Quantum Induced Bond Centering in Microsolvated HCl: Solvent

Letter pubs.acs.org/JPCL

Quantum Induced Bond Centering in Microsolvated HCl: Solvent Separated versus Contact Ion Pairs Łukasz Walewski,* Harald Forbert, and Dominik Marx Lehrstuhl für Theoretische Chemie, Ruhr−Universität Bochum, 44801 Bochum, Germany ABSTRACT: Nuclear quantum effects on the structure of dissociated HCl(H 2O)4 clusters are studied using ab initio path integral simulations. This cluster supports two distinct zwitterionic species serving as minimal microsolvation models for solvent-shared and contact ion pairs (SIP and CIP, respectively) involving the dissociated acid, i.e., Cl − and H3O+. The SIP structure is not much affected by quantum effects apart from expected broadening of distance distribution functions. In stark contrast, the CIP structure is qualitatively changed: the hydrogen bond that directly connects the ion pair, i.e., the Cl− and H3O+ species, becomes both centered and fluxional as a result of zero point motion. Thus, the detached proton is “pushed back” to Cl− and thereby stabilizes a Zundel-like structure motif, Cl···H···OH2, in a low−barrier hydrogen bonding scenario, which is relevant to acid dissociation in the bulk at ultrahigh concentrations.

SECTION: Molecular Structure, Quantum Chemistry,General Theory

D

Beyond microsolvation, ion pairs are of overriding importance in strong acids in the limit of high concentration where not enough solvent is available to establish solvation shells known from the respective dilute solutions. Recently, the issue of ion pairing versus ion solvation in aqueous HCl solutions up to ultrahigh concentrations has been investigated in detail.18,19 Based on X-ray absorption fine structure (XAFS) measurements 19 the hydrogen bonding structures of Cl−···H3O+ versus Cl−···H2O contacts have been compared.19 The donor−acceptor distance in the ion pair structure turns out to be significantly (0.16 Å) shorter than in the solvent shell of Cl−. Such a contracted structure of the CIP hydrogen bond is consistent with an earlier neutron diffraction experiment. 18 Most interestingly, however, the bridging proton was found to reside close to the bond center in the CIP structure, Cl−···H3O+, thus approaching hydrogen bond centering in an asymmetric donor−acceptor situation, Cl···H···OH2, whereas a standard hydrogen bond characterizes Cl−···H2O and thus ion solvation. In stark contrast, ab initio molecular dynamics (AIMD)20 simulations report distinctly asymmetric Cl−···H3O+ hydrogen bonds with preferred Cl−···H distances substantially longer than the measured value.21,22 Here, dissociated microsolvation aggregates such as SIP or CIP motifs might serve as well−controlled embryonic models for bulk electrolytes at ultrahigh concentration, where ion pairing is enforced simply by the lack of solvent. In this paper, we address the issue of nuclear quantum effects on the hydrogen bonding network of small microsolvated clusters, HCl(H2O)4, that support two important ion pairing

issociation of strong acids in different environments, such as those provided by bulk water, ice nanoparticles, or microsolvation aggregates, is one of the fundamental chemical reactions that has attracted considerable attention for decades. In particular, the molecular mechanism of ion formation and the subsequent stabilization of charged species by aqueous environments is of great importance to our understanding of elementary chemical reactions. Substantial knowledge on dissociated HCl in water, hydrochloric acid, has been collected in numerous experimental and theoretical accounts. Early theoretical studies focused on finding stable configurations of dissociated HCl−water clusters in the gas phase. A diamondlike structure of HCl(H2O)4, often referred to as solvent-shared (or solvent-separated) ion pair (SIP), was found with the hydronium (H3O+) and the chloride (Cl−) ions interfaced by three water molecules, thus forming six hydrogen bonds.1 Apart from the SIP global minimum structure, another dissociated isomer, the contact ion pair (CIP) with H3O+ and Cl− ions remaining in direct contact with each other, has been found.2 Thus, the CIP structure features a direct hydrogen bond between a halide anion and a hydronium cation. The stability of HCl(H2O)n clusters has been also studied systematically3,4 as a function of n with the conclusion that a minimum of four water molecules is indeed necessary to stabilize the dissociated zwitterionic form of microsolvated HCl. More recently, the issue of the dynamics of HCl−water clusters has been addressed,5−8 including the possible influence of quantum effects on structural rearrangements in such strongly hydrogenbonded systems.9 At the same time small HCl−water clusters were subject to experimental studies in cold and ultracold environments such as molecular beams 10,11 and helium nanodroplets.12−17 These studies support HCl dissociation and thus ion pairing at such microsolvation conditions. © 2011 American Chemical Society

