Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with split Wigner pseudospectral approach. II. Improvements and tests of additional potentials

Mixed H2S and H2O Clusters─New Insights into Dispersion-Dominated Hydrogen Bonding

Here, we report the results of an IR spectroscopy study on heteroclusters of H2S and H2O and several of their isotopomers using mass-selective IR spectroscopy in superfluid helium nanodroplets in the range of 2560-2800 cm-1. Based on DFT calculations on the B3LYP-D3/6-311++G(d,p) level of theory, we were able to assign the experimentally observed O-D stretching bands to heterodimer and heterotrimer clusters. Since no bands of the S-H-bound conformer HSH···OH2 could be observed, we were able to determine the O-H-bound conformer HOH···SH2 to be the global minimum structure. A trapping of the local minima in helium nanodroplets was not observed. This is in line with the weaker hydrogen bond expected for H2S complexes. In these clusters, the interaction energy is expected to be more dominated by dispersion and less dictated by highly directional electrostatic forces.

On the nature of hydrogen bonding in the H2S dimer

Hydrogen bonding is a central concept in chemistry and biochemistry, and so it continues to attract intense study. Here, we examine hydrogen bonding in the H2S dimer, in comparison with the well-studied water dimer, in unprecedented detail. We record a mass-selected IR spectrum of the H2S dimer in superfluid helium nanodroplets. We are able to resolve a rotational substructure in each of the three distinct bands and, based on it, assign these to vibration-rotation-tunneling transitions of a single intramolecular vibration. With the use of high-level potential and dipole-moment surfaces we compute the vibration-rotation-tunneling dynamics and far-infrared spectrum with rigorous quantum methods. Intramolecular mode Vibrational Self-Consistent-Field and Configuration-Interaction calculations provide the frequencies and intensities of the four SH-stretch modes, with a focus on the most intense, the donor bound SH mode which yields the experimentally observed bands. We show that the intermolecular modes in the H2S dimer are substantially more delocalized and more strongly mixed than in the water dimer. The less directional nature of the hydrogen bonding can be quantified in terms of weaker electrostatic and more important dispersion interactions. The present study reconciles all previous spectroscopic data, and serves as a sensitive test for the potential and dipole-moment surfaces.

Ortho-para interconversion of nuclear states of H2O through replica transition state: prospect of quantum entanglement at homodromic Bjerrum defect site

CONTEXT

From a nuclear spin prospective, water exists as para and ortho nuclear spin isomers (isotopomers). Spin interconversions in isolated molecules of water are forbidden, but many recent reports have shown them to happen in bulk, through dynamic proton exchanges happening between interconnected networks of a large array of water molecules. In this contribution, a possible explanation for an unexpected slow or delayed interconversion of ortho-para water in ice observed in an earlier reported experiment is provided. Using the results of quantum mechanical investigations, we have discussed the roles played by Bjerrum defects in the dynamic proton exchanges and ortho-para spin state interconversions. We guess that at the sites of the Bjerrum defects, there are possibilities of quantum entanglements of states, through pairwise interactions. Based on the perfectly correlated exchange happening via a replica transition state, we speculate that it can have significant influences on ortho-para interconversions of water. We also conjecture that the overall ortho-para interconversion is not a continuous process, rather can be imagined to be happening serendipitously, but within the boundary of the rules of quantum mechanics.

METHODS

All computations were performed with Gaussian 09 program. B3LYP/6-31++G(d,p) methodology was used to compute all the stationary points. Further energy corrections were computed using CCSD(T)/aug-cc-pVTZ methodology. Intrinsic reaction coordinate (IRC) path computations were carried out for the transition states.

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.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T)

Previous studies have shown that the weakly bonded H₂S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H₂S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H₂S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H₂S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H₂S dimer.

Many-Body Effects Determine the Local Hydration Structure of Cs+ in Solution

A systematic analysis of the hydration structure of Cs⁺ ions in solution is derived from simulations carried out using a series of molecular models built upon a hierarchy of approximate representations of many-body effects in ion-water interactions. It is found that a pairwise-additive model, commonly used in biomolecular simulations, provides poor agreement with experimental X-ray spectra, indicating an incorrect description of the underlying hydration structure. Although the agreement with experiment improves in simulations with a polarizable model, the predicted hydration structure is found to lack the correct sequence of water shells. Progressive inclusion of explicit many-body effects in the representation of Cs⁺-water interactions as well as accounting for nuclear quantum effects is shown to be necessary for quantitatively reproducing the experimental X-ray spectra. Besides emphasizing the importance of many-body effects, these results suggest that molecular models rigorously derived from many-body expansions hold promise for realistic simulations of aqueous solutions.

