Structure of Water Clusters. The Contribution of Many-Body Forces, Monomer Relaxation, and Vibrational Zero-Point Energy

Sulfur migration mechanism of pig manure in supercritical water: A combined experimental and DFT study

Pig manure (PM) is a high concentration organic waste rich in sulfur, and its biofuel contains various sulfur-containing pollutants, which reduces the safety of the products. Supercritical water (SCW) can dissolve most organic matter, which is a technology worthy of further study. In order to reduce sulfur pollution in the process of PM resource utilization and better control the conversion path of sulfur, it is necessary to explore the migration mechanism of sulfur in the whole PM-SCW gasification process. The experimental results indicated that H2S was the only gaseous product. Only inorganic compounds (S2-, S2O32- and SO42-) were detected in the liquid. Sulfur in the solid mainly included thiol/thioether, thiophene and sulfone. The influence of different reaction conditions (temperature, residence time, PM concentration and catalysts) on sulfur migration was studied in a batch reactor. It was worth noting that the catalysts had a significant effect on H2S absorption. The lowest H2S yield was 3.2 * 10-4 mol/kg and more than 70% of the sulfur was distributed in the liquid under the condition of addition of K2CO3. While, the RTH2110 fixed most of the sulfur of PM (the maximum value reached 50.94%) in the solid. Thus, adding the catalysts flexibly can choose composition of the products. Furthermore, six possible pathways of sulfur migration in the solid were designed and the kinetic parameters were calculated by density functional theory (DFT). The results provided a basis for controlling sulfur in PM. Subsequently, the sulfur migration pathways during PM-SCW gasification process were comprehensively summarized through the combination of experiment and DFT. It provided a method for sulfur treatment in PM, which had guiding significance for the realization of pollution-free treatment of PM.

Accurate calculation of tunneling splittings in water clusters using path-integral based methods

Tunneling splittings observed in molecular rovibrational spectra are significant evidence for tunneling motion of hydrogen nuclei in water clusters. Accurate calculations of the splitting sizes from first principles require a combination of high-quality inter-atomic interactions and rigorous methods to treat the nuclei with quantum mechanics. Many theoretical efforts have been made in recent decades. This Perspective focuses on two path-integral based tunneling splitting methods whose computational cost scales well with the system size, namely, the ring-polymer instanton method and the path-integral molecular dynamics (PIMD) method. From a simple derivation, we show that the former is a semiclassical approximation to the latter, despite that the two methods are derived very differently. Currently, the PIMD method is considered to be an ideal route to rigorously compute the ground-state tunneling splitting, while the instanton method sacrifices some accuracy for a significantly smaller computational cost. An application scenario of such a quantitatively rigorous calculation is to test and calibrate the potential energy surfaces of molecular systems by spectroscopic accuracy. Recent progress in water clusters is reviewed, and the current challenges are discussed.

Assessing the Experimental Hydrogen Bonding Energy of the Cyclic Water Dimer Transition State with a Cyclooctatetraene-Based Molecular Balance

We have conducted an experimental and computational study of cyclooctatetraene-1,4/1,6-dimethanol (1,4 and 1,6) as a molecular balance with the goal in mind to determine the otherwise inaccessible hydrogen bonding energy (HBE) of the cyclic water dimer, which constitutes a transition state. The 1,4/1,6 folding equilibrium is governed by an intramolecular hydrogen bond in the folded 1,6-isomer, in which the OH groups adopt a cyclic planar geometry, akin to the structure of the cyclic water dimer transition state. We characterized hydrogen bonding in 1,6 and reference complexes utilizing SAPT2 + (3)δMP2/aug-cc-pVTZ and selected quantum theory of atoms in molecule descriptors at M06-2XD3(0)/ma-def2-TZVPP. Additionally, we computed HBEs at the DLPNO-CCSD(T)/aug-cc-pVQZ level of theory. We find that hydrogen bonding in 1,6 is very similar to the interaction in the C_i symmetric cyclic water dimer TS, both in magnitude and character. We experimentally determined the Gibbs free energy of the folding process (ΔG_eq) in a variety of organic solvents via nuclear magnetic resonance spectroscopy measurements at room temperature. By combining experimentally obtained ΔG_eq values with corrections derived from accurate computational methods, we provide estimates for the HBE of cyclic water dimers and the cyclic water dimer TS, as the most stable cyclic water dimer.

