Beyond Badger's Rule: The Origins and Generality of the Structure-Spectra Relationship of Aqueous Hydrogen Bonds

Correlations between the Structures and Spectra of Protonated Water Clusters

Badger's rule-like correlations between OH stretching frequencies and intensities and the OH bond length are used to develop a spectral mapping procedure for studies of pure and protonated water clusters. This approach utilizes the vibrationally averaged OH bond lengths, which were obtained from diffusion Monte Carlo simulations that were performed using the general potential developed by Yu and Bowman. Good agreement is achieved between the spectra obtained using this approach and previously reported spectra for H+(H2O)n clusters, with n = 3, 4, and 5, as well as their perdeuterated analogues. The analysis of the spectra obtained by this spectral mapping approach supports previous work that assigned the spectrum of H+(H2O)6 to a mixture of Eigen and Zundel-like structures. Analysis of the calculated spectra also suggests a reassignment of the frequency of one of the transitions that involves the OH stretching vibration of the OH bonds in the hydronium core in the Eigen-like structure of H+(H2O)6 from 1917 cm-1 to roughly 2100 cm-1. For D+(D2O)6, comparison of the measured spectrum to those obtained by using the spectral mapping approach suggests that the carrier of the measured spectrum is one or more of the isomers of D+(D2O)6 that contain a four-membered ring and two flanking water molecules. While there are several candidate structures, the two flanking water molecules most likely form a chain that is bound to the hydronium core.

Descriptors of water aggregation

We rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (rOH) and HOH bond angle (θHOH), (ii) two-body: OO distance (rOO), OHO angle (θOHO), and HOOX dihedral angle (ϕHOOX), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θOOO), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (qm, m = 2, 3, 4, 5) and radius of gyration (Rg). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H2O)n, n = 3-25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that rOH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.

Predicting the Raman Spectra of Liquid Water with a Monomer-Field Model

The Raman spectrum of liquid water is quite complex, reflecting its strong sensitivity to the local environment of the individual waters. The OH-stretch region of the spectrum, which captures the influence of hydrogen bonding, has only just begun to be unraveled. Here we develop a model for predicting the Raman spectra of the OH-stretch region by considering how local electric fields distort the energy surface of each water monomer. We find that our model is capable of reproducing the bimodal nature of the main peak, with the shoulder at 3250 cm-1 resulting almost entirely from Fermi resonance. Furthermore, we capture the temperature and polarization dependence of the shoulder, which has proven to be difficult to obtain with previous methods, and analyze the origin of this dependence. We expect our model to be generally useful for understanding and predicting how Raman spectra change under different conditions and with different probe reporters beyond water.

Relation Between Bond Angle and Carbon-Oxygen Stretching Frequencies in CO2-Containing Compounds

The symmetric (νs) and antisymmetric (νas) O-C-O stretching modes of CO2-containing compounds encode structural information that can be difficult to decipher, due to the sensitivity of these spectral features to small shifts in charge distribution and structure, as well as the anharmonicities of these two vibrational modes. In this work, we discuss the relation between the frequency of these modes and the geometry of the O-C-O group, showing that the splitting between νs and νas (Δνas-s = νas - νs) can be predicted based only on the O-C-O bond angle obtained from quantum chemical calculations with reasonable accuracy (±46 cm-1, R2 = 0.994). The relationship is shown to hold for the infrared spectra of a variety of CO2-containing molecules measured in vacuo. The origins of this model are discussed in the framework of elementary mode analysis.

Experimental confirmation of the Badger-Bauer rule in the protonated methanol clusters: weak hydrogen bond formation as a measure of terminal OH acidity in hydrogen bond networks

We report a linear correlation between the OH stretch frequency shift of the protonated methanol cluster, H+(MeOH)n, upon the π-hydrogen bond formation with benzene and the enthalpy change in clustering of H+(MeOH)n to H+(MeOH)n+1. This result suggests a new method to explore hydrogen bond strength in hydrogen bond networks.