Molecular dimers of methane clathrates: ab initio potential energy surfaces and variational vibrational states

Motivated by the energetic and environmental relevance of methane clathrates, highly accurate ab initio potential energy surfaces (PESs) have been developed for the three possible dimers of the methane and water molecules: (H₂O)₂, CH₄·H₂O, and (CH₄)₂.

Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism

The nature of the intermolecular forces between water molecules is the same in small hydrogen-bonded clusters as in the bulk. The rotational spectra of the clusters therefore give insight into the intermolecular forces present in liquid water and ice. The water hexamer is the smallest water cluster to support low-energy structures with branched three-dimensional hydrogen-bond networks, rather than cyclic two-dimensional topologies. Here we report measurements of splitting patterns in rotational transitions of the water hexamer prism, and we used quantum simulations to show that they result from geared and antigeared rotations of a pair of water molecules. Unlike previously reported tunneling motions in water clusters, the geared motion involves the concerted breaking of two hydrogen bonds. Similar types of motion may be feasible in interfacial and confined water.

Ab initio water pair potential with flexible monomers

A potential energy surface for the water dimer with explicit dependence on monomer coordinates is presented. The surface was fitted to a set of previously published interaction energies computed on a grid of over a quarter million points in the 12-dimensional configurational space using symmetry-adapted perturbation theory and coupled-cluster methods. The present fit removes small errors in published fits, and its accuracy is critically evaluated. The minimum and saddle-point structures of the potential surface were found to be very close to predictions from direct ab initio optimizations. The computed second virial coefficients agreed well with experimental values. At low temperatures, the effects of monomer flexibility in the virial coefficients were found to be much smaller than the quantum effects.

Predictions for water clusters from a first-principles two- and three-body force field

A new rigid-monomer three-body potential has been developed for water by fitting it to more than 70 thousand trimer interaction energies computed ab initio using coupled-cluster methods and augmented triple-zeta-quality basis sets. This potential was used together with a modified form of a previously developed two-body potential and with a polarization model of four- and higher-body interactions to predict the energetics of the water trimer, hexamer, and 24-mer. Despite using the rigid-monomer approximation, these predictions agree better with flexible-monomer benchmarks than published results obtained with flexible-monomer force fields. An unexpected finding of our work is that simple polarization models predict four-body interactions to within a few percent, whereas for three-body interactions these models are known to have errors on the order of 50%.

Spectra of water dimer from a new ab initio potential with flexible monomers

We report the definition and testing of a new ab initio 12-dimensional potential for the water dimer with flexible monomers. Using our recent accurate CCpol-8s rigid water pair potential [W. Cencek, K. Szalewicz, C. Leforestier, R. van Harrevelt, and A. van der Avoird, Phys. Chem. Chem. Phys. 10, 4716 (2008)] as a reference for the undistorted monomers' geometries, a distortion correction has been added, which was taken from a former flexible-monomer ab initio potential. This correction allows us to retrieve the correct binding energy D(e)=21.0 kJ mol(-1), and leads to an equilibrium geometry in close agreement with the one obtained from benchmark calculations. The kinetic energy operator describing the flexible-monomer water dimer has been expressed in terms of Radau coordinates for each monomer and a recent general cluster polyspherical formulation describing their relative motions. Within this formulation, an adiabatic scheme has been invoked in order to decouple fast (intramolecular) modes and slow (intermolecular) ones. Different levels of approximation were tested, which differ in the way in which the residual potential coupling between the intramolecular modes located on different monomers and the dependence of the monomer rotational constants on the dimer geometry are handled. Accurate calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2) were performed, which show the best agreement with experiments achieved so far for any water potential. Intramolecular excitations of the two monomers were calculated within two limiting cases, to account for the lack of non-adiabatic coupling between intramolecular modes due to the intermolecular motion. In the first model, the excitation was assumed to stay either on the donor or the acceptor molecule, and to hop between the two moieties upon donor-acceptor interchange. In the second model, the excitation remains on the same molecule whatever is the dimer geometry. Marginal frequency differences, less than 2 cm(-1), were obtained for all modes, and the resulting infrared shifts are in good agreement with experiments.