A CCSD(T)-Based 4-Body Potential for Water

High-level, ab initio calculations find that the 4-body (4-b) interaction is needed to account for near-100% of the total interaction energy for water clusters as large as the 21-mer. Motivated by this, we report a permutationally invariant polynomial potential energy surface (PES) for the 4-body interaction. This machine-learned PES is a fit to 2119 symmetry-unique, CCSD(T)-F12a/haTZ 4-b interaction energies. Configurations for these come from tetramer direct-dynamics calculations, fragments from an MD water simulation at 300 K, and tetramer fragments in a variety of water clusters. The PIP basis is purified to ensure that the PES goes rigorously to zero in monomer+trimer and dimer+dimer dissociations. The 4-b energies of isomers of the hexamer calculated with the new PES are shown to be in better agreement with benchmark CCSD(T) results than those from the MB-pol potential. Tests on larger clusters further validate the high-fidelity of the PES. The PES is shown to be fast to evaluate, taking 2.4 s for 10⁵ evaluations on a single core of 2.4 GHz Intel Xeon processor, and significantly faster using a parallel version of the PES.

Photoelectron Spectroscopy of the Water Dimer Reveals Unpredicted Vibrational Structure

Hydrogen bonds and proton transfer reactions can be considered as being at the very heart of aqueous chemistry and of utmost importance for many processes of biological relevance. Nevertheless, these processes are not yet well understood, even in seemingly simple model systems like small water clusters. We present a study of the photoelectron spectrum of the water dimer, revealing previously unresolved vibrational structure with 10-30 meV (80-242 cm^-1) typical splitting, in disagreement with a previous theoretical photoionization study predicting an apparent main vibrational progression with an ∼130 meV spacing [Kamarchik et al.; J. Chem. Phys. 2010, 132, 194311]. The observed vibrational structure and its deviation from the theoretical prediction is discussed in terms of known difficulties with calculations of strongly coupled anharmonic systems involving large amplitude motions. Potential contributions of the nonzero vibrational energy of the neutral water dimer at a finite experimental internal temperature are addressed. The internal temperature is estimated from the breakdown diagram associated with the dissociative ionization of the water dimer to be around to 130 K. This analysis also provides two additional, independently measured values for the 0 K appearance energy of the hydronium ion (H₃O⁺) from dissociative ionization of the water dimer.

Observation of the Low-Frequency Spectrum of the Water Trimer as a Sensitive Test of the Water-Trimer Potential and the Dipole-Moment Surface

Intermolecular interactions in bulk water are dominated by pairwise and non‐pairwise cooperative interactions. While accurate descriptions of the pairwise interactions are available and can be tested by precise low‐frequency spectra of the water dimer up to 550 cm⁻¹, the same does not hold for the three‐body interactions. Here, we report the first comprehensive spectrum of the water trimer in the frequency region from 70 to 620 cm⁻¹ using helium‐nanodroplet isolation and free‐electron lasers. By comparison to accompanying high‐level quantum calculations, the experimentally observed intermolecular bands can be assigned. The transition frequencies of the degenerate translation, the degenerate in‐plane and the non‐degenerate out‐of‐plane libration, as well as additional bands of the out‐of‐plane librational mode are reported for the first time. These provide a benchmark for state‐of‐the‐art water potentials and dipole‐moment surfaces, especially with respect to three‐body interactions.