Synchronous Switching of Dielectric Constant and Photoluminescence in Cyanidonitridorhenate-Based Crystals

Switching of multiple physical properties by external stimuli in dynamic materials enables applications in, e.g., smart sensors, biomedical tools, as well as data-storage devices. Among stimuli-responsive materials, inorganic-organic molecular hybrids exhibiting thermal order-disorder phase transitions were tested as promising molecular switches of electrical characteristics, including dielectric constant. We aimed at broadening the multifunctional potential of such hybrid materials towards the switching of not only electrical but also other physical properties, e.g., light emission. We report two ionic salts based on luminescent tetracyanidonitridorhenate(V) anions bearing two different diamine ligands, 1,2-diaminoethane (1) and 1,3-diaminopropane (2), both crystallizing with polar N-methyl-dabconium cations. They exhibit an order-disorder phase transition related to the heating-induced turning-on of the rotation of polar cations. This leads to a unique synchronous switching of the dielectric constant as well as metal-complex-centered photoluminescence, as demonstrated by changes in, e.g., emission lifetime. The roles of organic cations, non-trivial Re(V) complexes, and their interaction in achieving the coupled thermal switching of electrical and optical properties are discussed utilizing experimental and theoretical approaches.

Direct Determination of the Relationship between the Intramolecular Oxygen-Hydrogen Bond Length and Its Stretching Vibrational Frequency of the Methanol Molecule in the Liquid State

Time-of-flight (TOF) neutron diffraction measurements on pure liquid deuterated methanol and concentrated methanolic LiClO4 and LiTFSA solutions have been carried out to investigate the effect of intermolecular hydrogen bonds on the intramolecular O-D distance (rOD) of the methanol molecule in the liquid state. Intramolecular parameters for the methanol molecule are determined by the least-squares fitting analysis of the neutron total interference term observed in the high-Q region. Attenuated total reflection (ATR) IR spectra have been measured for methanolic solutions of natural abundance to determine the gravitational center frequency (νOH) of the stretching vibrational band of the methanol molecule. The relationship between rOD and νOH is approximated well by a linear function. The value dνOH/drOD = -17000 ± 3000 cm-1 Å-1 has been derived from the slope of the fitted function. It has been revealed that the O-D bond length of the methanol molecule is sensitively affected by the intermolecular hydrogen bonding interaction.

Fragments-in-fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters

The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Frags-in-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R²  = 0.9975 of 348 data points). The difference being less than 0.5 kcal/mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.

Ion/Water Network Structural Dynamics in Highly Concentrated Lithium Chloride and Lithium Bromide Solutions Probed with Ultrafast Infrared Spectroscopy

The structural dynamics of highly concentrated LiCl and LiBr aqueous solutions were observed from 1-4 to 1-16 water molecules per ion pair using ultrafast polarization-selective pump-probe (PSPP) experiments on the OD stretch of dilute HOD. At these high salt concentrations, an extended ion/water network exists with complex structural dynamics. Population decays from PSPP experiments highlight two distinct water components. From the frequency-dependent amplitudes of the decays, the spectra of hydroxyls bound to halides and to water oxygens are obtained, which are not observable in the FT-IR spectra. PSPP experiments also measure frequency-dependent water orientational relaxation. At short times, wobbling dynamics within a restricted angular cone occurs. At high concentrations, the cone angles are dependent on frequency (hydrogen bond strength), but at higher water concentrations (>10 waters per ion pair), there is no frequency dependence. The average cone angle increases as the ion concentration decreases. The slow time constant for complete HOD orientational relaxation is independent of concentration but slower in LiCl than in LiBr. Comparison to structural MD simulations of LiCl from the literature indicates that the loss of the cone angle wavelength dependence and the increase in the cone angles as the concentration decreases occur as the prevalence of large ion/water clusters gives way to contact ion pairs.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D_e's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D_e's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

Stereochemistry Controls Dihydrogen Bonding Strengths in Chiral Amine Boranes Adducts

The growing interest in exploiting novel concepts of non-covalent interactions in catalysts and supramolecular chemistry made us revisit a special kind of hydrogen bonding: the dihydrogen bond (DHB), formed between a classical hydrogen bond donor and a hydridic hydrogen as acceptor. Herein, we investigate how the strength of the N-H^δ+ ⋅⋅⋅^δ- H-B interaction and hence the DHB-driven self-aggregation of amine-borane adducts is governed by steric effects by comparing the structures and binding enthalpies of various chiral derivatives. For a diastereomeric pair of amine-boranes prepared from a chiral secondary amine, we show that the stereochemistry at the nitrogen has significant influence on the interaction enthalpy. Based on this finding, N-chiral amine boranes can be envisioned to become interesting building blocks in supramolecular chemistry to fine-tune the formation dynamics of assemblies.

