Theoretical Prediction of Robust Second-Row Oxyanion Clusters in

---

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

pubs.acs.org/IC

Theoretical Prediction of Robust Second-Row Oxyanion Clusters in the Metastable Domain of Antielectrostatic Hydrogen Bonding Frank Weinhold* Theoretical Chemistry Institute and Department of Chemistry, University of WisconsinMadison, Madison, Wisconsin 53706, United States S Supporting Information *

ABSTRACT: We provide ab initio and density functional theory evidence for a family of surprisingly robust like-charged clusters of common HSO4− and H2PO4− oxyanions, ranging up to tetramers of net charge 4−. Our results support other recent theoretical and experimental evidence for “antielectrostatic” hydrogen-bonded (AEHB) species that challenge conventional electrostatic conceptions and force-field modeling of closed-shell ion interactions. We provide structural and energetic descriptors of the predicted kinetic well-depths (in the range 3−10 kcal/mol) and barrier widths (in the range 2−4 Å) for simple AEHB dimers, including evidence of extremely strong hydrogen bonding in the fluoride−bisulfate dianion. For more complex polyanionic species, we employ naturalbond-orbital-based descriptors to characterize the electronic features of the cooperative hydrogen-bonding network that are able to successfully defy Coulomb explosion. The computational results suggest a variety of kinetically stable AEHB species that may be suitable for experimental detection as long-lived gas-phase species or structural units of condensed phases, despite the imposing electrostatic barriers that oppose their formation under ambient conditions.

■

INTRODUCTION The well-known dictum of classical electrostatics “like charges repel, unlike charges attract” underlies most current teaching of hydrogen bonding in elementary chemistry textbooks.1 Nevertheless, the paradoxical possibility of “antielectrostatic” hydrogen-bonded (AEHB) formation between like-charged ions has recently been theoretically predicted2 and experimentally confirmed.3−5 Such like-charge attraction between the ionic Lewis base B:(±) and the hydridic Lewis acid H−A(±) can lead to long-lived B:(±)···H−A(±) species whenever the short-range quantum forces of hydrogen bonding (resonance-type threecenter/four-electron nB → σ*AH interactions6) overcome the long-range Coulombic forces of classical electrostatics. Competitive opposition between electrostatics and hydrogen bonding is also demonstrated in a recent study of the ion product of neutral water,7 where cooperative hydrogen-bonding networks provide the mechanistic framework for appreciable (pH 7) self-dissociation to H+(aq) and OH−(aq) ions, contrary to the common presumption that “unlike charges attract”. All such antielectrostatic hydrogen-bonding phenomena challenge classical electrostatic conceptions8 and associated force-field modeling, supporting recent initiatives of the International Union of Pure and Applied Chemistry (IUPAC) to revise the Gold Book definition of hydrogen bonding.9 AEHB species can also be recognized as an aspect of the recently recognized “electrostatically shielded” domain of covalent and dative bonding between like-charged molecular ions.10 It is noteworthy that metastable AEHB species exhibit significant analogies to radioactive nuclei. In the nuclear case, the dense confinement of positively charged protons is © XXXX American Chemical Society

maintained by the short-range nuclear strong force, whereas in the electronic case, the corresponding confinement of likecharged ions is maintained by the short-range (exchange-type) forces of hydrogen bonding. As discussed by Feynman et al.,11 the explosive energy of nuclear decay corresponds to the release of long-range electrostatic repulsions between protons when the confinement potential is disrupted (e.g., by collisions with slow neutrons). In the AEHB case, the energy release is similarly that of the “Coulomb explosion” of like-charged ions when confinement by the surrounding hydrogen-bonding network is breached by thermal collisions or other disruptions. In either case, strategic competition between classical longrange electrostatic repulsions and quantum-type short-range attractions provides a mechanism for long-lived metastable species of unusually high energy content. Early theoretical studies of AEHB complexation focused primarily on simple cation−cation or anion−anion dimers. Conspicuous examples of AEHB building blocks in X-ray structures were recognized12 that exhibit “electrostatics defying interactions” with surrounding counterions or other screening effects of a crystalline13 or biological14 environment. Recent experimental detection of AEHB species in liquid phases3−5 also suggests the role of the surrounding ionic liquid, host− guest encapsulation, or protective ligating environment. In the ionic liquid case,3 the hydrogen-bonding hydroxyl groups are covalently tethered to imidazolium cations, and aggregation into highly charged AEHB units (up to 4+!) could presumably Received: November 19, 2017