Infrared shifts of the water dimer from the fully flexible ab initio HBB2 potential

We report calculations of the infrared shifts for the water dimer, as obtained from the recent ab initio fully flexible HBB2 potential of Bowman and co-workers. The rovibrational calculations, which formally are 12-dimensional plus overall rotation, were performed within the [6+6]d adiabatic separation which decouples the 'fast' intramolecular modes from the 'slow' intermolecular ones. Apart from this decoupling, each set of modes is treated in a fully variational approach. The intramolecular motion was described in terms of Radau coordinates, using the f-embedding formulation of Wei & Carrington, and neglecting the rovibrational Coriolis coupling terms. Within this adiabatic approximation, the intermolecular motion is handled in a similar way as for rigid monomers, except for the rotational constants B's, averaged over intramolecular modes that depend now on the intermolecular geometry. Comparison with experimental data shows an excellent overall agreement.

Polarizable interaction potential for water from coupled cluster calculations. II. Applications to dimer spectra, virial coefficients, and simulations of liquid water

The six-dimensional CC-pol interaction potential for the water dimer was used to predict properties of the dimer and of liquid water, in the latter case after being supplemented by a nonadditive potential. All the results were obtained purely from first principles, i.e., without any fitting to experimental data. Calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2), a very sensitive test of the potential surface, gave results in good agreement with experimental high-resolution spectra. Also the virial coefficients and properties of liquid water agree well with measured values. The present model performs better than published force fields for water in a simultaneous reproduction of experimental data for dimer spectra, virials, and properties of the liquid.

Predictions of the Properties of Water from First Principles

A force field for water has been developed entirely from first principles, without any fitting to experimental data. It contains both pairwise and many-body interactions. This force field predicts the properties of the water dimer and of liquid water in excellent agreement with experiments, a previously elusive objective. Precise knowledge of the intermolecular interactions in water will facilitate a better understanding of this ubiquitous substance.

Can the pH value of water solutions be estimated by quantum chemical calculations of small water clusters?

In the study, various water clusters were explored from the point of view of the proton transfer between H-bonded neighbors. A relatively modest approach--the MP26-31++G(d,p) level--was chosen as acceptable considering the fact that also larger systems have to be included. The tight ion-pair model (with usually three fixed O-O distances) was adopted for the autodissociation process. First, cluster-estimated pH values rapidly decrease as cluster size increases from 2 to 6. For larger clusters in gas phase, the topology of H bonds plays an important role, varying pH from 7 to 13 in hexamers and from 5 to 15 in octamer clusters. The relationship energy/distance was quantified, too. Enhancing our model with the conductorlike screening model (COSMO) approach brought significant improvement in description of the autodissociation reaction with a stable zwitterionic structure. However, when the O-O restrictions were released, the small barrier for backward reaction disappeared, reforming neutral cluster spontaneously. Also Boltzmann weighting procedure was applied, and for the explored clusters in vacuo, the series of pH 25-18-14-13-10 was obtained for cluster sizes n=2, 3, 4, 6, 8. Using the COSMO approach, the analogous series is 15-14-12-10-9. The limit of the series is still about two to three units above the experimentally known pH. In order to reach the size-independent (bulk) value, larger clusters are needed. However, the situation is far from hopeless since (as it was proven in the study) four-coordinated molecules are not involved in the proton transfer process directly; they can only be a part of the surrounding environment.

Interaction potential for water dimer from symmetry-adapted perturbation theory based on density functional description of monomers

A new six-dimensional interaction potential for the water dimer has been obtained by fitting interaction energies computed at 2510 geometries using a variant of symmetry-adapted perturbation theory (SAPT) based on density functional theory (DFT) description of monomers, referred to as SAPT(DFT). The stationary points, second virial coefficient, vibration-rotation-tunneling spectrum, and structure of liquid water computed with the new potential are in very good agreement with experiment and advanced ab initio calculations, confirming the high level of accuracy provided by SAPT(DFT).