Thermally-Activated Tunneling in the Two-Water Bridge Catalyzed Tautomerization of Phosphinylidene Compounds

Phosphinylidenes are an important class of organophosphorus compounds that can exhibit tautomerization between tricoordinated P(III) hydroxide (R1 R2 POH) and a pentacoordinated P(V) oxide (R1 R2 P(O)H) form. Herein we show, using the canonical variational transition state theory combined with multidimensional small-curvature tunneling approximation, the dominance of proton tunneling in the two-water-bridged tautomerizations of phosphinous acid and model phosphinylidenes comprising phosphosphinates, H-phosphonates, H-phosphinates and secondary phosphine oxides. Based on the studied system, the contribution of thermally-activated tunneling is predicted to speed up the semiclassical reaction rate by ca. threefold to as large as two orders of magnitude at 298.15 K in the gas phase. The large KIE and the concavity in the Arrhenius plots are further fingerprints of tunneling. The simulations also predicted that the rapid tunneling rate and short half-life span for the forward reaction, as opposed to the reverse reaction in fluorinated secondary phosphine oxides, would result in P(V) being elusive and only P(III) being isolable, which agrees with previous experiments where only P(III) was detected by IR and NMR spectroscopy. We also explored the role of solvent and predicted tunneling to be substantial.

The coupling of the hydrated proton to its first solvation shell

The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

Character of the OH Bend-Stretch Combination Band in the Vibrational Spectra of the "Magic" Number H3O+(H2O)20 and D3O+(D2O)20 Cluster Ions

The fundamental transitions that contribute to the diffuse OH stretching spectrum of water are known to increase in width and intensity with increasing red shift from the free OH frequency. In contrast, the profile of the higher-energy combination band involving the OH stretching and the intramolecular HOH bending modes displays a qualitatively different spectral shape with a much faster falloff on the lower-energy side. We elucidate the molecular origin of this difference by analyzing the shapes of the combination bands in the IR spectra of cryogenically cooled H₃O⁺(H₂O)₂₀ and D₃O⁺(D₂O)₂₀ clusters. The difference in the shapes of the bands is traced to differences in the dependence of their transition dipole matrix elements on the hydrogen-bonding environment. The fact that individual transitions across the combination band envelope have similar intensities makes it a useful way to determine the participation of various sites in extended H-bonding networks.

Rapid Water Dynamics Structures the OH-Stretching Spectra of Solitary Water in Ionic Liquids and Dipolar Solvents

In a recent study [ J. Phys. Chem. B 126, 4584 (2022)] we used infrared spectroscopy to investigate the solvation and dynamics of solitary water in ionic liquids and dipolar solvents. Complex shapes observed for water OH-stretching bands common to all high-polarity solvents were assigned to water in several solvation states. In the present study, classical molecular dynamics simulations of a single water molecule in four ionic liquids and three dipolar solvents were used to test and refine this interpretation. Consistent with past assignments, simulations show solitary water usually donates two hydrogen bonds to distinct solvent molecules. Such symmetrically solvated water produces the primary pair of peaks identified in the OH spectra of water in nearly all solvents. We had further proposed that additional features flanking this main peak are due to asymmetric solvation states, states in which only one OH group makes a hydrogen bond to solvent. Such states were found in significant concentrations in all of the systems simulated. Simulations of the OH stretching spectra using a semiclassical description and the vibrational map developed by Auer and Skinner [ J. Chem. Phys. 128, 224511 (2008)] provided semi-quantitative agreement with experiment. Analysis of species-specific spectra also confirmed assignment of the additional features in the experimental spectra to asymmetrically solvated water. The simulations also showed that rapid water motions cause a marked motional narrowing compared to the inhomogeneous limit, and that this narrowing is largely responsible for making the additional features due to minority solvation states manifest in the spectra.