A

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Optimized B3LYP/aug-cc-pVTZ structures for the nine AEHB cluster species studied in this work [F−···HSO4−, F−···H2PO4−, (HSO4−)2, (H2PO4−)2, lin and cyc (H2PO4−)3, and lin, cyc, and pyr (H2PO4−)4], showing the atom numbering and isomer labeling used throughout the text. See the SI for optimized coordinates and frequencies.

interactions may also be noted.25 In the present study, we seek to challenge conventional electrostatics-based conceptions of hydrogen bonding in a still more direct fashion by searching for robustly bound higher-order AEHB aggregates of small gasphase oxyanions in direct (tether-free) spatial contact, allowing no evasion of the extreme electrostatic repulsions (and, thus, high energy content) of isolated polyanions stripped of any possible screening effects from a surrounding medium. The surprising AEHB propensity of common bisulfate4,18 or biphosphate anions19,20 offers a clue to possible candidates for higher-order AEHB polyanions. The ready formation of selfcomplementary (and thereby cooperative) O:···H−O hydrogen-bonding patterns favors HSO4− as a building block for AEHB aggregation. Similar possibilities are offered by hydrogenated anions of other common second-row oxyacids such as biphosphate (H2PO4−), which offers still another proton for potential hydrogen bonding. However, common misrepresentations of the Lewis-structural bonding pattern of second-row oxyacids conceal still another important advantage of HSO4− and related ions for AEHB aggregation. Under the persistent influence of Pauling’s principle of electroneutrality,26 bonding representations for H2SO4 or H3PO4 and their derivatives are still frequently written as shown in 1 and 2 (both taken from the current

be further enhanced by lengthening the tether or otherwise altering the dielectric background.15,16 In the host−guest case,4 the AEHB dimers are self-complementary bisulfate HSO4− anions in direct spatial contact, apparently stabilized by the encapsulating effects of the cyanostar macrocycle. In the pseudopeptide ligation case,5 highly charged biphosphate clusters are similarly stabilized by a sandwich of macrocyclic polyazole sites. However, for both the ionic liquid3 and cyanostar macrocycle4 cases, the intrinsic (meta)stability of the AEHB complex as an isolated gas-phase species was also established by computational means. In the former case, AEHB clustering of hydroxyimidazolium clusters was shown3 to closely resemble the cooperative hydrogen-bonding networks of previously studied neutral alcohol clusters.17 For bisulfate18 and biphosphate19,20 anion dimers, the computational stability of isolated species was confirmed and attributed to “electrophilic−nucleophilic interactions” by Mata et al. Building on earlier mass spectrometric and theoretical studies,21−23 Kass and co-workers 24 recently attempted the experimental detection of gas-phase AEHB dimers but obtained only “incipient” evidence for proton transfer in the initial anion− molecule complex to achieve the desired anion−anion pair. Other recent studies of like-ion attraction based on alternative CH-ion, halogen-bond, or n−π*-type donor−acceptor (DA) B

