Systematic Study of Different Types of Interactions in α-, ß- and γ-Cyclodextrin: Quantum Chemical Investigation.

In this work, comprehensive ab initio quantum chemical calculations using the DFT level of theory were performed to characterize the stabilization interactions (H-bonding and hyperconjugation effects) of two stable symmetrical conformations of α-, ß-, and γ-cyclodextrins (CDs). For this purpose, we analyzed the electron density using "Atom in molecules" (AIM), "Natural Bond Orbital" (NBO), and energy decomposition method (CECA) in 3D and in Hilbert space. We also calculated the H-bond lengths and OH vibrational frequencies. In every investigated CD, the quantum chemical descriptors characterizing the strength of the interactions between the H-bonds of the primary OH (or hydroxymethyl) and secondary OH groups are examined by comparing the same quantity calculated for ethylene glycol, α-d-glucose (α-d-Glcp) and a water cluster as reference systems. By using these external standards, we can characterize more quantitatively the properties of these bonds (e.g., strength). We have demonstrated that bond critical points (BCP) of intra-unit H-bonds are absent in cyclodextrins, similar to α-d-Glcp and ethylene glycol. In contrast, the CECA analysis showed the existence of an exchange (bond-like) interaction between the interacting O…H atoms. Consequently, the exchange interaction refers to a chemical bond, namely the H-bond between two atoms, unlike BCP, which is not suitable for its detection.

Outstanding Properties of the Hydration Shell around ß-d-Glucose: A Computational Study.

Ab initio molecular dynamics (AIMD) simulations have been performed on aqueous solutions of four simple sugars, α-d-glucose, ß-d-glucose, α-d-mannose, and α-d-galactose. Hydrogen-bonding (HB) properties, such as the number of donor- and acceptor-type HB-s, and the lengths and strengths of hydrogen bonds between sugar and water molecules, have been determined. Related electronic properties, such as the dipole moments of water molecules and partial charges of the sugar O atoms, have also been calculated. The hydrophilic and hydrophobic shells were characterized by means of spatial distribution functions. ß-d-Glucose was found to form the highest number of hydrophilic and the smallest number of hydrophobic connections to neighboring water molecules. The average sugar-water H-bond length was the shortest for ß-d-glucose, which suggests that these are the strongest such H-bonds. Furthermore, ß-d-glucose appears to stand out in terms of the symmetry properties of both its hydrophilic and hydrophobic hydration shells. In summary, in all aspects considered here, there seems to be a correlation between the distinct characteristics of ß-d-glucose reported here and its outstanding solubility in water. Admittedly, our findings represent only some of the important factors that influence the solubility.

Connecting Diffraction Experiments and Network Analysis Tools for the Study of Hydrogen-Bonded Networks.

A self-consistent scheme is presented that is applicable for revealing details of the microscopic structure of hydrogen-bonded liquids, including the description of the hydrogen-bonded network. The scheme starts with diffraction measurements, followed by molecular dynamics simulations. Computational results are compared with the experimentally accessible information on the structure, which is most frequently the total scattering structure factor. In the case of an at least semiquantitative agreement between experiment and simulation, sets of particle coordinates from the latter may be exploited for revealing nonmeasurable structural details. Calculations of some properties concerning the hydrogen-bonded network are also described, in the order of increasing complexity: starting with the definition of a hydrogen bond, first and second neighborhoods are described via spatial correlations functions. Attention is then turned to cyclic and noncyclic hydrogen-bonded clusters, before cluster size distributions and percolation are discussed. We would like to point out that, as a result of applying the novel protocol, these latter, rather abstract, quantities become consistent with diffraction data: it may thus be argued that the approach reviewed here is the first one that establishes a direct link between measurements and elements of network theories. Applications for liquid water, simple alcohols, and alcohol-water liquid mixtures demonstrate the usefulness of the aforementioned characteristics. The procedure can readily be applied to more complicated hydrogen-bonded networks, like mixtures of polyols (diols, triols, sugars, etc.) and water, and complex aqueous solutions of even larger molecules (even of proteins).