High-Density “Windowpane” Coordination Patterns of Water Clusters and Their NBO/NRT Characterization

Cluster mixture models for liquid water at higher pressures suggest the need for water clusters of higher coordination and density than those commonly based on tetrahedral H-bonding motifs. We show here how proton-ordered water clusters of increased coordination and density can assemble from a starting cyclic tetramer or twisted bicyclic (Möbius-like) heptamer to form extended Aufbau sequences of stable two-, three-, and four-coordinate “windowpane” motifs. Such windowpane clusters exhibit sharply reduced (~90°) bond angles that differ appreciably from the tetrahedral angles of idealized crystalline ice I_h. Computed free energy and natural resonance theory (NRT) bond orders provide quantitative descriptors for the relative stabilities of clusters and strengths of individual coordinative linkages. The unity and consistency of NRT description is demonstrated to extend from familiar supra-integer bonds of the molecular regime to the near-zero bond orders of the weakest linkages in the present H-bond clusters. Our results serve to confirm that H-bonding exemplifies resonance–covalent (fractional) bonding in the sub-integer range and to further discount the dichotomous conceptions of “electrostatics” for intermolecular bonding vs. “covalency” for intramolecular bonding that still pervade much of freshman-level pedagogy and force-field methodology.

Vibrational Signatures of HNO3 Acidity When Complexed with Microhydrated Alkali Metal Ions, M+·(HNO3)(H2O)n=5 (M = Li, K, Na, Rb, Cs), at 20 K

The speciation of strong acids like HNO₃ under conditions of restricted hydration is an important factor in the rates of chemical reactions at the air-water interface. Here, we explore the trade-offs at play when HNO₃ is attached to alkali ions (Li⁺-Cs⁺) with four water molecules in their primary hydration shells. This is achieved by analyzing the vibrational spectra of the M⁺·(HNO₃)(H₂O)₅ clusters cooled to about 20 K in a cryogenic photofragmentation mass spectrometer. The local acidity of the acidic OH group is estimated by the extent of the red shift in its stretching frequency when attached to a single water molecule. The persistence of this local structural motif (HNO₃-H₂O) in all of these alkali metal clusters enables us to determine the competition between the effect of the direct complexation of the acid with the cation, which acts to enhance acidity, and the role of the water network in the first hydration shell around the ions, which acts to counter (screen) the intrinsic effect of the ion. Analysis of the vibrational features associated with the acid molecule, as well as those of the water network, reveals how cooperative interactions in the microhydration regime conspire to effectively offset the intrinsic enhancement of HNO₃ acidity afforded by attachment to the smaller cations.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

Capturing Individual Hydrogen Bond Strengths in Ices via Periodic Local Vibrational Mode Theory: Beyond the Lattice Energy Picture

Local stretching force constants derived from periodic local vibrational modes at the vdW-DF2 density functional level have been employed to quantify the intrinsic hydrogen bond strength of 16 ice polymorphs, ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI, XII, XIII, XIV, XV, XVII, and XIX, that are stable under ambient to elevated pressures. Based on this characterization on 1820 hydrogen bonds, relationships between local stretching force constants and structural parameters such as hydrogen bond length and angle were identified. Moreover, different bond strength distributions, from uniform to inhomogeneous, were observed for the 16 ices and could be explained in relation to different local structural elements within ices, that is, rings, that consist of different hydrogen bond types. In addition, criteria for the classification of hydrogen bonds as strong, intermediate, and weak were introduced. The latter was used to explore a different dimension of the water-ice phase diagram. These findings will provide important guidelines for assessing the credibility of new ice structures.

Experimental Determination of Relationship between Intramolecular O-D Bond Length and Its Stretching Vibrational Frequency of D2O Molecule in the Liquid State

Experimental evidence has been obtained for the structure-spectra relationship of hydrogen bonds in aqueous solutions. Intramolecular O-D distance, r_OD, has been determined by the least-squares fitting analysis of the neutron interference term in the high-Q region observed for pure D₂O and concentrated aqueous solutions. The average O-D stretching frequency, ν_OD, has been obtained from the position of the center of gravity of the observed ATR-IR O-D stretching band. The linear relationship between r_OD and ν_OD has been confirmed in the liquid state. The slope of dν_OD/dr_OD is evaluated to be -21 000 ± 1000 cm^-1 Å^-1.