Received: October 14, 2011 Accepted: November 21, 2011 Published: November 21, 2011 3069

dx.doi.org/10.1021/jz2013819 | J. Phys. Chem.Lett. 2011, 2, 3069−3074

The Journal of Physical Chemistry Letters

Letter

motifs, SIP and CIP. To this end we perform ab initio path integral (AIPI) simulations where the atomic nuclei are treated as quantum degrees of freedom, which allows for direct comparisons to AIMD where these degrees of freedom are treated in the classical limit; the interactions are always computed “on the fly” based on concurrent electronic structure calculations. As opposed to the SIP structure, where Cl − is bound by an Eigen-like cation [H3O(H2O)3]+ by accepting three hydrogen bonds, the CIP species shows extraordinarily pronounced quantum effects not discussed so far. These quantum effects are shown to center the hydrogen bond between the anion and cation, i.e. Cl···H···OH2, and thus yield a microsolvated Zundel−like complex. It is expected that the revealed quantumness of the very hydrogen bond that holds together a CIP, involving a hydronium cation, will not only play a role in microsolvation, but also in bulk solution at ultrahigh concentrations where CIPs necessarily dominate. The SIP structure is reported to be the most stable among known dissociated forms of the HCl(H2O)4 cluster2,3 (see inset in panel (a) of Figure 1). As many as six hydrogen bonds

Table 1. Interatomic Distances (in Å) in Selected Hydrogen Bonds in the SIP and CIP Structures of the HCl(H2O)4 Cluster Reported for the Optimized Structures (eq), Averaged over Classical Ab Initio (cl) and Quantum Path Integral (qm) Trajectories at 100 K rOO