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

(H2PO4−)4 polyanions were located (including multiple isomers of trimer and tetramer), indicating a significantly higher biphosphate propensity for clustering. All species were fully optimized at the B3LYP/aug-cc-pVTZ level with the Gaussian 09 program,35 and the F−···HSO4− species was also optimized at the ab initio Møller−Plesset (MP2/aug-cc-pVTZ) and dispersion-corrected B3LYP-D3/aug-ccpVTZ levels for comparison. Analytical positive frequencies were obtained for all species to verify the local stability of each optimized structure. The final optimized structures for representative AEHB species [F − ···HSO 4 − , F − ···H 2 PO 4 − , (HSO 4 − ) 2 , (H 2 PO 4 − ) 2 , (H2PO4−)3, and three isomers of (H2PO4−)4] are shown in the panels of Figure 1. Structural Features. The AEHB structures of Figure 1 exhibit commonalities as well as important distinguishing features. From a glance at the structures (except the simple F−···HSO4− dimer, where only one hydrogen bond is possible), one can see that each monomer attaches itself to the remaining members of the cluster by 2−4 hydrogen bonds, thereby creating a dense network of hydrogen-bond connections. Indeed, every H atom (or rather, every vacant σ*OH acceptor orbital) seems to be maximally interacting with every available nearby donor orbital in the electron-rich polyanion environment. Nevertheless, finding a maximal number of hydrogen bonds for each monomer is not the full story. Common to all successful AEHB clusters is maximal Grotthus proton ordering, i.e., complementary pairing of DA interactions between units to achieve maximum cooperativity of the overall hydrogen-bonding network. Indeed, departures from maximal Grotthus ordering in the initial-guess geometry result predictably in Coulomb explosion to ionic fragments, consistent with the known importance of cooperativity effects (nonpairwise additivity) in other hydrogen-bonding phenomena.7,36,37 In general, each monomer ion strives to attain balanced (canceling) DA interactions with its surrounding monomers, avoiding capacitive charge buildup with respect to its charge in isolation. Moreover, if a given monomer is left with, e.g., net donor character, it will tend to be neutralized by a monomer of net acceptor character in a symmetrically related position, so as to again minimize internal charge variations within the cluster. Such cooperative overall balancing of hydrogenbond DA interactions is more easily achieved with the symmetric double-donor/double-acceptor coordination sites of H2PO4− than, e.g., the double-donor/single-acceptor sites of HSO4− or all-donor sites of F−, thereby accounting for the enhanced promiscuity of biphosphate anions in AEHB clustering. Note that the symmetry of the preferred DA patterns tends to reduce the overall dipole moment of the AEHB cluster, contrary to the dipole−dipole alignments (with net dipole enhancement) that would be suggested by classical electrostatics. Most exceptional in Figure 1 is the near-symmetric proton bridging (RF···H = 1.188 Å; RO···H = 1.187 Å) between F and O termini in the F−···HSO4− dimer (upper left panel). This emulates the strong and symmetric hydrogen bonds of the bifluoride anion (FHF−) or Zundel cation (H5O2+) in the singly ionic domain,38 where the distinction between the “hydrogen bond” and “covalent bond” becomes arbitrary and low-order perturbative estimates of the DA interaction strength are inadequate. As described below, the binding properties of F−··· HSO4− exceed those of the apparently analogous F−···HCO3− species2 by more than 2 orders of magnitude, indicating its highly anomalous character with respect to other known AEHB species. Despite the unusual strength of bisulfate hydrogen bonding with a single fluoride ion, the unbalanced 3D/1A coordination pattern of HSO4− proves ineffective in higher polyanion clustering beyond the dimer level. The F−···HSO4− dimer is therefore considered to be an outlier in broader statistical correlations to be presented below. Relaxed-Scan Potential Curves for Dissociative Coulomb Explosion. For each dimer species in Figure 1, we first calculate a relaxed potential scan by varying the separation of the monomer centers at each step of the scan and optimizing all other geometrical variables at each step. The resulting potential energy curves for each dimer [F−···HSO4−, F−···H2PO4−, (HSO4−)2, (H2PO4−)2] are shown in the successive panels a−d of Figure 2. In each panel, we show both

Wikipedia entries for “sulfuric acid” or “phosphoric acid,” respectively).

Such structures suggest hexavalent or pentavalent central atoms and one or more carbonyl-type (Ö :) oxygen linkages. However, it was pointed out27 that such “Lewis structures” are not those advocated by Lewis himself but should instead be replaced by Lewis-compliant tetravalent bonding patterns such as 1′ and 2′, with formal single bonds (only), terminal O− anions, highly cationic central atoms, and no significant “πbonded oxygen” character. Structures 1′ and 2′ are readily shown27 to be superior by the criteria of natural bond orbital (NBO)28 and natural resonance theory (NRT)29 analysis. The significant positive charge of the central S (2.513+) or P (2.516+) atom is also confirmed by natural population analysis,30 Bader atoms-in-molecules analysis,31 and other methods of charge assessment for modern wave functions. Most importantly, structures 1′ and 2′ suggest no appreciable π-bonding capacity in these molecules but rather highly polar σ bonds (σSO or σPO) with formal anionic character at each oxygen terminus. The terminal O atoms thereby exhibit enhanced donor (Lewis base) strength, comparable to that of OH− or other anions, which strengthens their capacity for the DA interactions of hydrogen bonding.32

In the present work, we explore AEHB polyanion species involving HSO4− and H2PO4− ions, quantify the well-depths and barriers of successful AEHB confinement potentials, and analyze the electronic factors that account for the polyanion structure and stability. Our emphasis is on the qualitative features of AEHB bonding that are rather insensitive to the theoretical level, and for this purpose, we employ standard density functional theory methods and basis sets33 (specifically, the B3LYP/aug-cc-pVTZ hybrid density functional with a Dunning-style augmented triple-ζ basis), with analysis by NBO/NRT-based methods.34 Additional computational details and optimized coordinates of stationary-state species are included in the Supporting Information (SI).