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4. J Phys Chem A 2021;125:7185-7197. [PMID: 34433268 DOI: 10.1021/acs.jpca.1c05025]

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

Pauling's Conceptions of Hybridization and Resonance in Modern Quantum Chemistry

We employ the tools of natural bond orbital (NBO) and natural resonance theory (NRT) analysis to demonstrate the robustness, consistency, and accuracy with which Linus Pauling's qualitative conceptions of directional hybridization and resonance delocalization are manifested in all known variants of modern computational quantum chemistry methodology.

Isomer-Specific Vibrational Spectroscopy of Microhydrated Lithium Dichloride Anions: Spectral Fingerprint of Solvent-Shared Ion Pairs

The vibrational spectroscopy of lithium dichloride anions microhydrated with one to three water molecules, [LiCl2 (H2 O)1-3 ]- , is studied in the OH stretching region (3800-2800 cm-1 ) using isomer-specific IR/IR double-resonance population labelling experiments. The spectroscopic fingerprints of individual isomers can only be unambiguously assigned after anharmonic effects are considered, but then yield molecular level insight into the onset of salt dissolution in these gas phase model systems. Based on the extent of the observed frequency shifts ΔνOH of the hydrogen-bonded OH stretching oscillators solvent-shared ion pair motifs (<3200 cm-1 ) can be distinguished from intact-core structures (>3200 cm-1 ). The characteristic fingerprint of a water molecule trapped directly in-between two ions of opposite charge provides an alternative route to evaluate the extent of ion pairing in aqueous electrolyte solutions.

Demystifying the Diffuse Vibrational Spectrum of Aqueous Protons Through Cold Cluster Spectroscopy

The ease with which the pH is routinely determined for aqueous solutions masks the fact that the cationic product of Arrhenius acid dissolution, the hydrated proton, or H⁺(aq), is a remarkably complex species. Here, we review how results obtained over the past 30 years in the study of H⁺⋅(H₂O)_n cluster ions isolated in the gas phase shed light on the chemical nature of H⁺(aq). This effort has also revealed molecular-level aspects of the Grotthuss relay mechanism for positive-charge translocation in water. Recently developed methods involving cryogenic cooling in radiofrequency ion traps and the application of two-color, infrared-infrared (IR-IR) double-resonance spectroscopy have established a clear picture of how local hydrogen-bond topology drives the diverse spectral signatures of the excess proton. This information now enables a new generation of cluster studies designed to unravel the microscopic mechanics underlying the ultrafast relaxation dynamics displayed by H⁺(aq).

Role of Intermolecular Charge Fluxes in the Hydrogen-Bond-Induced Frequency Shifts of the OH Stretching Mode of Water

The relation between the vibrational properties and the electrostatic situations of the vibrating functional group is useful to predict vibrational spectroscopic features based on, for example, classical molecular dynamics of liquids or biomolecular systems, but to pursue its generality or the extent of applicability, it is required to understand the mechanisms giving rise to it. Here such an analysis is carried out for the OH stretching mode of water. By examining the correlations among various (structural, vibrational, and electrostatic) properties and by analyzing the spatial characteristics of the behavior of electrons occurring upon the vibration, it is shown that the dependence of the vibrational frequency and the dipole derivative of the OH stretching mode on the electric field is not of purely electrostatic origin, and the delocalized electronic motions occurring with this mode, called intermolecular charge fluxes, related to both the dipole first and second derivatives play important roles.

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide-water complexes X^-(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^-(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C_2v-symmetric saddle point, with a tunneling barrier height that is <2 kcal/mol except in the case of F^-(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (<2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^-(H₂O) and provides a driving force for the formation of quasi-linear X··· H-O hydrogen bonds. Charge-transfer energies correlate well with measured O-H vibrational redshifts for the halide-water complexes and also for OH^-(H₂O) and NO₂^-(H₂O), providing some indication of a general mechanism.