rO···H

rH−O

rCl,O

rCl···H

rH−O

3.06 3.07 3.06

Cl−···H2O 2.09 2.11 2.10

1.01 1.00 1.00

3.14 3.17 3.27

Cl−···H2O 2.17 2.21 2.33

1.00 0.99 0.97

2.87 2.83 2.82

Cl−···H3O+ 1.82 1.74 1.50

1.08 1.12 1.32

SIP eq cl qm

2.57 2.57 2.58

H2O···H3O+ 1.55 1.55 1.55

2.57 2.59 2.64

H2O···H3O+ 1.53 1.57 1.67

2.68 2.70 2.78

H2O···H2O 1.68 1.72 1.82

1.04 1.04 1.05 CIP

eq cl qm

eq cl qm

1.05 1.03 0.98

1.01 1.00 0.98

both as donor (D) and acceptor (A), the proton is displaced from the D−A bond center by 0.26 Å (see panel (a) of Figure 1). On the other hand, hydrogen bonds, where the Cl− ion is the acceptor, feature a displacement of 0.55 Å, which is due to the significant difference in size between the chloride ion and the oxygen when acting as acceptors. The classical distributions P(δ) for both hydrogen bond types in the SIP cluster are peaked at the corresponding equilibrium values showing no unexpected effects due to the thermal motions (cf. solid and vertical dotted lines in panels (a) and (b) in Figure 1). The protons are quasi−rigidly bound to the respective donors, and no proton fluctuations along the hydrogen bond are observed as the fluctuations of the H···A distances are independent from the O−H distance (see panel (a) of Figure 2 for the twodimensional classical distribution P(rOH,rHCl) calculated for the Cl−···H2O hydrogen bond in the SIP cluster). The lack of correlation between the two distances is an evidence that the water molecules in the SIP species remain unaltered and that Cl− is loosely bound to the otherwise solid network of water molecules, which could be considered an Eigen-like cation, [H3O(H2O)3]+. Quantum mechanical fluctuations do not affect the SIP cluster beyond introducing broadening compared to the purely thermal treatment (see dashed lines in panels (a) and (b) of Figure 1). In particular, the average quantum structure remains unchanged as compared to the equilibrium; heavy atom distances deviate only by about 0.01 Å (see Table 1). The main contribution to the rmsd, which amounts to 0.14 Å, is due to the reorientations of the three dangling OH bonds, i.e., protons not involved in the hydrogen bond formation as discussed in the next paragraph. As a result, the hydrogen bonding network of the SIP, as defined by the equilibrium structure, is preserved when adding thermal fluctuations as well as quantum effects at 100 K. The only flexible fragments of the otherwise quasi-rigid SIP cluster structure are the dangling OH bonds (see inset in panel (a) of Figure 1). Each of them has two stable conformations with respect to the plane formed by the oxygen atom to which it is covalently bound, the chloride ion and the hydronium’s

Figure 1. Probability distribution functions P(δ) of the asymmetric stretch coordinate δ, as defined in the text, calculated for H2O···H3O+ and Cl−···H2O hydrogen bonds in the SIP species (panels (a) and (b), respectively) and for H2O···H3O+ and Cl−···H3O+ hydrogen bonds in the CIP species (panels (c) and (d), respectively). Distribution functions extracted from classical AIMD (solid lines) and quantum AIPI (dashed lines) simulations are compared with the equilibrium values (vertical dotted lines) calculated for the optimized structures; the SIP distributions were averaged over three equivalent hydrogen bonds. Insets in panels (a) and (c) show the equilibrium structures of the SIP and CIP species, respectively.

stabilize the intermediate layer of three water molecules separating the Cl−/H3O+ ion pair and provide its extraordinary stability. Classical thermal fluctuations at 100 K result in the usual broadening of the distribution function of interatomic distances, but do not affect the average structure, whose rootmean-square deviation (rmsd) from the equilibrium structure is only 0.01 Å. Most of the structural effect comes from a minor elongation of the H···Cl distance from 2.09 Å at equilibrium to 2.11 Å at 100 K (see Table 1). The distribution function of the asymmetric stretch coordinate δ, defined as the proton displacement from the geometric hydrogen bond midpoint δ = (rAH−rHD)/2, allows one to characterize the hydrogen bond type (see Figure 1). In hydrogen bonds with oxygen acting 3070