■

COMPUTATIONAL RESULTS: BINARY AND HIGHER HYDROGEN-BONDED CLUSTERS OF BISULFATE AND BIPHOSPHATE IONS

As candidate AEHB species involving HSO4− or H2PO4− ions, we first considered mixed dimers (F−···HSO4− and F−···H2PO4−) with monatomic fluoride anions for comparison with the analogous F−··· HCO3− bicarbonate complex.2 We then searched for locally stable minima of pure polybisulfate (HSO4−)i or polybiphosphate (H2PO4−)i clusters in the range i = 2−4. Only dimers (HSO4−)2 were found to be stable for bisulfates, but successful (H2PO4−)2, (H2PO4−)3, and C

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

interion separations for each species (e.g., RF···S for F−···HSO4−) is therefore taken to be sufficiently large to match the potential energy value at the bottom of the short-range potential well. The geometry at the relaxed-scan barrier top is then taken as an initial guess for full transition-state optimization by the QST3 method, leading to the activation energy ΔE⧧ (indicated by the vertical arrow in each panel of Figure 2). The transition state differs imperceptibly from the plotted barrier top in each case, indicating that the relaxed-scan curves of Figure 2 adequately resemble the full intrinsic reaction coordinate (IRC) potential for each species, except for occasional hysteresis-type discontinuities (see, e.g., Figure 2d) associated with relaxations in other coordinates. The dissociation pathways for higher-order linear, cyclic, and polycyclic clusters were investigated in a similar manner, with the resulting barrier profiles shown in Figure 3. The higher-order (H2PO4−)3 and (H2PO4−)4 clusters shown in the lower panels of Figure 1 apparently have no stable counterparts involving F− or HSO4− anions, so primary attention was centered on the rich possibilities for higher-order biphosphate clusters. On the basis of considerations described in the following section, the most likely dissociation coordinate for the linear (H2PO4−)3 trimer or (H2PO4−)4 tetramer can be taken in the former case as the RP···P distance between a monomer and dimer or in the latter case as that between two dimers, leading to the relaxed scans shown in Figures 3a,c. Potential barriers for isomeric cyclic trimer (Figure 3b) and tetramer (Figure 3d) or pyramidal tetramer (Figure 3d) were similarly obtained from relaxed scans of RP···P for the weakest link suggested by NBO/NRT bondorder estimates (see the following section). Hysteresis-type discontinuities are particularly evident in the cyclic trimer (Figure 3b), where relaxations from bifurcated to linear hydrogen bonding involve a significant dependence on torsional coordinates near the transitionstate region. However, in all cases, the top-of-the-barrier geometry serves as a guess input for QST3 optimization to the transition state, allowing final determination of the thermodynamic and kinetic activation parameters for each polyion species. Table 1 displays the key thermodynamic (ΔE and ΔG(0)) and kinetic (ΔE⧧ and ΔG(0)⧧) potential parameters for all polyion species of Figures 2 and 3. Energetic Properties of Individual Species. As remarked above, the F−···HSO4− complex exhibits remarkable structural signatures of extremely strong hydrogen bonding and a deep potential well (ΔE⧧ = 7.19 kcal/mol), exceeding by ca. 100-fold the corresponding value (0.05 kcal/mol) for the analogous F−···HCO3−.2 For an ab initio comparison, we repeated optimization at the MP2/aug-cc-pVTZ level and found geometry (RF···H = 1.103 Å; RO···H = 1.264 Å) and energy (ΔE = 40.34 kcal/mol; ΔG(0) = 46.54 kcal/mol) values that are similar to the B3LYP values but indicate a still higher dissociation barrier (8.53 kcal/mol) and a degree of proton transfer from O to F (increased FH···SO42− character) that is anomalous compared to other species. Dispersion-corrected B3LYP-D3/aug-cc-pVTZ dissociation barrier (7.26 kcal/mol) and structural features are also similar to those at the B3LYP level (see the SI). The potential barriers opposing direct thermal traversal or tunneling-type dissociation of the remaining F − ···H 2 PO 4 − , (HSO4−)2, and (H2PO4−)2 dimers (Figures 2a−c) are also substantial in height (3−10 kcal/mol) and width (2−4 Å), suggesting the suitability of these species for low-temperature experimental detection. The robust binding of these dimers apparently is more due to the larger number of contributing hydrogen bonds than to extraordinary strength of a single hydrogen bond, as in F−···HSO4−. As shown in Figure 2d, the relaxed-scan dissociation curve for (H2PO4−)2 exhibits apparent numerical anomalies. At near-equilibrium separation (RP···P ≈ 3.85 Å), the low-energy geometry is C2-symmetric, but near 4.0 Å, the C2 curve is crossed by a lower-energy C2hsymmetric curve, which continues toward the transition state. Other crossings or hysteresis effects are apparent at larger separations, presumably because of additional hydrogen bonds whose contributions to a proper IRC-type collective coordinate lead to increasing deviations from the simple RP···P scan variable. Qualitatively, one can see that the biphosphate ion offers a “water-like” selection of two donor and two acceptor sites (2D/2A), distributed around the near-