Molecular complexes in close and far away

In this review, gas-phase chemistry of interstellar media and some planetary atmospheres is extended to include molecular complexes. Although the composition, density, and temperature of the environments discussed are very different, molecular complexes have recently been considered as potential contributors to chemistry. The complexes reviewed include strongly bound aggregates of molecules with ions, intermediate-strength hydrogen bonded complexes (primarily hydrates), and weakly bonded van der Waals molecules. In low-density, low-temperature environments characteristic of giant molecular clouds, molecular synthesis, known to involve gas-phase ion-molecule reactions and chemistry at the surface of dust and ice grains is extended here to involve molecular ionic clusters. At the high density and high temperatures found on planetary atmospheres, molecular complexes contribute to both atmospheric chemistry and climate. Using the observational, laboratory, and theoretical database, the role of molecular complexes in close and far away is discussed.

Water Dimers in the Atmosphere III: Equilibrium Constant from a Flexible Potential

We present new results for the water dimer equilibrium constant K(p)(T) in the range 190-390 K, using a flexible potential energy surface fitted to spectroscopical data. The increased numerical complexity due to explicit consideration of the monomer vibrations is handled via an adiabatic (6 + 6)d decoupling between intra- and intermolecular modes. The convergence of the canonical partition function of the dimer is ensured by computing all energy levels up to dissociation for total angular momentum values J = 0-5 and using an extrapolation scheme to higher values. The newly calculated values for K(p)(T) are in very good agreement with available experimental data at room temperature. At higher temperatures, an analysis of the convergence of the partition function reveals that quasi-bound states are likely to contribute to the equilibrium constant. Additional thermodynamical quantities (deltaG, deltaH, deltaS, and C(p)) have also been determined and fit to quadratic expressions a + bT + cT2.

The World of Non-Covalent Interactions: 2006

The review focusses on the fundamental importance of non-covalent interactions in nature by illustrating specific examples from chemistry, physics and the biosciences. Laser spectroscopic methods and both ab initio and molecular modelling procedures used for the study of non-covalent interactions in molecular clusters are briefly outlined. The role of structure and geometry, stabilization energy, potential and free energy surfaces for molecular clusters is extensively discussed in the light of the most advanced ab initio computational results for the CCSD(T) method, extrapolated to the CBS limit. The most important types of non-covalent complexes are classified and several small and medium size non-covalent systems, including H-bonded and improper H-bonded complexes, nucleic acid base pairs, and peptides and proteins are discussed with some detail. Finally, we evaluate the interpretation of experimental results in comparison with state of the art theoretical models: this is illustrated for phenol...Ar, the benzene dimer and nucleic acid base pairs. A review with 270 references.

High-Resolution Electronic Spectrum of the p-Difluorobenzene−Water Complex: Structure and Internal Rotation Dynamics

The rotationally resolved S(1) <-- S(0) electronic spectrum of the water complex of p-difluorobenzene (pDFB) has been observed in the collision-free environment of a molecular beam. Analyses of these data show that water forms a planar sigma-bonded complex with pDFB via two points of attachment, a stronger F---H-O hydrogen bond and weaker H---O-H hydrogen bond, involving an ortho hydrogen atom of the ring. Despite the apparent rigidity of this structure, the water molecule also is observed to move within the complex, leading to a splitting of the spectrum into two tunneling subbands. Analyses of these data show that this motion is a combined inversion-internal rotation of the attached water, analogous to the "acceptor-switching" motion in the water dimer. The barriers to this motion are significantly different in the two electronic states owing to changes in the relative strengths of the two hydrogen bonds that hold the complex together.

The isomers of HF–HCN formed in helium nanodroplets: Infrared spectroscopy and ab initio calculations

Binary complexes containing hydrogen cyanide and hydrogen fluoride are formed in helium nanodroplets, and studied using high-resolution infrared laser spectroscopy. Rotationally resolved spectra are reported for the H-F and C-H stretches of the linear HCN-HF complex, a system that has been thoroughly studied in the gas phase. We report the high-resolution spectra of the higher energy, bent HF-HCN isomer, which is also formed in helium. Stark spectra are reported for both isomers, providing dipole moments of these complexes. The experimental results are compared with ab initio calculations, also reported here. Spectra are reported for several ternary complexes, including (HCN)2-HF, HCN-(HF)2, HF-(HCN)2, and HF-HCN-HF.