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expansion is furthermore enhanced when adding quantumness to the nuclei (cf. “cl” and “qm” entries in Table 1). The quantum-induced expansion follows the same scenario for all the bonds: increase of the donor−acceptor distance and expansion of the hydrogen−acceptor distance in conjunction with a minor contraction of the covalent donor−hydrogen bond. Consequently, quantum mechanical fluctuations push the hydrogen bond acceptor further away from the donor and at the same time tighten the covalent bond between the donor and the hydrogen atom. As a result, these three ring-forming hydrogen bonds in the CIP cluster become not only more expanded but also, due to the quantum fluctuations, more asymmetrical than what purely classical thermal motion can account for. This is nicely exemplified by the average displacement of the hydrogen position from the midpoint of the donor−acceptor distance (δ) in the H2O···H3O+ bond, which shifts from 0.24 Å at equilibrium to 0.27 Å in the classical dynamics and even further to as much as 0.35 Å in the quantum case (see shifts of the peak positions in the asymmetric stretch coordinate distributions in panel (c) of Figure 1). A strikingly reversed quantum effect is observed in the case of the bridging hydrogen bond between the chloride ion and the hydronium, Cl−···H3O+, which directly connects the two ions within the CIP. Already classical thermal motion at 100 K shifts the average position of the proton slightly toward the bond midpoint: from 0.37 Å in the equilibrium structure to a value of 0.31 Å. However, quantum effects are exclusively responsible in bringing the proton almost to the center of the bond, namely only ∼0.09 Å away (see panel (d) of Figure 1 for corresponding P(δ) distributions; see also top left and middle left panels in Figure 3 for average O−H and H−Cl distances). This unexpected result of quantum mechanical fluctuations pushing the proton back toward the conjugate base counteracts, in a sense, dissociation of the acid into Cl− and H3O+ ions, thus rendering the term “ion pair” questionable in the present context. Despite this effect, the Cl−···H3O+ bond contracts only slightly (by ∼0.04 Å) due to thermal fluctuations compared to the equilibrium structure, but its length stays unchanged (within the accuracy of our data) after adding quantum effects at 100 K (see Table 1 for average Cl−O distance). Moreover, there is a noticeable correlation between the rOH and rHCl distances on the classical level, showing that whenever the proton moves further away from the hydrogen bond donor, it comes closer to the acceptor and vice versa (see panel (c) in Figure 2). Apart from an enhanced amplitude of the fluctuations, the corresponding quantum distribution P(rOH,rHCl) shows an even more pronounced correlation of the two distances (cf. panels (c) and (d) in Figure 2). As a result, the proton moves along the Cl···O axis in a way that almost perfectly conserves the donor−acceptor distance in the CIP structure, which is not the case in the SIP species (cf. panels (b) and (d) in Figure 2). In a nutshell, a scenario is revealed in which quantum effects on the central bond of the CIP structure do not work on the donor−acceptor distance, but exclusively center the proton within that hydrogen bond. A refined analysis of thermal versus quantum delocalization can be achieved using a tensorial quantity with principal axes corresponding to the amount of delocalization along a given direction in space as visualized by ellipsoids.23 The ellipsoids representing the purely thermal fluctuations of the heavy atoms in the four-membered ring of the CIP structure are elongated along the axis perpendicular to the ring (see top panels in Figure 3). Such out-of-plane motion is more likely than in-

Figure 2. Density plots of two-dimensional probability distribution functions for the SIP (panels (a) and (b)) and CIP (panels (c) and (d)) species at 100 K sampled during the classical AIMD (panels (a) and (c)) and quantum AIPI (panels (b) and (d)) simulations as a function of the two interatomic distances rOH and rHCl. The probability increases from violet to red to yellow.

oxygen atom. The SIPC3 conformation with all free protons residing at the same side of the corresponding plane, which is the global minimum, has a three-fold rotational symmetry about the Cl−−H3O+ pseudo-axis; note that there are two equivalent such forms. The nonsymmetrical SIPC1 conformation is formed when one of the dangling OH bonds points in the opposite direction than the other two. At sufficiently high temperature the cluster can switch between its C3 and C1 forms by spontaneously flipping one or more of the dangling OH bonds. At 100 K, however, there is not enough kinetic energy available for the proton to surmount the potential energy barrier of about 1.2 kcal/mol that separates the two species (noting that kBT ≈ 0.2 kcal/mol at T = 100 K). As a result, such flipping events are observed very rarely on the time scale of our classical simulations. Quantum effects are exclusively responsible for lowering the effective energy barrier enough to allow these dangling OH bonds to reorient vividly and, thus, to interconvert the SIPC3 and SIPC1 species easily at this temperature. The properties of the HCl(H2O)4 cluster change dramatically upon formation of the CIP (see inset in panel (c) of Figure 1 for the equilibrium structure). Unusually strong quantum effects observed in the CIP structure push the dissociated ion pair, Cl−···H3O+, back toward the undissociated limit, H2O···HCl. To highlight this unexpected behavior, we first note that already in the classical approximation some extraordinary features of the CIP cluster become apparent. Although the extent of thermal broadening of the O−H bond length distributions, as quantified by the rmsd (not shown), is similar to that observed in the SIP structure, the maxima and thus average values are significantly shifted with respect to the equilibrium structure. The donor−acceptor as well as the hydrogen−acceptor distance in H2O···H3O+, H2O···H2O, and Cl−···H2O hydrogen bonds (all forming the four−membered ring in CIP) expand due to the thermal fluctuations at 100 K (cf. “eq” and “cl” entries in Table 1). This intermolecular 3071



