Structural Characterization of Sulfur-Containing Water Clusters

Article pubs.acs.org/JPCA

Structural Characterization of Sulfur-Containing Water Clusters Using a Density-Functional Based Tight-Binding Approach Kseniia A. Korchagina, Aude Simon, Mathias Rapacioli, Fernand Spiegelman, and Jérôme Cuny* Laboratoire de Chimie et Physique Quantiques (LCPQ), Université de Toulouse III [UPS] and CNRS, 118 Route de Narbonne, F-31062 Toulouse, France S Supporting Information *

ABSTRACT: A global optimization search of low-energy isomers is carried out to investigate the structural and stability properties of sulfur-containing water clusters, including both (H2O)nSO42− and (H2O)nH2SO4 aggregates. The systematic optimization algorithm involves a combination of parallel-tempering molecular dynamics and periodic gradient-driven quenches with energy and energy-gradient calculations performed using the Self-Consistent-Charge Density-Functional based Tight-Binding (SCC-DFTB) scheme. Comparisons with new MP2 and DFT calculations on the smallest systems and previous ab initio investigations of the literature show that the SCC-DFTB approach provides a fairly accurate description of both neutral and ionic species, comparable to that of DFT. Structural and stability features of larger sulfur-containing clusters, with up to 20 water molecules, are also determined using the SCC-DFTB scheme. The interest of this work is 2fold: (i) the benchmark on small species demonstrates the ability of SCC-DFTB to describe complex potential energy landscapes involving hydrogen-bonds and proton transfers; (ii) it opens the way to the study of large clusters that can hardly be performed within ab initio approaches.

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stabilized.17,24 Up to n = 6, only sulfate-bridging water molecules are observed at low temperature, whereas an IR signature of water−water hydrogen bonds (HB) appears for n ≥ 7.18 Wang et al. also demonstrated a decrease of the electron binding energy of small (H2O)nSO42− aggregates (n = 4−7) when the temperature is increased from 12 K to room temperature,23 which was interpreted as the coexistence at high temperature of several isomers above the global minima. The number of water molecules required to close the first solvation shell of SO42− has been the subject of some controversy. Several studies postponed this closure to occur at n ≈ 12,17,18,22 even though the exact number is still subject to discussion.25,26 For the largest aggregates (up to ∼250), O’Brien and coauthors observed that the IR spectra of (H2O)nSO42− clusters with n ≤ 43 do not display any IR signature of dangling hydrogen atom, whereas for n > 43 a band corresponding to free-OH groups was detected.20 It was also suggested that the HB network of the water molecules within the second and third solvation shell of the ion is fully H-bonded.21 The structures of (H2O)nH2SO4 clusters have also been investigated mainly in view to establish and understand the possible nucleation mechanisms of H2SO4/ H2O particles in the atmosphere.27−31 Other studies have focused on the search for chemical agents accelerating the nucleation,32−36 which is still a question under debate.

INTRODUCTION Chemical processes occurring in the lower layers of the atmosphere (troposphere and stratosphere) are of fundamental interest as they have a strong impact on the climate and its evolution.1,2 Consequently, since the early 1970s, a significant effort has been devoted to the experimental characterization of the chemical composition and behavior of atmospheric particles.3−8 Among these studies, in situ ion composition measurements demonstrated the existence of charged molecular aggregates in the stratosphere,4−6 in particular negatively charged species such as nitrate- and sulfate-containing water clusters. Exposed to short-wave solar radiation that facilitate nucleation, ion−ion recombination, and exchange and growth of particles, the latter species lead to the formation of aerosol layers.9−12 These grown atmospheric particles initiate the process of acid cloud formation and participate in reactions leading to the destruction of the ozone layers in polar regions.13−15 Hence, sulfate−water clusters have a strong impact on the physicochemical properties of the atmosphere and represent a class of species promoting important phenomena. Sulfates also display important industrial applications as they are largely found in fertilizers and can be used as algaecides. Sulfate species have thus motivated a large number of theoretical and experimental studies. From an experimental point of view, infrared (IR)16−21 and photoelectron spectroscopy22,23 have been widely used to characterize the structures of (H2O)nSO42− aggregates from small (n = 3) to large sizes (n = 250). It was shown that the SO42− anion needs at least three water molecules to be © 2016 American Chemical Society

Received: August 15, 2016 Revised: October 24, 2016 Published: November 3, 2016 9089

DOI: 10.1021/acs.jpca.6b08251 J. Phys. Chem. A 2016, 120, 9089−9100

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The Journal of Physical Chemistry A

discussed in comparison with DFT and wave function-based methods. The outline of the article is as follows: the computational model is described in computational details, the results of the simulations are presented in results and discussion, and the main outcomes and perspectives are summarized in the conclusion.