Ion and water transport reasonably involves rotation and pseudorotation: measurement and modeling the temperature dependence of small-angle neutron scattering from aqueous SrI2

X-ray and neutron scattering have provided insight into the short range (<8 Å) structures of ionic solutions for over a century. For longer distances, single scattering bands have, however, been seen. For the non-hydrolyzing salt SrI2 in aqueous (D2O) solution, a structure sufficient to scatter slow neutrons has been seen to persist down to a concentration of 0.1 mol L-1 where the measured average spacing between scatterers is over 20 Å. Theoretical studies of such long distance solution structures are difficult, and these difficulties are discussed. The width of the distribution in distances between the scatterers (ions, ion pairs, etc.) remains less than 10 Å, which approximates the average size of the ions and their first hydration shell. Here, we measure the temperature dependence from 10 °C to 90 °C of the small angle neutron scattering (SANS) by a 0.5 molar SrI2 solution in D2O and find that this surprisingly narrow distribution of the distances remains constant within experimental uncertainty. This structure of the ions in the solution appears to endure because changes in interion distances along any single spatial dimension require displacements near the size of a water molecule. Together, the experimental measurements support a rotatory mechanism for simultaneous ion transport and water countertransport. Since rotation minimizes displacement of the solution framework, it is suggested that water transport alone also involves rotation of multimolecular structures, and that the interpretation of single-molecule water rotation is confounded by pseudorotation that results from paired picosecond proton exchanges. It is pointed out that NMR-determined millisecond to microsecond proton exchange times of chelated-metal-ion bound waters and the much faster chelate rotational correlation times around 10 picoseconds, both of which require making and breaking of hydrogen bonds, are difficult to impossible to reconcile.

Accurate calculation of zero point energy from molecular dynamics simulations of liquids and their mixtures

The two-phase thermodynamic (2PT) method is used to compute the zero point energy (ZPE) of several liquids and their mixtures. The 2PT method uses the density of states (DoS), which is computed from the velocity autocorrelation (VAC) function obtained from a short classical molecular dynamics trajectory. By partitioning the VAC and the DoS of a fluid into solid and gaslike components, quantum mechanical corrections to thermodynamical properties can be computed. The ZPE is obtained by combining the partition function of the quantum harmonic oscillator with the vibrational part of the solidlike DoS. The resulting ZPE is found to be in excellent agreement with both experimental and ab initio results. Solvent effects such as hydrogen bonding and polarization can be included by the utilization of ab initio density functional theory based molecular dynamics simulations. It is found that these effects significantly influence the DoS of water molecules. The obtained results demonstrate that the 2PT model is a powerful method for efficient ZPE calculations, in particular, to account for solvent effects and polarization.

Observation of the Low-Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces

Using the helium nanodroplet isolation setup at the ultrabright free-electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm^-1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in-plane and out-of-plane librational modes. This experimental data set provides a sensitive test for state-of-the-art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high-level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full-dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

Encapsulation of a Water Octamer Chain in a Chiral 2D Sheetlike Supramolecular Coordination Network Composed of Dinickel-Dicarboxylate Subunits

Four new chiral supramolecular coordination networks of Ni(II) of general formula [Ni₂(Hhissal)₂(dicarboxylate)(H₂O)₂]·nH₂O (where Hhissal = histidinesalicylate; dicarboxylate = adipate; n = 8 for 1, succinate; n = 4 for 2, maleate; n = 4 for 3, fumarate; and n = 6 for 4) are reported. On the basis of the single-crystal X-ray study, an unprecedented zig-zag chain structure of water octamer encapsulated in 1 has been identified. The supramolecular network of the dimetal subunits is formed through hydrogen bonding interactions between the amine N-H of Hhissal and the oxygen atom of the coordinated water molecule of one subunit with the uncoordinated oxygen atom and the coordinated oxygen atom of the carboxylate group of Hhissal of the next subunit, respectively. The strength of hydrogen bonding within this water cluster (the range of O···O distances is 2.702-2.760 Å) is similar to that found in ice. These networks are further characterized by elemental analysis, IR spectroscopy, powder X-ray diffraction, polarimetry, UV-vis/diffuse reflectance and circular dichroism spectroscopy, and thermogravimetric analysis. A comparison of their properties indicates that these are isostructural with a variation of encapsulated water clusters.