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waters, does not feature quantum effects beyond trivial broadening of bond length distribution functions. In contrast, dramatic quantum effects are found for the CIP species. Here, the anion, Cl−, is directly connected via a hydrogen bond to the cation, hydronium H3O+, within a four-membered ring formed together with two intact water molecules (the fourth water molecule bridges the ion pair in terms of a three−membered ring). The proton within this specific hydrogen bond is observed to center upon inclusion of quantum effects, whereas both the equilibrium structure and the thermal average feature a clear-cut (i.e., short) covalent O−H bond, thus forming hydronium that donates a usual (i.e., long) hydrogen bond to the anion, Cl−···H. Based on these findings, quantum effects can be said to push back the proton to the conjugate base thus counteracting acid dissociation. Simultaneously, the proton’s quantum spread becomes spherical, as opposed to disklike protons in all other cases of “normal” hydrogen bonds. All this consistently implies that this CIP features a low-barrier hydrogen bond as its core structural motif, Cl···H···OH2, and thus a Zundel-like scenario including fluxionality. These findings have implications beyond clusters and microsolvation. The recent XAFS data19 provide a detailed picture about the structure of ion pairs in aqueous HCl at ultrahigh concentration. In the Cl−/H3O+ CIP, the bridging proton was found to reside close to the bond center, thus approaching a hydrogen bond centering in a heteronuclear asymmetric donor−acceptor situation, whereas a standard hydrogen bond characterizes Cl−···H2O and thus ion solvation. In particular, the bridging proton in the CIP motif is 1.60 and 1.37 Å away from the Cl and O sites, respectively, yielding a contracted donor−acceptor distance of 2.98 Å in the Cl···H···OH2 structure.19 Thus, the O site in CIP cannot be said to be a hydronium cation, H3O+, which is characterized by three short, covalent O−H bonds. Instead, this part of the CIP structure, Cl···H···OH2, is similar to the structure of the Zundel ion, [H2O···H···OH2]+. The CIP pattern is also distinctly different from the solvation shell of Cl-(aq), resulting in measured Cl···H and Cl···O distances of 2.23 and 3.14 Å, respectively, and, thus, a O−H distance in the usual range of covalent OH bonds, i.e., roughly 1 Å. It is puzzling that state-of-the-art AIMD simulations do not yield the observed donor−acceptor contraction in the CIP. 21,22 In addition, they consistently predict distinctly asymmetric bonds:21,22 Cl−···[H−OH2]+ with Cl···H distances substantially longer than the measured value. The resulting picture is that of a well-defined hydronium cation that donates a normal hydrogen bond to Cl−. A key assumption underlying these simulations,21,22 however, is the classical approximation to nuclear motion, thus yielding “classical” structures that usually describe the properties of aqueous solutions extremely well. Going back to our results on the CIP cluster, we find that indeed the traditional ion pair structure, Cl−···[H−OH2]+, is recovered once we switch off quantum effects. Collecting all facts, the most straightforward explanation would be that nuclear quantum effects are important in determining the structure of CIPs in such solutions, thereby introducing quantum fluxionality. This conjecture suggests carrying out AIPI simulations of HCl in bulk water at the concentration limit to unravel the hereby predicted important quantum (isotope) effects on hydrogen bonding at such extreme conditions. At the same time, experimental investigation of the isotope effect on the structure of HCl(aq) at extreme

Figure 3. Nuclear probability distribution functions for the Cl−···H3O+ (left) and H2O···H3O+ (right) hydrogen bonds in the CIP species at 100 K defined by the covariance matrix Uij of the atomic trajectories r⃗(t), Uij = ⟨(r⃗(t) − r⃗0)i (r⃗(t) − r⃗0)j⟩ and visualized as ellipsoids with principal axes equal to those of Uij; all ellipsoids were scaled by a factor of 2 for clarity. The plane of the four-membered ring is perpendicular to the paper plane (see inset in panel (c) of Figure 1 for the equilibrium structure), and r0⃗ is a reference structure. Numbers are average distances between atomic positions in the reference structure in Å. Top: classical thermal anisotropy (here r⃗0 is the average structure obtained from the classical ab initio trajectory); Middle: quantum thermal anisotropy (here r⃗0 is the average path centroid structure obtained from the quantum path integral trajectory and r(⃗ t) is the instantaneous centroid position); Bottom: diagonal part of the nuclear one-particle density matrix (here r⃗0 is the instantaneous centroid position at a given simulation step and r(⃗ t) describes all path integral bead positions at the same trajectory step).