To complement these experimental investigations, many theoretical studies have been conducted, sometimes in parallel, to characterize the equilibrium structures on the potential energy surfaces (PES) of (H 2 O) n SO 4 2− (n = 1− 50)18,20,21,23,25,26,37−46 and (H2O)nH2SO4 (n = 1−9)47−53 aggregates. These studies are of fundamental interest to provide a clearer understanding of the structure of such aggregates and to assign experimental IR signals to specific isomers. They also illustrate the large variety of low-energy structures found for each cluster size,43 as well as the sensitivity of their energetic ordering with respect to the applied computational approach.43,44 These theoretical studies are based on three main levels of theory: (i) ab initio quantum chemical calculations such as the second-order Møller−Plesset perturbation theory (MP2) and coupled cluster theory including singles, doubles, and perturbative triples (CCSD(T)); (ii) methods based on the density functional theory (DFT); (iii) force-field (FF) potentials. FF potentials provide access to large system sizes and allow for efficient exploration of the PES when coupled to an efficient global optimization scheme. For instance, such a study was performed by Smeeton et al. for (H2O)nSO42− (n = 3−50) clusters.45 A polarizable force-field AMOEBA (atomic multipole optimized energetics for biomolecular applications)54−60 was also developed by Ponder and co-workers and has proved to efficiently and accurately describe the PES of sulfate−water clusters.26,43,44,58 This potential provides relative energies of low-lying configurations qualitatively comparable (by ∼2 kcal·mol−1) to RIMP2+ΔCCSD(T) reference energies. However, these potentials have weaknesses. For instance, they are poorly transferable, cannot describe chemical bond formation and/or breaking, and do not provide an explicit description of the electronic structure. In contrast, wave function- and DFT-based methods are more accurate, even though functionals, basis sets, and dispersion corrections have to be chosen with care as demonstrated by Mardirossian et al.44 However, the computational cost of these approaches prevents a proper exploration of the PES and global minima search even for small-size clusters. In between the FF and ab initio approaches, one can identify intermediate levels of theory such as the self-consistent-charge density-functional based tight-binding method (SCCDFTB).61−64 The latter scheme provides an explicit electronic structure description, allowing the treatment of bond breaking and formation while keeping a low computational cost due to the use of a minimal valence basis set and parametrized integrals. The SCC-DFTB method has already been successfully applied to the description of complex molecular systems, among which are water clusters and polycyclic aromatic hydrocarbons (PAHs).65−69 More recently, Jahangiri et al. also showed that various formulations of the SCC-DFTB method provide a good description of the structure, energetics, charge distributions, and vibrational spectra of various anioncontaining water clusters, in particular the (H 2O)SO42− dimer.70 The present article is a contribution to the benchmark and validation of the SCC-DFTB scheme for sulfur-containing water clusters. We achieve a global structural investigation of (H2O)nSO42− (n = 2−6, 10, 12, 13, 15, 20) and (H2O)nH2SO4 (n = 2−6, 10, 15, 20) by coupling a SCC-DFTB description with parallel-tempering molecular dynamics simulations. This allows for an extensive exploration of their PES, followed by extensive gradient quenching to obtain a variety of low-energy isomers. The structural features and stability properties are

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COMPUTATIONAL DETAILS Description of the PES. To describe the PES of the various aggregates studied in this work, we used the SCCDFTB scheme implemented in the deMonNano code.71 In this approach, the electronic energy is given by the following equation: occ

E SCC − DFTB =

∑ ⟨ψi|Ĥ 0|ψi⟩ + ∑ Uαβ + i

−

αβ

1 2

∑ ΔqαΔqβγαβ αβ

C αβ fdamp (R αβ) 6 6 R αβ αβ

∑

(1)

where the first term is a band energy term defined from parametrized integrals and the second term is a repulsive interaction expressed as a sum over all pairs of atoms. In the present study, we used the mio-set for Slater−Koster tables of integrals and repulsive interactions.72 The third term of eq 1 is the second order correction term expressed as a function of the atomic charge fluctuations Δq, and the last term is an empirical correction that describes the dispersion interactions.73−75 As proposed by Rapacioli and co-workers,64 improvement of the description of the electrostatic interactions in molecular cluster can be obtained by replacing the original Mulliken charges by the class IV/charge model 3 (CM3) charges,76,77 defined as atoms

qαC M3 = qαMull +

∑

[DZαZα′Bκκ ′ + C ZαZα′Bκκ ′2 ]

α ′≠ α

(2)