Two Faces of the Two-Phase Thermodynamic Model.

The quantum harmonic model and the two-phase thermodynamic method (2PT) are widely used to obtain quantum-corrected properties such as isobaric heat capacities or molar entropies. 2PT heat capacities were calculated inconsistently in the literature. For water, the classical heat capacity was also considered, but for organic liquids, it was omitted. We reanalyzed the performance of different quantum corrections on the heat capacities of common organic solvents against experimental data. We have pointed out serious flaws in previous 2PT studies. The vibrational density of states was calculated incorrectly causing a 39% relative error in diffusion coefficients and 45% error in the 2PT heat capacities. The wrong conversion of isobaric and isochoric heat capacities also caused about 40% error but in the other direction. We have introduced the concept of anharmonic correction (AC), which is simply the deviation of the classical heat capacity from that of the harmonic oscillator model. This anharmonic contribution is around +30 to 40 J/(mol K) for water depending on the water model and -8 to -10 J/(mol K) for hydrocarbons and halocarbons. AC is unrealistically large, +40 J/(K mol) for alcohols and amines, indicating some deficiency of the OPLS force field. The accuracy of the computations was also assessed with the determination of the self-diffusion coefficients.

Properties of Hydrogen-Bonded Networks in Ethanol-Water Liquid Mixtures as a Function of Temperature: Diffraction Experiments and Computer Simulations.

New X-ray and neutron diffraction experiments have been performed on ethanol-water mixtures as a function of decreasing temperature, so that such diffraction data are now available over the entire composition range. Extensive molecular dynamics simulations show that the all-atom interatomic potentials applied are adequate for gaining insight into the hydrogen-bonded network structure, as well as into its changes on cooling. Various tools have been exploited for revealing details concerning hydrogen bonding, as a function of decreasing temperature and ethanol concentration, like determining the H-bond acceptor and donor sites, calculating the cluster-size distributions and cluster topologies, and computing the Laplace spectra and fractal dimensions of the networks. It is found that 5-membered hydrogen-bonded cycles are dominant up to an ethanol mole fraction xeth = 0.7 at room temperature, above which the concentrated ring structures nearly disappear. Percolation has been given special attention, so that it could be shown that at low temperatures, close to the freezing point, even the mixture with 90% ethanol (xeth = 0.9) possesses a three-dimensional (3D) percolating network. Moreover, the water subnetwork also percolates even at room temperature, with a percolation transition occurring around xeth = 0.5.

Chloride ions as integral parts of hydrogen bonded networks in aqueous salt solutions: the appearance of solvent separated anion pairs.

Hydrogen bonding to chloride ions has been frequently discussed over the past 5 decades. Still, the possible role of such secondary intermolecular bonding interactions in hydrogen bonded networks has not been investigated in any detail. Here we consider computer models of concentrated aqueous LiCl solutions and compute the usual hydrogen bond network characteristics, such as distributions of cluster sizes and of cyclic entities, both for models that take and do not take chloride ions into account. During the analysis of hydrogen bonded rings, a significant amount of 'solvent separated anion pairs' have been detected at high LiCl concentrations. It is demonstrated that taking halide anions into account as organic constituents of the hydrogen bonded network does make the interpretation of structural details significantly more meaningful than when considering water molecules only. Finally, we compare simulated structures generated by 'good' and 'bad' potential sets on the basis of the tools developed here, and show that this novel concept is, indeed, also helpful for distinguishing between reasonable and meaningless structural models.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water.

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Molecular Dynamics Simulation Studies of the Temperature-Dependent Structure and Dynamics of Isopropanol-Water Liquid Mixtures at Low Alcohol Content.