plane fluctuations, which are restricted by the hydrogen bonds that hold the ring together (see inset in panel (c) of Figure 1 for the equilibrium structure); the oxygen that donates a hydrogen bond to the water molecule in the three-membered ring experiences the largest fluctuations. Adding quantum fluctuations at 100 K results in a more pronounced anisotropy of the ellipsoids. Interestingly, not only the protons but also the oxygen sites are very strongly influenced by these quantum effects, thus making the CIP structure softer, whereas the much heavier Cl site is not perturbed significantly (see middle panel in Figure 3). In addition, the shortest principal axis of all ellipsoids is oriented along the hydrogen bond, whereas the longest axis is perpendicular to the four−membered ring. The quantum delocalization of the nuclei as represented by the average spread of the corresponding paths in the simulation is analyzed in the bottom panel in Figure 3; the two heavy nuclei, Cl and O, are spherical and well localized as expected. The O− H···Cl hydrogen bond again shows distinctly different characteristics compared to O−H···O: the proton in the latter has a disklike (oblate) shape, whereas the former is close to spherical. This goes hand in hand with the observation that protons in “normal” hydrogen bonds are oblate, whereas they are spherical in centered hydrogen bonds,23 which supports our conclusions for CIP. AIPI simulations show that the SIP and CIP structure motifs of dissociated HCl in a microsolvation environment consisting of four water molecules, HCl(H2O)4, show distinctly different nuclear quantum effects at 100 K. The SIP structure can be constructed conceptually by attaching the Cl− anion to an Eigen cation, [H3O(H2O)3]+, via three accepted hydrogen bonds. This species, where anion and cation share three solvent 3072