Rovibrational and dynamical properties of the hydrogen bonded complex (CH2)2S-HF: A combined free jet, cell, and neon matrix-Fourier transform infrared study

Fourier transform infrared spectra of the nu(s) (HF stretching) band of the (CH(2))(2)S-HF complex have been recorded at 0.1-0.5 cm(-1) resolution in a cooled cell, in a supersonic jet expansion seeded with argon and in a neon matrix at 4.5 K. The combination of controlled temperature effects over a range of 40-250 K and a sophisticated band contour simulation program allows the separation of homogeneous and inhomogeneous contributions and reveals significant anharmonic couplings between intramolecular and intermolecular vibrational modes similar to our previous work on (CH(2))(2)S-DF. The sign of the coupling constants is consistent with the expected strengthening of the hydrogen bond upon vibrational excitation of HF which also explains the observed small variations of the geometrical parameters in the excited state. The analysis of sum and difference combination bands involving nu(s) provides accurate values of intermolecular harmonic frequencies and anharmonicities and a good estimate of the dissociation energy of the complex. Frequencies and coupling parameters derived from gas phase spectra compare well with results from neon matrix experiments. The effective linewidth provides a lower bound for the predissociation lifetime of 10 ps. The comparison between effective linewidths and vibrational densities of states for (CH(2))(2)S-HF and -DF complexes highlights the important role of intramolecular vibrational redistribution in the vibrational dynamics of medium strength hydrogen bonds.

Six-dimensional vibrational analysis of coupled intermolecular vibrations in a binary cluster

We report on full- (six-) dimensional calculations of the intermolecular vibrations of a binary aromatic-solvent cluster. An exact Hamiltonian for this kind of interaction is modified in a general manner in order to perform calculations of molecules without symmetry. The binary cluster phenol(H2O)1 is used as a test case since its intermolecular vibrations are anharmonic and highly coupled. The formulation of the Schrodinger equation leads to a complex-valued eigenvalue problem with a dimension larger than two million, which is solved by filter diagonalization to obtain both eigenvalues and eigenvectors. With the knowledge of the eigenvectors, an interpretation of all eigenvalues is possible by a characterization with pseudoquantum numbers that are related to the widely used nomenclature of intermolecular normal motions in aromatic(solvent) clusters.

An ab initio study of tunneling splittings in the water dimer

Tunneling splittings in the water dimer have been determined by the semiclassical WKB method, based on pathways characterized at the computational level of second-order Møller-Plesset (MP2) theory with basis sets of aug-cc-pVTZ quality. This calculation takes into account all three acceptor tunneling, donor-acceptor interchange, and bifurcation tunneling rearrangements of the water dimer. The tunneling splittings were evaluated as 7.73 cm(-1) (large splitting) and 0.42 cm(-1) (small splitting), which are in good agreement with the corresponding experimental values of 11.18 cm(-1) and 0.70 cm(-1), respectively.

Vibrational dynamics of medium strength hydrogen bonds: Fourier transform infrared spectra and band contour analysis of the DF stretching region of (CH[sub 2])[sub 2]S–DF

Fourier transform infrared spectra of the nu(s) band of the (CH2)(2)S-DF complex have been recorded at 0.1-0.5 cm(-1) resolution in a cooled cell and in a supersonic jet expansion seeded with argon. A sufficient density of (CH(2))(2)S-DF heterodimers is produced by a double injection nozzle device, which limits the possibility of reaction between thiirane and DF before the expansion. The observation of partially resolved PQR branch structures at cell temperatures as high as 252 K indicates relatively small effective line widths, which allow a detailed analysis of the underlying vibrational couplings and of the structural properties of the complex. The analysis of cell and free jet spectra in the temperature range 50-250 K is performed with a software package for the simulation and fitting of multiple hot band progressions in asymmetric rotors. The analysis reveals that the three low frequency hydrogen-bond modes are strongly coupled to the DF stretch with anharmonic coupling constants, which indicates a strengthening of the hydrogen bond upon vibrational excitation of DF. Rovibrational parameters and a reliable upper bound for the homogeneous line width have been extracted.