Figure 2. Dissociative energy profiles (relaxed potential energy scans) for AEHB dimers: (a) F−···HSO4−; (b) F−···H2PO4−; (c) (HSO4−)2; (d) (H2PO4−)2. the height ΔE (kcal/mol, relative to asymptotic dissociated ions; vertical) and width RX···Y (Å, horizontal) of the potential barrier opposing tunneling-type dissociation, as well as the overall energy release of Coulomb explosion to this asymptotic limit; the range of D

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

The higher-order polyionic clusters of Figure 3 continue to exhibit surprisingly varied and robust potential wells, despite the increasing opposition of Coulomb repulsion. As shown in Figure 1, an increasing variety of metastable lin, cyc, and pyr isomeric forms are found for higher clusters. Bolstered by the usual cooperative effects of Grotthustype proton ordering,7,36 the cyclic clusters exhibit particularly significant well-depths in higher-order AEHB complexes (viz., 6.97 or 3.94 kcal/mol for triply or quadruply charged species, respectively), despite their greatly increased energy content with respect to ionic dissociation. Thus, neither high ionic charge nor high energy content seems to preclude possible kinetic trapping of still larger and more diverse isomeric polyion clusters than those considered here.

■

NBO DESCRIPTION OF POLYANION CLUSTER NETWORKS The NBO 6.0 program39 offers a variety of tools to analyze more complex hydrogen-bonding networks and provide comparisons among the various dimeric and higher-order polyions described above. In the present section, we employ such NBO-based descriptors to assess the relative hydrogenbond strengths (and dissociative vulnerabilities) in both simple and complex AEHB cluster topology. In NBO theory, the simplest energetic measure of DA stabilization, e.g., for two-electron nO′−σ*OH interactions in closed-shell species, is given by the second-order perturbative estimate40 (2) ΔE DA (nO ′−σ *OH ) = −2⟨nO ′|F|σ *OH ⟩2 /(εn − εσ *)

(1)

where F is the effective one-electron Hamiltonian (Fock or Kohn−Sham operator) and εn and εσ* are orbital energies (diagonal F-matrix elements) of the donor nO′ and acceptor σ*OH NBOs of interest. However, the attractive stabilization afforded by ΔE(2) DA must be offset by the steric repulsion of the corresponding nO′−σOH donor−donor (DD) interaction, which is obtained in NBO theory as a simple pairwise estimate (PW) ΔEDD (nO′−σOH) of its contribution to the total steric exchange energy.41 This suggests an elementary estimate (εHB) of the net hydrogen-bonding interaction energy, viz. (2) (PW) εHB ≡ ΔE DA (nO ′−σ *OH ) − ΔE DD (nO ′−σOH)