Series of molecular dynamics simulations for 2-propanol-water mixtures, as a function of temperature (between freezing and room temperature) and composition (xip = 0, 0.5, 0.1, and 0.2), have been performed for temperatures reported in the only available experimental structure study. It is shown that when the all-atom optimized potentials for liquid simulations interatomic potentials for the alcohol are combined with the TIP4P/2005 water model, then the near-quantitative agreement with measured X-ray data, in the reciprocal space, can be achieved. Such an agreement justifies detailed investigations of structural, energetic, and dynamic properties on the basis of simulation trajectories. Here, we focus on characteristics related to hydrogen bonds (HB): cluster-, and in particular, ring formation, energy distributions, and lifetimes of HB-s have been scrutinized for the entire system, as well as for the water and isopropanol subsystems. It is demonstrated that similar to ethanol-water mixtures, the occurrence of 5-membered-hydrogen-bonded rings are significant, particularly at higher alcohol concentrations. Concerning HB energetics, an intriguing double maximum appears on the alcohol-alcohol HB energy distribution function. HB lifetimes have been found significantly longer in the mixtures than they are in pure liquids.

Variations of the Hydrogen Bonding and Hydrogen-Bonded Network in Ethanol-Water Mixtures on Cooling.

Molecular dynamics computer simulations have been conducted for ethanol-water liquid mixtures in the water-rich side of the composition range, with 10, 20, and 30 mol % of alcohol, at temperatures between room temperature and the experimental freezing point of the given mixture. All-atom-type (optimized potential for liquid simulations) interatomic potentials have been assumed for ethanol, in combination with two kinds of rigid water models (SPC/E and TIP4P/2005). Both combinations have provided excellent reproductions of the experimental X-ray total structure factors at each temperature; this yielded a strong basis for further structural analyses. Beyond partial radial distribution functions, various descriptors of hydrogen-bonded assemblies, as well as of the hydrogen-bonded network have been determined. A clear tendency was observed toward that an increasing proportion of water molecules participate in hydrogen bonding with exactly two donor and two acceptor sites as temperature decreases. Concerning larger assemblies held together by hydrogen bonding, the main focus was put on the properties of cyclic entities: it was found that, similarly to methanol-water mixtures, the number of hydrogen-bonded rings has increased with lowering temperature. However, for ethanol-water mixtures, the dominance of 5-fold rings, and not 6-fold rings, could be observed.

Structural and Dynamic Heterogeneity of Capillary Wave Fronts at Aqueous Interfaces.

Using a unique combination of slab-layering analyses and identification of truly interfacial molecules, this work examines water/vapor and water/n-hexane interfaces, specifically the structural and dynamic perturbations of the interfacial water molecules at different locations within the surface capillary waves. From both the structural and dynamic properties analyzed, it is found that these interfacial water molecules dominate the perturbations within the interfacial region, which can extend deep into the water phase relative to the Gibbs dividing surface. Of more importance is the demonstration of structural and dynamic heterogeneity of the interfacial water molecules at the capillary wave front, as indicated by the dipole orientation and the structural and dynamic behavior of hydrogen bonds and their networks.

Conceptual Problem with Calculating Electron Densities in Finite Basis Density Functional Theory.

It is discussed that finite basis Density Functional Theory (DFT) calculations using a single Kohn-Sham determinant cannot reproduce, in a strict mathematical sense, the exact electron density corresponding to the same finite basis. This is because the DFT density derives from an idempotent first order density matrix, while the exact (full CI) density can only be obtained from a nonidempotent one. The problem is absent for the original Kohn-Sham integro-differential equations or if a strictly complete basis set is assumed.

Many-Body Energy Decomposition with Basis Set Superposition Error Corrections.

The problem of performing many-body decompositions of energy is considered in the case when BSSE corrections are also performed. It is discussed that the two different schemes that have been proposed go back to the two different interpretations of the original Boys-Bernardi counterpoise correction scheme. It is argued that from the physical point of view the "hierarchical" scheme of Valiron and Mayer should be preferred and not the scheme recently discussed by Ouyang and Bettens, because it permits the energy of the individual monomers and all the two-body, three-body, etc. energy components to be free of unphysical dependence on the arrangement (basis functions) of other subsystems in the cluster.