78

where Bκκ′ is the Mayer’s bond order, and CZαZα′, DZαZα′ are empirical parameters to determine. In their studies of water clusters,66 Simon and co-workers developed a SCC-DFTB potential that provides geometries and vibrational and energetic characteristics close to experimental values79 and to high quality CCSD(T)/aug-cc-pVTZ calculations. The parametrization of the CM3 charges used in this work, namely, DOH = 0.129, was retained in the present study, while DOS was determined in order to reproduce the MP2/aug-cc-pVTZ value of the electrostatic potential (ESP) derived from the SO42− atomic charges. This yields a value DOS = 0.238. The DSH parameter was set to zero. Exploration of the PES. A variety of algorithms exist to achieve global optimization. In the present study, we used a 2fold scheme: finite temperature exploration of the PES combined with periodic gradient quenching to reach the minima. The finite temperature exploration was conducted with the molecular dynamics parallel-tempering (MDPT) algorithm,80−82 as implemented in the deMonNano code.69,71 We used a temperature range going from 20 to 320 K with 60 replicas, i.e., a linear distribution of temperatures with a 5 K step. The trajectories were 4 ns long for each cluster, and the integration time step of the equations of motion was 0.2 fs. We found that a reasonable time interval for the PT exchanges was 400 fs. We used a Nosé−Hoover chain of five thermostats with frequencies 800 cm−1 to achieve an exploration in the canonical ensemble.83,84 9090


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The Journal of Physical Chemistry A To obtain the low-lying energy minima, we proceeded as follows: for one in four temperatures, 1000 geometries were periodically selected and locally optimized using a conjugate gradient algorithm.85 This led to a total of 15000 optimized geometries per aggregate. To classify the resulting isomers for each (H2O)nSO42− aggregate, we used the “n.s.w-l” nomenclature proposed by Lambrecht et al.43 Within this notation, n is the number of water molecules, s is the number of sulfate− water HB, w is the number of water−water HB bonds, and l is a number associated with each isomer in a given “n.s.w” series. The labeling of the (H2O)nH2SO4 isomers was done in a slightly different way, namely, “n.s.s′.w-l”, where s and s′ corresponds to two different connection patterns: s for a hydrogen of a water molecule bound to an oxygen of H2SO4 and s′ for a hydrogen of the sulfuric acid bound to an oxygen of a water molecule. To differentiate between isomers, the optimized configurations were sorted with respect to their energy and oxygen topology. In the following, the isomers are characterized by their relative energies, Erel, above the absolute minimum, Erel(ZPE) being the equivalent relative energy including the zero-point energy (ZPE) calculated from the harmonic modes. Furthermore, to evaluate the strength of the water−sulfate and −sulfuric acid interaction and to further assess the accuracy of the SCC-DFTB approach, we also evaluated binding energies for a variety of selected isomers. The detailed results and discussions on the structures and binding energies of small aggregates (n = 0−6) are reported in the Supporting Information (SI), while only the most relevant features are discussed in the main text. DFT and Wave Function Calculations. In order to establish reference binding energies and geometries, we performed ab initio MP2 calculations in combination with the aug-cc-pVTZ basis set of Dunning and co-workers,86,87 which has been used as a reference scheme in a number of studies on small sulfate−water clusters,43,70 and has been proved to provide binding energies close to CCSD(T)/aug-cc-pVTZ and CCSD(T)/CBS* quality. 44 Except for one case, 51 no application of this method has been performed for sulfuric acid clusters. We also carried out DFT calculations using three distinct exchange-correlation functionals: (i) the popular hybrid B3LYP functional,88 which was used in most studies on (H2O)nH2SO4 clusters although it poorly performs for (H2O)nSO42− binding energies,43 (ii) the M11-L functional from the Minnesota functionals family, which was shown to behave satisfactorily for inorganic molecules and noncovalent interactions,89 (iii) the M11 hybrid meta-GGA functional, which was shown to provide accurate binding energies for (H2O)nSO42− clusters.44,90 Three basis sets were tested: 6-311+ +G(d,p),91 TZVP,92,93 and QZVP.94 Finally, we also tested the impact of basis set superposition errors (BSSE) by using the counterpoise method of Boys and Bernardi.95 All DFT and wave function calculations were performed with the Gaussian 09 package.96

Figure 1. SCC-DFTB geometries of (H2O)SO42− and (H2O)H2SO4.