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Molecular Dynamics Simulations. Chem. Phys. Lett. 2011, 501, 238− 244. (8) Forbert, H.; Masia, M.; Kaczmarek-Kedziera, A.; Nair, N. N.; Marx, D. Aggregation-Induced Chemical Reactions: Acid Dissociation in Growing Water Clusters. J. Am. Chem. Soc. 2011, 133, 4062−4072. (9) Takayanagi, T.; Takahashi, K.; Kakizaki, A.; Shiga, M.; Tachikawa, M. Path-Integral Molecular Dynamics Simulations of Hydrated Hydrogen Chloride Cluster HCl(H 2 O)4 on a Semiempirical Potential Energy Surface. Chem. Phys. 2009, 358, 196−202. (10) Weimann, M.; Fárník, M.; Suhm, M. A. A First Glimpse at the Acidic Proton Vibrations in HCl-Water Clusters via Supersonic Jet FTIR Spectroscopy. Phys. Chem. Chem. Phys. 2002, 4, 3933−3937. (11) Huneycutt, A. J.; Stickland, R. J.; Hellberg, F.; Saykally, R. J. Infrared Cavity Ringdown Spectroscopy of Acid−Water Clusters: HCl−H2O, DCl−D2O, and DCl−(D2O)2. J. Chem. Phys. 2003, 118, 1221−1229. (12) Ortlieb, M.; Birer, Ö .; Letzner, M.; Schwaab, G. W.; Havenith, M. Observation of Rovibrational Transitions of HCl, (HCl)2, and H2O−HCl in Liquid Helium Nanodroplets. J. Phys. Chem. A 2007, 111, 12192−12199. (13) Skvortsov, D.; Lee, S. J.; Choi, M. Y.; Vilesov, A. F. Hydrated HCl Clusters, HCl(H2O)1−3, in Helium Nanodroplets: Studies of Free OH Vibrational Stretching Modes. J. Phys. Chem. A 2009, 113, 7360− 7365. (14) Gutberlet, A.; Schwaab, G.; Birer, Ö .; Masia, M.; Kaczmarek, A.; Forbert, H.; Havenith, M.; Marx, D. Aggregation-Induced Dissociation of HCl(H2O)4 below 1 K: The Smallest Droplet of Acid. Science 2009, 324, 1545−1548. (15) Zwier, T. S. Squeezing the Water out of HCl(aq). Science 2009, 324, 1522−1523. (16) Morrison, A. M.; Flynn, S. D.; Liang, T.; Douberly, G. E. Infrared Spectroscopy of (HCl) m(H2O) n Clusters in Helium Nanodroplets: Definitive Assignments in the HCl Stretch Region. J. Phys. Chem. A 2010, 114, 8090−8098. (17) Flynn, S. D.; Skvortsov, D.; Morrison, A. M.; Liang, T.; Choi, M. Y.; Douberly, G. E.; Vilesov, A. F. Infrared Spectra of HCl−H 2O Clusters in Helium Nanodroplets. J. Phys. Chem. Lett. 2010, 1, 2233− 2238. (18) Mancinelli, R.; Sodo, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. Influence of Concentration and Anion Size on Hydration of H+ Ions and Water Structure. J. Phys. Chem. B 2009, 113, 4075−4081. (19) Fulton, J. L.; Balasubramanian, M. Structure of Hydronium (H3O+)/Chloride (Cl−) Contact Ion Pairs in Aqueous Hydrochloric Acid Solution: A Zundel-like Local Configuration. J. Am. Chem. Soc. 2010, 132, 12597−12604. (20) Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods; Cambridge University Press: Cambridge, 2009. (21) Sillanpäa,̈ A. J.; Laasonen, K. Structure and Dynamics of Concentrated Hydrochloric Acid Solutions. A First Principles Molecular Dynamics Study. Phys. Chem. Chem. Phys. 2004, 6, 555− 565. (22) Heuft, J. M.; Meijer, E. J. A Density Functional Theory Based Study of the Microscopic Structure and Dynamics of Aqueous HCl Solutions. Phys. Chem. Chem. Phys. 2006, 8, 3116−3123. (23) Benoit, M.; Marx, D. The Shapes of Protons in Hydrogen Bonds Depend on the Bond Length. ChemPhysChem 2005, 6, 1738−1741. (24) Marx, D.; Parrinello, M. Ab Initio Path-Integral Molecular Dynamics. Z. Phys. B 1994, 95, 143−144. (25) Marx, D.; Parrinello, M. Ab Initio Path Integral Molecular Dynamics: Basic Ideas. J. Chem. Phys. 1996, 104, 4077−4082. (26) Tuckerman, M. E.; Marx, D.; Klein, M. L.; Parrinello, M. Efficient and General Algorithms for Path Integral Car−Parrinello Molecular Dynamics. J. Chem. Phys. 1996, 104, 5579−5588. (27) Marx, D. Advanced Car−Parrinello Techniques: Path Integrals and Nonadiabaticity in Condensed Matter Simulations. In Computer Simulations in Condensed Matter: From Materials to Chemical Biology; Ferrario, M., Ciccotti, G., Binder, K., Eds.; Springer: Berlin/ Heidelberg, 2006; Vol. 2, pp 507−539. (28) CP2k Developers Team, http://cp2k.berlios.de.

concentrations, ideally as a function of concentration, temperature, and pressure, is recommended.