Decreasing temperature enhances the formation of sixfold hydrogen bonded rings in water-rich water-methanol mixtures.

The evolution of the structure of liquid water-methanol mixtures as a function of temperature has been studied by molecular dynamics simulations, with a focus on hydrogen bonding. The combination of the OPLS-AA (all atom) potential model of methanol and the widely used SPC/E water model has provided excellent agreement with measured X-ray diffraction data over the temperature range between 298 and 213 K, for mixtures with methanol molar fractions of 0.2, 0.3 and 0.4. Hydrogen bonds (HB-s) have been identified via a combined geometric/energetic, as well as via a purely geometric definition. The number of recognizable hydrogen bonded ring structures in some cases doubles while lowering the temperature from 298 to 213 K; the number of sixfold rings increases most significantly. An evolution towards the structure of hexagonal ice, that contains only sixfold hydrogen bonded rings, has thus been detected on cooling water-methanol mixtures.

On Dipole Moments and Hydrogen Bond Identification in Water Clusters.

It is demonstrated that the localized orbitals calculated for a water cluster have small delocalization tails along the hydrogen bonds, that are crucial in determining the resulting dipole moments of the system. (By cutting them, one gets much smaller dipole moments for the individual monomers-close to the values one obtains by using a Bader-type analysis.) This means that the individual water monomers can be delimited only in a quite fuzzy manner, and the electronic charge density in a given point cannot be assigned completely to that or another molecule. Thus, one arrives to the brink of breaking the concept of a water cluster consisting of individual molecules. The analysis of the tails of the localized orbitals can also be used to identify the pairs of water molecules actually forming hydrogen bonds.

Hierarchy of the Collective Effects in Water Clusters.

The results of dipole moment as well as of intra- and intermolecular bond order calculations indicate the big importance of collective electrostatic effects caused by the nonimmediate environment in liquid water models. It is also discussed how these collective effects are built up as consequences of the electrostatic and quantum chemical interactions in water clusters.

Speciation and the structure of lead(II) in hyper-alkaline aqueous solution.

The identity of the predominating lead(ii) species in hyper-alkaline aqueous solution has been determined by Raman spectroscopy, and ab initio quantum chemical calculations and its structure has been determined by EXAFS. The observed and calculated Raman spectra for the [Pb(OH)3](-) complex are in agreement while they are different for two-coordinated complexes and complexes containing Pb[double bond, length as m-dash]O double bonds. Predicted bond lengths are also consistent with the presence of [Pb(OH)3](-) and exclude the formation of Pb[double bond, length as m-dash]O double bond(s). These observations together with experimentally established analogies between lead(ii) and tin(ii) in hyper-alkaline aqueous solutions suggest that the last stepwise hydroxido complex of lead(ii) is [Pb(OH)3](-). The Pb-O bond distance in the [Pb(OH)3](-) complex as determined is remarkably short, 2.216 Å, and has low symmetry as no multiple back-scattering is observed. The [Pb(OH)3](-) complex has most likely trigonal pyramidal geometry as all reported three-coordinated lead(ii) complexes in the solid state. From single crystal X-ray data, the bond lengths for O-coordinated lead(ii) complexes with low coordination numbers are spread over an unusually wide interval, 2.216-2.464 Å for N = 3. The Pb-O bond distance is at the short side and within the range of three coordinated complexes, as also observed for the trihydroxidostannate(ii) complex indicating that the hydroxide ion forms short bonds with d(10)s(2) metal ions with occupied anti-bonding orbitals.

Large polarization but small electron transfer for water around Al(3+) in a highly hydrated crystal.