Correlation effects and many-body interactions in water clusters

Background: The quantum-chemical description of the interactions in water clusters is an essential basis for deriving accurate and physically sound models of the interaction potential for water to be used in molecular simulations. In particular, the role of many-body interactions beyond the two-body interactions, which are often not explicitly taken into account by empirical force fields, can be accurately described by quantum chemistry methods on an adequate level, e.g., random-phase approximation electron correlation methods. The relative magnitudes of the different interaction energy contributions obtained by accurate ab initio calculations can therefore provide useful insights that can be exploited to develop enhanced force field methods. Results: In line with earlier theoretical studies of the interactions in water clusters, it has been found that the main contribution to the many-body interactions in clusters with a size of up to N = 13 molecules are higher-order polarisation interaction terms. Compared to this, many-body dispersion interactions are practically negligible for all studied sytems. The two-body dispersion interaction, however, plays a significant role in the formation of the structures of the water clusters and their stability, since it leads to a distinct compression of the cluster sizes compared to the structures optimized on an uncorrelated level. Overall, the many-body interactions amount to about 13% of the total interaction energy, irrespective of the cluster size. The electron correlation contribution to these, however, amounts to only about 30% to the total many-body interactions for the largest clusters studied and is repulsive for all structures considered in this work. Conclusion: While this shows that three- and higher-body interactions can not be neglected in the description of water complexes, the electron correlation contributions to these are much smaller in comparison to the two-body electron correlation effects. Efficient quantum chemistry approaches for describing intermolecular interactions between water molecules may therefore describe higher-body interactions on an uncorrelated Hartree-Fock level without a serious loss in accuracy.

Size-Resolved Photoelectron Anisotropy of Gas Phase Water Clusters and Predictions for Liquid Water

We report the first measurements of size-resolved photoelectron angular distributions for the valence orbitals of neutral water clusters with up to 20 molecules. A systematic decrease of the photoelectron anisotropy is found for clusters with up to 5-6 molecules, and most remarkably, convergence of the anisotropy for larger clusters. We suggest the latter to be the result of a local short-range scattering potential that is fully described by a unit of 5-6 molecules. The cluster data and a detailed electron scattering model are used to predict the anisotropy of slow photoelectrons in liquid water. Reasonable agreement with experimental liquid jet data is found.

Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory

Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

Assessing the Performance of the Diffusion Monte Carlo Method As Applied to the Water Monomer, Dimer, and Hexamer

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 10(3)). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 10(5) walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

Molecular dynamics simulation of the cooperative effect by different force fields in monosodium glutamate aqueous solution

Different force fields (GROMOS and OPLS) in conjunction with different water (SPC, SPCE, TIP3P, TIP4P and TIP5P) were assessed using molecular dynamics simulations of monosodium glutamate (MSG) aqueous solution.

The use of many-body expansions and geometry optimizations in fragment-based methods

Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures.

Three-dimensional hydrogen-bonded assembly in 2,2′-disulfanylidene-5,5′-biimidazolidinylidene-4,4′-dione–dimethylformamide–water (3/2/4)

The title compound, 3C6H4N4O2S2·2C3H7NO·4H2O, comprises three 2,2′-disulfanylidene-5,5′-biimidazolidinylidene-4,4′-dione molecules, two dimethylformamide molecules and four water molecules arranged around a crystallographic inversion centre. The non-H atoms within the 5,5′-biimidazolidinylidene molecule are coplanar and these molecules aggregate through N—H...S hydrogen-bonding interactions with cyclic motifs [graph setR22(8)], giving two-dimensional ribbon structures which are close to being parallel. The two independent water molecules associate to form centrosymmetric cyclic hydrogen-bonded (H2O)4tetrameric units [graph setR44(8)]. The ribbon structures extend along theaaxis and are linked through the water tetramers and the dimethylformamide molecules by a combination of two- and three-centre hydrogen bonds, giving an overall three-dimensional structure.