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COMPUTATIONAL METHOD

Nuclear quantum effects in microsolvated HCl were studied using the AIPI approach20,24−27 according to Feynman’s formulation of quantum statistical mechanics. For the present study, the AIPI methodology as implemented by us in the CP2k program package28,29 is used. All calculations were carried out in the framework of density functional theory using the BLYP functional30,31 expanding the electronic density using an augmented mixed Gaussian and plane waves (GAPW) method.32 An augmented correlation-consistent polarized triple-ζ basis set (aug-cc-pVTZ)33,34 was used for the localized functions, and a cutoff of 280 Ry was applied for the plane waves while treating all electrons explicitly.35 A cubic 16 Å supercell was used with a nonperiodic version of the Poisson solver36 to properly treat isolated systems.20 The nuclei were propagated on the Born−Oppenheimer surface of the electronic ground state using a time step of 0.2 fs and the temperature was kept at 100 K using massive Nosé−Hoover chain thermostatting.37 The AIPI simulations, discretizing the thermal PI into P = 16 beads, were supplemented by “classical” AIMD simulations, in which the nuclei are treated as classical point particles, to discriminate between quantum and thermal effects at identical conditions. AIPI runs were (formally) 20 ps long, while the AIMD trajectories were extended over 30 ps.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS The work has been partially funded by Deutsche Forschungsgemeinschaft (DFG MA 1547) within the framework of Forschergruppe FOR 618 on “Molecular Aggregation” and by Research Department “Interfacial Systems Chemistry” (RD IFSC) at RUB. The simulations have been carried out using resources from BOVILAB@RUB and Rechnerverbund−NRW (LiDO Dortmund and Cheops Köln).

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REFERENCES

(1) Lee, C.; Sosa, C.; Planas, M.; Novoa, J. J. A Theoretical Study of the Ionic Dissociation of HF, HCl, and H2S in Water Clusters. J. Chem. Phys. 1996, 104, 7081−7085. (2) Bacelo, D. E.; Binning, R. C.; Ishikawa, Y. Ab Initio Monte Carlo Simulated Annealing Study of HCl(H2O)n (n = 3, 4) Clusters. J. Phys. Chem. A 1999, 103, 4631−4640. (3) Re, S.; Osamura, Y.; Suzuki, Y.; Schaefer, H. F. Structures and Stability of Hydrated Clusters of Hydrogen Chloride, HCl(H2O)n, n = 1−5. J. Chem. Phys. 1998, 109, 973−977. (4) Odde, S.; Mhin, B. J.; Lee, S.; Lee, H. M.; Kim, K. S. Dissociation Chemistry of Hydrogen Halides in Water. J. Chem. Phys. 2004, 120, 9524−9535. (5) Ndongmouo, U. F. T.; Lee, M.-S.; Rousseau, R.; Baletto, F.; Scandolo, S. Finite-Temperature Effects on the Stability and Infrared Spectra of HCl(H2O)6 Clusters. J. Phys. Chem. A 2007, 111, 12810− 12815. (6) Masia, M.; Forbert, H.; Marx, D. Connecting Structure to Infrared Spectra of Molecular and Autodissociated HCl−Water Aggregates. J. Phys. Chem. A 2007, 111, 12181−12191. (7) Sugawara, S.; Yoshikawa, T.; Takayanagi, T.; Tachikawa, M. Theoretical Study on Mechanisms of Structural Rearrangement and Ionic Dissociation in the HCl(H2O)4 Cluster with Path-Integral 3073



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(29) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach. Comput. Phys. Commun. 2005, 167, 103−128. (30) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098−3100. (31) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle− Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (32) Lippert, G.; Hutter, J.; Parrinello, M. The Gaussian and Augmented-Plane-Wave Density Functional Method for Ab Initio Molecular Dynamics Simulations. Theor. Chem. Acc. 1999, 103, 124− 140. (33) Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (34) Woon, D. E.; Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. III. The Atoms Aluminum Through Argon. J. Chem. Phys. 1993, 98, 1358−1371. (35) Krack, M.; Parrinello, M. All-Electron Ab-Initio Molecular Dynamics. Phys. Chem. Chem. Phys. 2000, 2, 2105−2112. (36) Martyna, G. J.; Tuckerman, M. E. A Reciprocal Space Based Method for Treating Long Range Interactions in Ab Initio and ForceField-Based Calculations in Clusters. J. Chem. Phys. 1999, 110, 2810− 2821. (37) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé−Hoover Chains: The Canonical Ensemble via Continuous Dynamics. J. Chem. Phys. 1992, 97, 2635−2643.

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Quantum Induced Bond Centering in Microsolvated HCl: Solvent

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