Cryogenic ion trap vibrational spectroscopy of the microhydrated sulfate dianions SO42-(H2O)3-8

Infrared photodissociation spectra of the D2-tagged microhydrated sulfate dianions with three to eight water molecules are presented over a broad spectral range that covers the OH stretching and H2O bending modes of the solvent molecules at higher energies, the sulfate stretching modes of the solute at intermediate energies and the intermolecular solute librational modes at the lowest energies. A low ion temperature combined with messenger-tagging ensures well-resolved vibrational spectra that allow for structure assignments based on a comparison to harmonic and anharmonic IR spectra from density functional theory (DFT) calculations. DFT ab initio molecular dynamics simulations are required to disentangle the broad and complex spectral signatures of microhydrated sulfate dianions in the OH stretching region and to identify systematic trends in the correlation of the strength and evolution of the solute-solvent and solvent-solvent interactions with cluster size. The onset for the formation of the second solvation shell is observed for n = 8.

Molecular designs for expanding the limits of ultralong C-C bonds and ultrashort HH non-bonded contacts

Recent experiments have reported the formation of very long C-C bonds (d_C-C > 1.80 Å) and very short HH non-bonded contacts (d_HH < 1.5 Å) in several sets of molecules. Both these rare phenomena arise due to specific donor-acceptor interactions and London dispersion interactions respectively. Favorable negative hyperconjugation, namely H₂N(lone-pair) →σ*(C-C), creates an ultralong C-C bond in diamino-o-carborane with d_C-C > 1.829 Å and a planar amine reminiscent of a transition-state like structure for ammonia inversion. The small and narrow barrier favours rapid inversion through quantum mechanical tunnelling (QMT) and produces a translationally averaged planar amine as observed in the experiments. On the other hand, designing specific confined molecular cavities or chambers like in,in-bis(hydrosilane) or its germanane analogs furnishes an ultrashort HH distance = 1.47 Å and 1.38 Å respectively. The predisposition of such closely placed HH contacts arises from the rather effective attractive dispersion interactions between them. Controlling the strength of the dispersion interactions provides a rich landscape for realizing such close HH distances. Molecular design ably assisted by computational modeling to further tune these interactions provides new avenues to break the glass-ceilings of ultralong C-C bonds or ultrashort HH contacts. Dispersion-corrected DFT calculations and ab initio molecular dynamics simulations generate a large library of such unique features in a diverse class of molecules. This feature article highlights the design principles to realize hitherto longest C-C bonds/shortest HH contacts.

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

Unusually strong hydrogen bond cooperativity in particular (H2O)20 clusters

Drawing upon an intuitive charge-transfer-based picture of hydrogen bonding, we demonstrate that cooperativity effects acting in concert can lead to unusually strong hydrogen bonds in neutral water clusters. The structure, vibrational, and NMR properties of a (H2O)20 pentagonal dodecahedron cluster containing such a strong hydrogen bond were studied using second-order perturbation theory and density functional theory. The hydrogen bond length was found to be shorter than 2.50 Å. A large redshift of over 2000 cm-1 with respect to the isolated water molecule was predicted for the OH stretching frequency of the donor water molecule. A large downfield shift to 13.5 ppm of the isotropic part of the 1H magnetic shielding tensor together with an unusually large shielding anisotropy of 49.9 ppm was obtained. The hydrogen bond energy was calculated using symmetry-adapted perturbation theory and was found to be more than three times stronger than a typical hydrogen bond in liquid water.

In Situ Assessment of Intrinsic Strength of X-I⋯OA-Type Halogen Bonds in Molecular Crystals with Periodic Local Vibrational Mode Theory