Communication: determination of the bond dissociation energy (D0) of the water dimer, (H2O)2, by velocity map imaging

The bond dissociation energy (D(0)) of the water dimer is determined by using state-to-state vibrational predissociation measurements following excitation of the bound OH stretch fundamental of the donor unit of the dimer. Velocity map imaging and resonance-enhanced multiphoton ionization (REMPI) are used to determine pair-correlated product velocity and translational energy distributions. H(2)O fragments are detected in the ground vibrational (000) and the first excited bending (010) states by 2 + 1 REMPI via the C̃ (1)B(1) (000) ← X̃ (1)A(1) (000 and 010) transitions. The fragments' velocity and center-of-mass translational energy distributions are determined from images of selected rovibrational levels of H(2)O. An accurate value for D(0) is obtained by fitting both the structure in the images and the maximum velocity of the fragments. This value, D(0) = 1105 ± 10 cm(-1) (13.2 ± 0.12 kJ/mol), is in excellent agreement with the recent theoretical value of D(0) = 1103 ± 4 cm(-1) (13.2 ± 0.05 kJ∕mol) suggested as a benchmark by Shank et al. [J. Chem. Phys. 130, 144314 (2009)].

Quantum nature of the hydrogen bond

Hydrogen bonds are weak, generally intermolecular bonds, which hold much of soft matter together as well as the condensed phases of water, network liquids, and many ferroelectric crystals. The small mass of hydrogen means that they are inherently quantum mechanical in nature, and effects such as zero-point motion and tunneling must be considered, though all too often these effects are not considered. As a prominent example, a clear picture for the impact of quantum nuclear effects on the strength of hydrogen bonds and consequently the structure of hydrogen bonded systems is still absent. Here, we report ab initio path integral molecular dynamics studies on the quantum nature of the hydrogen bond. Through a systematic examination of a wide range of hydrogen bonded systems we show that quantum nuclear effects weaken weak hydrogen bonds but strengthen relatively strong ones. This simple correlation arises from a competition between anharmonic intermolecular bond bending and intramolecular bond stretching. A simple rule of thumb is provided that enables predictions to be made for hydrogen bonded materials in general with merely classical knowledge (such as hydrogen bond strength or hydrogen bond length). Our work rationalizes the influence of quantum nuclear effects, which can result in either weakening or strengthening of the hydrogen bonds, and the corresponding structures, across a broad range of hydrogen bonded materials. Furthermore, it highlights the need to allow flexible molecules when anharmonic potentials are used in force field-based studies of quantum nuclear effects.

A combined Raman- and infrared jet study of mixed methanol-water and ethanol-water clusters

The vibrational dynamics of vacuum-isolated hydrogen-bonded complexes between water and the two simplest alcohols is characterized at low temperatures by Raman and FTIR spectroscopy. Conformational preferences during adaptive aggregation, relative donor/acceptor strengths, weak secondary hydrogen bonding, tunneling processes in acceptor lone pair switching, and thermodynamic anomalies are elucidated. The ground state tunneling splitting of the methanol-water dimer is predicted to be larger than 2.5 cm(-1). Two types of alcohol-water trimers are identified from the spectra. It is shown that methanol and ethanol are better hydrogen bond donors than water, but even more so better hydrogen bond acceptors. As a consequence, hydrogen bond induced red shifts of OH modes behave non-linearly as a function of composition and the resulting cluster excess quantities correspond nicely to bulk excess enthalpies at room temperature. The effects of weak C-H···O hydrogen bonds are quantified in the case of mixed ethanol-water dimers.