= donor−acceptor attraction − donor−donor repulsion

(2)

for each O′···H−O feature of a complex hydrogen-bonding network. The simple εHB estimate should prove useful for correlative comparisons of the short-range (quantum-exponential) aspects of hydrogen bonding, where background longrange Coulomb repulsions are varying only weakly in the narrow range of characteristic hydrogen-bond separations. More generally, NRT analysis29 provides a quantitative measure of bond order bAB for each strong (bOH) or weak (bO′···H and bO′···O) interaction of a chosen O′···HO triad. Such NRT bond orders have been shown6 to exhibit strong correlations with experimental bond lengths, energies, and stretching frequencies that are regarded as reliable signatures of hydrogen bonding,9 consistent with empirical bond order− bond length,42 bond order−bond energy,43 and bond order− bond frequency (Badger’s rule)44 relationships that are useful in other contexts. In the present case, we employ local NRT45 for the three atoms of each O′···H−O linkage to obtain consistent bOH bond-order measures across the manifold of AEHB cluster topologies.

Figure 3. Similar to Figure 2, for higher-order trimeric and tetrameric biphosphate clusters (cf. Figure 1): (a) lin (H2PO4−)3; (b) cyc (H2PO4−)3; (c) lin (H2PO4−)4; (d) cyc (H2PO4−)4 and pyr (H2PO4−)4.

tetrahedral (“carbon-like”) geometry of its central core. This coordinative motif apparently offers near-ideal flexibility for extending cooperative DA hydrogen-bonding patterns into three-dimensional structures. E

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Table 1. B3LYP/aug-cc-pVTZ Energies and Standard-State Gibbs Free Energies (kcal/mol) for Dissociation Potentials of AEHB Species, Showing Net Energy Release (ΔE and ΔG(0)), Activation Barrier Height (ΔE⧧ and ΔG(0)⧧), and Barrier Width Opposing “Coulomb Explosion” to Monomers for All AEHB Clusters Described in This Work AEHB complex −

ΔE (kcal/mol)

ΔG(0) (kcal/mol)

ΔE⧧ (kcal/mol)

ΔG(0)⧧ (kcal/mol)

barrier width (Å)

+41.86 +38.86 +39.38 +32.45 +114.78 +102.11 +236.07 +233.63 +197.17

+47.76 +46.70 +52.32 +48.07 +143.38 +130.52 +328.72 +274.04 +238.05

7.19 9.88 3.22 8.48 6.97 3.55 0.38 3.92 0.64

8.89 8.86 1.99a 2.76 3.83 12.36 −0.40 2.94a −0.43

3.1 4.1 2.2 4.5 3.7 2.5 0.8 1.8b,c 1.1

−

F ···HSO4 F−···H2PO4− (HSO4−)2 (H2PO4−)2 (H2PO4−)3 (cyc) (H2PO4−)3 (lin) (H2PO4−)4 (pyr) (H2PO4−)4 (cyc) (H2PO4−)4 (lin) a

Questionable numerics: converged QST3 transition-state geometry yields a second imagnary frequency in the analytical FREQ evaluation; see the SI. bUnable to a complete relaxed scan to this separation. cVisual estimate from Figure 3.

Table 2. NRT Bond Orders (bX···H, bOH, and bX^O) and a Comparison of the ROH and ROO Bond Lengths for the NHB Hydrogen Bonds of Each AEHB Complex, with Specific Atom Numbers (and Symmetry-Equivalent Linkages) of Each X: H−O Triad (cf. Figure 1)a

a

AEHB complex

NHB

X: H−O (#)

bX···H

bOH

bX^O

ROH (Å)

ROO (Å)

F−···HSO4− F−···H2PO4− (HSO4−)2 (H2PO4−)2 (H2PO4−)3 (cyc) (H2PO4−)3 (lin)

1 2 2 4 6 6

(H2PO4−)4 (pyr)

8

(H2PO4−)4 (cyc) (H2PO4−)4 (lin)

8 8

7: 6−5 8: 6−4 (2) 3: 12−9 (2) 12: 5−4 (4) 10: 5−4 (6) 9: 5−4 (4) 2: 14−10 (2) 17: 27−7 (2) 6: 28−18 (2) 6: 22−11 (2) 13: 26−17 (2) 3: 26−25 (8) 2: 14−12 (2) 9: 6−4 (4) 10: 20−18 (2)

0.4642 0.0849 0.0834 0.0502 0.0506 0.0228 0.0767 0.0360 0.0483 0.0763 0.1065 0.0589 0.0264 0.0283 0.0265

