCD-structure relationship that includes the solvent network around the chiral solute. We suggest that fundamental modes with strong polarisation such as the carbonyl stretching vibration can borrow VCD from the chirally restructured solvent cage, which extends the common explanatory models of VCD generation in aqueous solution.

Assessing cluster models of solvation for the description of vibrational circular dichroism spectra: synergy between static and dynamic approaches

Solvation effects are essential for defining the shape of vibrational circular dichroism (VCD) spectra.