Precise molecular-level information on the water molecule is precious, since it affects our interpretation of the role of water in a range of important applications of aqueous media. Here we propose that electronic structure calculations for highly hydrated crystals yield such information. Properties of nine structurally different water molecules (19 independent OO hydrogen bonds) in the Al(NO3)3·9H2O crystal have been calculated from DFT calculations. We combine the advantage of studying different water environments using one and the same compound and method (instead of comparing a set of independent experiments, each with its own set of errors) with the advantage of knowing the exact atomic positions, and the advantage of calculating properties that are difficult to extract from experiment. We find very large Wannier dipole moments for H2O molecules surrounding the cations: 4.0-4.3 D (compared to our calculated value of 1.83 D in the gas phase). These are induced by the ions and the H-bonds, while other water interactions and the relaxation of the internal water geometry in fact decrease the dipole moments. We find a good correlation between the water dipole moment and the OO distances, and an even better (non-linear) correlation with the average electric field over the molecule. Literature simulation data for ionic aqueous solutions fit quite well with our crystalline 'dipole moment vs. OO distance' curve. The progression of the water and cation charges from 'small clusters ⇒ large clusters ⇒ the crystal' helps explain why the net charges on all the water molecules are so small in the crystal.

Hydrogen bond network topology in liquid water and methanol: a graph theory approach.

Networks are increasingly recognized as important building blocks of various systems in nature and society. Water is known to possess an extended hydrogen bond network, in which the individual bonds are broken in the sub-picosecond range and still the network structure remains intact. We investigated and compared the topological properties of liquid water and methanol at various temperatures using concepts derived within the framework of graph and network theory (neighbour number and cycle size distribution, the distribution of local cyclic and local bonding coefficients, Laplacian spectra of the network, inverse participation ratio distribution of the eigenvalues and average localization distribution of a node) and compared them to small world and Erdos-Rényi random networks. Various characteristic properties (e.g. the local cyclic and bonding coefficients) of the network in liquid water could be reproduced by small world and/or Erdos-Rényi networks, but the ring size distribution of water is unique and none of the studied graph models could describe it. Using the inverse participation ratio of the Laplacian eigenvectors we characterized the network inhomogeneities found in water and showed that similar phenomena can be observed in Erdos-Rényi and small world graphs. We demonstrated that the topological properties of the hydrogen bond network found in liquid water systematically change with the temperature and that increasing temperature leads to a broader ring size distribution. We applied the studied topological indices to the network of water molecules with four hydrogen bonds, and showed that at low temperature (250 K) these molecules form a percolated or nearly-percolated network, while at ambient or high temperatures only small clusters of four-hydrogen bonded water molecules exist.

Reactivity models of hydrogen activation by frustrated Lewis pairs: synergistic electron transfers or polarization by electric field?

Two alternative qualitative reactivity models have recently been proposed to interpret the facile heterolytic cleavage of H2 by frustrated Lewis pairs (FLPs). Both models assume that the reaction takes place via reactive intermediates with preorganized acid/base partners; however, they differ in the mode of action of the active centers. In the electron transfer (ET) model, the hydrogen activation is associated with synergistic electron donation processes with the simultaneous involvement of active centers and the bridging hydrogen, showing similarity to transition-metal-based and other H2-activating systems. In contrast, the electric field (EF) model suggests that the heterolytic bond cleavage occurs as a result of polarization by the strong EF present in the cavity of the reactive intermediates. To assess the applicability of the two conceptually different mechanistic views, we examined the structural and electronic rearrangements as well as the EFs along the H2 splitting pathways for a representative set of reactions. The analysis reveals that electron donations developing already in the initial phase are general characteristics of all studied reactions, and the related ET model provides qualitative interpretation for the main features of the reaction pathways. On the other hand, several arguments have emerged that cast doubt on the relevance of EF effects as a conceptual basis in FLP-mediated hydrogen activation.

Association of frustrated phosphine-borane pairs in toluene: molecular dynamics simulations.

Explicit solvent molecular dynamics simulations of the ((t)Bu)(3)P/B(C(6)F(5))(3) pair in toluene allowed the estimation of the degree of intermolecular association and the population of encounter complex states in solution phase.