0.5358 0.8962 0.8914 0.9219 0.9211 0.9705 0.9100 0.9502 0.9242 0.8946 0.8624 0.9182 0.9522 0.9456 0.9518

0.0000 0.0190 0.0253 0.0279 0.0284 0.0050 0.0090 0.0138 0.0275 0.0291 0.0311 0.0229 0.0213 0.0261 0.0217

1.1873 0.9978 0.9899 0.9831 0.9875 0.9833 0.9970 0.9773 0.9828 0.9922 1.0050 0.9851 0.9851 0.9858 0.9908

2.7549 2.8298 2.7648 2.8223 2.7475 2.9735 2.8934 2.7726 2.6775 2.7994 2.8981 2.8085 2.8057

The corresponding free monomer OH values are bOH = 0.9842 and ROH = 0.9647 Å for HSO4− and bOH = 0.9991 and ROH = 0.9619 Å for H2PO4−.

more typical hydrogen bonds imperceptible. The least-squares fit (dashed line) displays a reasonable bOH−ROH correlation (Pearson correlation coefficient χ2 = 0.75), despite wide variations in the polyion composition, topology, and total charge of the correlated species. Table 3 similarly presents individual (εHB) and summed (∑HB εHB) values of the hydrogen-bond interaction energy estimates of eq 2, together with the associated DA (ΔE(2) n−σ*) and DD (ΔE(PW) n−σ ) contributions for each hydrogen bond. The strength of each εHB interaction is expected to correlate with the measurable elongation of the ROH bond length, red shift of the νOH vibrational frequency, downfield chemical shift δH of the proton NMR shielding, or other known signatures of hydrogen bonding.6 As an example, the εHB estimates of Table 3 are compared with the optimized ROH bond lengths of Table 2 in the correlation diagram of Figure 5. The εHB−ROH statistical correlation is seen to be of good quality (χ2 = 0.91), consistent with that known for elementary hydrogen-bonding dimers8 where the hydrogen-bonding dissociation energy can be determined directly, without the ambiguities of the transitionstate barrier that control the AEHB case. Numerical bO···H or εHB values can assist in identifying likely pathways for the dissociative breakup of complex AEHB

Table 2 displays calculated B3LYP/aug-cc-pVTZ NRT bond orders for all three-center X:···H−O triads of AEHB species considered in this work. The table includes the number of hydrogen bonds (NHB), atom numbers for each X: H−O triad (with the number of symmetry-related linkages in parentheses), and associated ROH bond lengths for each hydrogen bond. In each case, we display NRT bond orders for the formal covalent bond bOH and hydrogen bond bX····H (generally much weaker than bOH except in the highly anomalous F−···HSO4− dimer) a well as the weaker bX^O long-bond interaction46 that completes the full resonance-type description of the three-center/fourelectron bonding triad. These bond orders are seen to satisfy a type of conservation principle47 bOH + bX ··· H + bX

^O

≈ 1s

(3)

that reflects their resonance-theoretical origin. Figure 4 presents the bOH versus ROH (bond order−bond length) correlation diagram for all hydrogen bonds of AEHB species 2−9 in Table 2 and precursor free-OH bonds of isolated HSO4− and H2PO4−. For reasons mentioned above, F−···HSO4− is excluded as an outlier from all such statistical correlations; its inclusion in Figure 4 would actually improve the χ2 correlation coefficient (to χ2 = 0.96) but in a manner that so alters the scale of the figure as to render the variations of F

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 4. NRT bond order−bond length correlation for hydrogen bonds of AEHB species 2−9 (Table 2) and free bisulfate and biphosphate monomers. The least-squares fit (slope = −0.2608 and intercept = 1.228) is satisfied with the correlation coefficient χ2 = 0.75.