Periodic local vibrational modes were calculated with the rev-vdW-DF2 density functional to quantify the intrinsic strength of the X-I⋯OA-type halogen bonding (X = I or Cl; OA: carbonyl, ether and N-oxide groups) in 32 model systems originating from 20 molecular crystals. We found that the halogen bonding between the donor dihalogen X-I and the wide collection of acceptor molecules OA features considerable variations of the local stretching force constants (0.1–0.8 mdyn/Å) for I⋯O halogen bonds, demonstrating its powerful tunability in bond strength. Strong correlations between bond length and local stretching force constant were observed in crystals for both the donor X-I bonds and I⋯O halogen bonds, extending for the first time the generalized Badger’s rule to crystals. It is demonstrated that the halogen atom X controlling the electrostatic attraction between the σ-hole on atom I and the acceptor atom O dominates the intrinsic strength of I⋯O halogen bonds. Different oxygen-containing acceptor molecules OA and even subtle changes induced by substituents can tweak the n→σ∗(X-I) charge transfer character, which is the second important factor determining the I⋯O bond strength. In addition, the presence of the second halogen bond with atom X of the donor X-I bond in crystals can substantially weaken the target I⋯O halogen bond. In summary, this study performing the in situ measurement of halogen bonding strength in crystalline structures demonstrates the vast potential of the periodic local vibrational mode theory for characterizing and understanding non-covalent interactions in materials.

Hiding in the Crowd: Spectral Signatures of Overcoordinated Hydrogen-Bond Environments

Molecules with an excess number of hydrogen-bonding partners play a crucial role in fundamental chemical processes, ranging from anomalous diffusion in supercooled water to transport of aqueous proton defects and ordering of water around hydrophobic solutes. Here we show that overcoordinated hydrogen-bond environments can be identified in both the ambient and supercooled regimes of liquid water by combining experimental Raman multivariate curve resolution measurements and machine learning accelerated quantum simulations. In particular, we find that OH groups appearing in spectral regions usually associated with non-hydrogen-bonded species actually correspond to hydrogen bonds formed in overcoordinated environments. We further show that only these species exhibit a turnover in population as a function of temperature, which is robust and persists under both constant pressure and density conditions. This work thus provides a new tool to identify, interpret, and elucidate the spectral signatures of crowded hydrogen-bond networks.

Hydrated Metal Ion Salts of the Weakly Coordinating Fluoroanions PF6-, TiF62-, B12F122-, Ga(C2F5)4-, B(3,5-C6H3(CF3)2)4-, and Al(OC(CF3)3)4-. In Search of the Weakest HOH···F Hydrogen Bonds

FTIR spectra of microcrystalline samples of 11 metal ion salt hydrates of a variety of weakly coordinating fluoroanions are reported. The compounds studied were Li(H₂O)₄(Al(OC(CF₃)₃)₄), Li(H₂O)(B(3,5-C₆H₃(CF₃)₂)₄), Li(H₂O)_n(Ga(C₂F₅)₄), Li(H₂O)(PF₆), Li₂(H₂O)₂(TiF₆), Li₂(H₂O)₄(B₁₂F₁₂), Na(H₂O)(PF₆), Na₂(H₂O)₂(B₁₂F₁₂), K₂(H₂O)₂(B₁₂F₁₂), Rb₂(H₂O)₂(B₁₂F₁₂), Cs₂(H₂O)(B₁₂F₁₂), and their partially or completely deuterated isotopologs and isotopomers. The O-D···F hydrogen bonds in Li(HOD)(H₂O)₃(Al(OC(CF₃)₃)₄) (ν(OD) = 2706 cm^-1), Li(HOD)(B(3,5-C₆H₃(CF₃)₂)₄) (ν(OD) = 2705 cm^-1), and Li(HOD)(H₂O)_n(Ga(C₂F₅)₄) (ν(OD) = 2697 cm^-1) rival HOD absorbed in polyvinylidene difluoride (ν(OD) = 2696 cm^-1) and HOD···FCH₃ in a frozen Ar matrix (ν(OD) = 2685 cm^-1) for the weakest hydrogen bonds between a water molecule and an F atom in any compound. As weak as they are, minor differences in O-H···F hydrogen bonds in the same fluoroanion salt can be distinguished spectroscopically. Uncoupled HOD molecules in asymmetric F···HOD···F' hydrogen bonding environments in Rb⁺, Cs⁺, Mg²⁺, and Co²⁺ hydrates of B₁₂F₁₂^2- gave rise to two observable ν(OD) bands even though the two R(O···F) distances differ by only 0.010(4) Å (Mg²⁺), 0.033(2) Å (Co²⁺), 0.074(4) Å (Rb⁺), and 0.106(6) Å (Cs⁺). A plot of ν(OD) for hydrates with a single uncoupled HOD molecule per metal ion (e.g., Li(HOD)(H₂O)₃(Al(OC(CF₃)₃)₄)) vs R(O···F) distance from single-crystal X-ray or neutron diffraction structures was prepared. The ν(OD) values range from 2305 to 2706 cm^-1 and the R(O···F) distances range from 2.58 to 3.17 Å. The plot consists of 53 {ν(OD), R(O···F)} data points, 23 of which are new and have ν(OD) > 2600 cm^-1, in contrast to a 1994 ν(OD) vs R(O···F) plot with 28 data points, none of which had ν(OD) > 2600 cm^-1. There is a clear and significant difference between the new ν(OD) vs R(O···F) plot and a literature ν(OD) vs R(O···O) plot for hydrates containing O-D···O hydrogen bonds. For a given ν(OD) stretching frequency, the exponential regression curves show that R(O···F) is typically 0.1-0.2 Å shorter than R(O···O), in harmony with the lower basicity and smaller size of F atoms vs O atoms.