Figure 5. NBO bond energy−bond length (εHB vs ROH) correlation for hydrogen bonds of AEHB species 2−9 (Table 3). The least-squares regression (slope = 0.002946; intercept = 0.9790) is satisfied with the correlation coefficient χ2 = 0.91.

polyions. For example, from the εHB values for the pyramidal (H2PO4−)4 tetramer in Table 3, we can judge that the equivalent O17···H27−O7 and O14···H23−O10 hydrogen bonds connecting the P1−P8 dimer to the P15−P22 dimer (each with εHB = 1.22 kcal/mol) should be the weakest links that most likely determine the transition state and IRC of AEHB fission. This breakup pattern is also that predicted by natural cluster unit analysis39b (p B-187ff of ref 45). The individual εHB linkages for (H2PO4−)4 isomers appear to equal or surpass those for the (H2PO4−)2 dimer (with ΔE⧧ ≈ 8.5 kcal/mol well depth), suggesting that appreciable confinement barriers (and sharply higher E release upon fission) may persist in higher polyanion clusters, despite the increasingly unfavorable ionic close packing in cyclic or pyramidal cluster geometry. As an additional indicator, Table 4 compares the calculated vibrational properties for the apparent lowest-energy dissocia-

tion mode of each AEHB complex. The results show a qualitatively similar range of dissociation frequencies (ca. 100− 200 cm−1), force constants (a few tenths mdyn/Å), and IR intensities (strong for asymmetric dissociation and weak or vanishing for symmetric dissociation) that characterize the dimers as well as the cyclic trimer and tetramer, both of which evidently benefit from the strong cooperative enhancement of closed-cycle Grotthus hydrogen-bonding patterns. However, the vibrational signatures (as shown in the fourth column of Table 4) indicate appreciably weaker kinetic stability for linear or pyramidal tetramers. All of these experimentally measurable properties suggest that highly charged oxyanionic species, once trapped, should exhibit fairly typical patterns of hydrogen-bonding behavior. The successful gas-phase capture of any such species should

Table 3. Individual and Summed Hydrogen-Bond Energy Estimates (εHB) and Contributing Terms DA (ΔE(2) n−σ*) and DD (ΔE(PW) n−σ ) [Equation 2; All Quantities in kcal/mol] for the NHB Hydrogen Bonds of Each AEHB Complex, with Specific Atom Numbers (and Symmetry-Related Linkages) of Each X: H−O Triad (cf. Figure 1) AEHB complex

NHB

X: H−O (#)

ΔE(2) n−σ* (DA)

ΔE(PW) n−σ (DD)

εHB

∑εHB

F−···HSO4− F−···H2PO4− (HSO4−)2 (H2PO4−)2 (H2PO4−)3 (cyc) (H2PO4−)3 (lin)

1 2 2 4 6 6 8

(H2PO4−)4 (cyc) (H2PO4−)4 (lin)

8 8

150.33 24.45 17.58 11.22 14.41 11.52 22.48 7.50 10.60 18.67 28.65 11.39 12.30 12.17 15.90

54.20 18.29 12.79 10.08 12.23 10.28 16.40 6.28 8.96 14.36 20.03 10.32 9.89 10.51 12.12

96.13 6.16 4.79 1.14 2.18 1.24 6.08 1.22 1.64 4.31 8.62 1.07 2.41 1.66 3.78

96.13 12.32 9.58 4.56 12.48 17.12

(H2PO4−)4 (pyr)

7: 6−5 8: 6−4 (2) 3: 12−9 (2) 12: 5−4 (4) 10: 5−4 (6) 9: 5−4 (4) 2: 14−12 (2) 17: 27−7 (2) 6: 28−18 (2) 6: 22−11 (2) 13: 26−17 (2) 3: 25−26 (8) 2: 14−12 (2) 9: 6−4 (4) 10: 20−18 (2) G

31.58

8.56 19.02

DOI: 10.1021/acs.inorgchem.7b02943 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

under isolated gas-phase conditions remains highly desirable as the ultimate test of the AEHB concept.

Table 4. Vibrational Properties of AEHB Complexes, Showing the Overall Point-Group Symmetry and the Mode Number, Frequency ν (cm−1), Force Constant (mdyn/Å), and IR Intensity (km/mol) for the Apparent Lowest-Energy Vibrational Mode of Cluster Dissociation (B3LYP/aug-ccpVTZ Level) AEHB complex

symmetry

mode #

ν (cm−1)

force constant

IR intensity

F−···HSO4− F−···H2PO4− (HSO4−)2 (H2PO4−)2 (H2PO4−)3 (cyc) (H2PO4−)3 (lin) (H2PO4−)4 (pyr) (H2PO4−)4 (cyc) (H2PO4−)4 (lin)

Cs C2v C2 D2h C3h C1 C2

4 3 4 6 10 6 4

392 231 103 153 131 81 54

0.33 0.59 0.10 0.22 0.16 0.05 0.02

2195 74