Theoretical Studies of IR and NMR Spectral Changes Induced by Sigma-Hole Hydrogen, Halogen, Chalcogen, Pnicogen, and Tetrel Bonds in a Model Protein Environment

Various types of σ-hole bond complexes were formed with FX, HFY, H2FZ, and H3FT (X = Cl, Br, I; Y = S, Se, Te; Z = P, As, Sb; T = Si, Ge, Sn) as Lewis acid. In order to examine their interactions with a protein, N-methylacetamide (NMA), a model of the peptide linkage was used as the base. These noncovalent bonds were compared by computational means with H-bonds formed by NMA with XH molecules (X = F, Cl, Br, I). In all cases, the A-F bond, which lies opposite the base and is responsible for the σ-hole on the A atom (A refers to the bridging atom), elongates and its stretching frequency undergoes a shift to the red with a band intensification, much as what occurs for the X-H bond in a H-bond (HB). Unlike the NMR shielding decrease seen in the bridging proton of a H-bond, the shielding of the bridging A atom is increased. The spectroscopic changes within NMA are similar for H-bonds and the other noncovalent bonds. The C=O bond of the amide is lengthened and its stretching frequency red-shifted and intensified. The amide II band shifts to higher frequency and undergoes a small band weakening. The NMR shielding of the O atom directly involved in the bond rises, whereas the C and N atoms both undergo a shielding decrease. The frequency shifts of the amide I and II bands of the base as well as the shielding changes of the three pertinent NMA atoms correlate well with the strength of the noncovalent bond.

High-Level VSCF/VCI Calculations Decode the Vibrational Spectrum of the Aqueous Proton

The hydrated excess proton is a common species in aqueous chemistry, which complexes with water in a variety of structures. The infrared spectrum of the aqueous proton is particularly sensitive to this array of structures, which manifests as continuous IR absorption from 1000 to 3000 cm^-1 known as the "proton continuum". Because of the extreme breadth of the continuum and strong anharmonicity of the involved vibrational modes, this spectrum has eluded straightforward interpretation and simulation. Using protonated water hexamer clusters from reactive molecular dynamics trajectories, and focusing on their central H⁺(H₂O)₂ structures' spectral contribution, we reproduce the linear IR spectrum of the aqueous proton with a high-level local monomer quantum method and highly accurate many-body potential energy surface. The accuracy of this approach is first verified in the vibrational spectra of the two isomers of the protonated water hexamer in the gas phase. We then apply this approach to 800 H⁺(H₂O)₆ clusters, also written as [H⁺(H₂O)₂](H₂O)₄, drawn from multistate empirical valence bond simulations of the bulk liquid to calculate the infrared spectrum of the aqueous proton complex. Incorporation of anharmonic effects to the vibrational potential and quantum mechanical treatment of the proton produces a better agreement to the infrared spectrum compared to that of the double-harmonic approximation. We assess the correlation of the proton stretching mode with different atomistic coordinates, finding the best correlation with ⟨R_OH⟩, the expectation value of the proton-oxygen distance R_OH. We also decompose the IR spectrum based on normal mode vibrations and ⟨R_OH⟩ to provide insight on how different frequency regions in the continuum report on different configurations, vibrational modes, and mode couplings.