binding energies of these two complexes also compare well with reference calculations. Indeed, for (H2O)SO42− and (H2O)H2SO4, the SCC-DFTB binding energies are −31.12 and −12.33 kcal·mol−1, respectively, whereas they are −29.90 and −11.85 kcal·mol−1 at the MP2/aug-cc-pVTZ level of theory. In both cases, the SCC-DFTB displays an error of ∼4% as compared to the reference calculations. These results on (H2O)SO42− are consistent with those recently obtained by Jahangiri et al. using various formulation of the SCC-DFTB formalism.70 Finally, it is worth pointing out that the binding energy difference between (H2O)SO42− and (H2O)H2SO4 was expected due to a stronger electrostatic contribution to the binding energy in the case of SO42−. For the two series of (H2O)nSO42− and (H2O)nH2SO4 clusters with n = 2−6, we present in the SI a detailed description of all the low-energy configurations obtained from the MDPT exploration of the potential energy landscapes. The geometries and binding energies of the various isomers are carefully described and compared with the ones previously reported in the literature that were obtained using higher level of theory, mainly DFT or MP2. In Figure 2 are reported the lowest-energy isomers presently found for each (H2O)nSO42− aggregate as well as a number of higher energy structures of particular interest. The data displayed in Figure 2 and in the SI show that SCCDFTB provides a description of the PES of the (H2O)nSO42− clusters in agreement with DFT as the lowest-energy structures obtained are, in most cases, identical to those previously reported. For instance, 2.4.0−1 is the lowest-energy configuration reported in the DFT-based study of Pye and Rudolph.37 3.6.0−1, 3.6.0−2, and 3.6.0−3 are three lowest energy structures already reported by Pye and Rudolph37 and Lambrecht et al.,43 although the global minimum is different in each study (3.6.0−1 in the present study, 3.6.0−3 for Lambrecht et al., and 3.6.0−2 for Pye and Rudolph). For (H2O)4SO42−, the SCC-DFTB lowest-energy conformation belongs to the 4.8.0 series, which is consistent with the studies by Gao et al.42 and Wang et al.23 who found 4.8.0−2 as being the global minimum, but differs from the results by Lambrecht et al. that predict 4.5.3−1 to be the global minimum.43 For the larger clusters, i.e., (H2O)5SO42− and (H2O)6SO42−, water− water HB start to be competitive with sulfate−water HB. This leads to a wide spectrum of low-energy isomers and an energetic ordering strongly sensitive to ZPE corrections. Nevertheless, the SCC-DFTB lowest-energy minimum of (H2O)5SO42− is still the structure with the highest number of sulfate−water HB, i.e., 5.10.0−1, which is consistent with the studies by Gao et al.,42 Pye et al.,37 and Wang et al.23 However, other isomers displaying water−water HB are now relatively close in energy, as for instance 5.7.3−1, which is only 0.34 kcal· mol−1 above 5.10.0−1. Isomer 5.7.3−1 is the lowest-energy isomer of (H2O)5SO42− found by Lambrecht et al.43 For

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RESULTS AND DISCUSSION SCC-DFTB Performances on Small Aggregates. For the isolated SO42− and H2SO4 molecules, the SCC-DFTB approach provides equilibrium geometries that are similar to MP2/augcc-pVTZ and DFT results as presented and discussed in the SI. More importantly, the SCC-DFTB geometries of the two dimers (H2O)SO42− and (H2O)H2SO4 (see Figure 1) are also in very good agreement with higher level computational methods as shown in Table S2 in the SI. The SCC-DFTB 9091


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Figure 2. Selected low-energy isomers of (H2O)nSO42− (n = 2−6) obtained in the present study. The corresponding relative energies (in kcal·mol−1) without (bold) and with (italic) ZPE corrections are also provided.

Figure 3. Selected low-energy isomers of (H2O)nH2SO4 (n = 2−6) obtained in the present study. The corresponding relative energies (in kcal· mol−1) without (bold) and with (italic) ZPE corrections are also provided.

(H2O)6SO42−, the isomer without water−water HB, i.e., 6.12.0−1, remains the global minimum when ZPE corrections are included. In contrast, without considering ZPE corrections, two quasi-isoenergetic isomers, 6.9.3−1 and 6.8.4−1, compete to be the lowest-energy structure and six other isomers are lying less than 1 kcal·mol−1 higher. Our global minimum without ZPE, the 6.9.3−1 isomer, is the same as that reported by Gao et al.42 and Wang et al. 23 Interestingly, the minima of (H2O)6SO42− presented in the SI, already display the three main motifs of water molecules that appear in the first solvation shell of larger (H2O)nSO42− clusters: (i) a three-membered ring of water molecules linked to three of the sulfate’s oxygens,

appearing in the 6.9.3−1 and 6.6.6−1 isomers; (ii) a fourmembered ring of water molecules linked to three of the sulfate’s oxygens, appearing in the 6.8.4 series; (iii) a “cube-like” motif composed of five water molecules and three of sulfate’s oxygens as in the 6.7.5-type isomers. These motifs do not contain any dangling hydrogen atom, which leads to closed HB networks. Experimentally, Zhou et al. suggested that up to n = 6, only sulfate-bridging water molecules are present at low temperature, whereas for n ≥ 7 an IR signature of water−water HB appears in the spectra of (H2O)nSO42− clusters.18 Although this transition appears to be strongly sensitive to small energy 9092


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on top of the water aggregate and participates to the HB network as a single or double HB donor, which leads to a lone oxygen atom or hydroxyl group, respectively. The second and most striking feature is that no deprotonated (i.e., ionic) structure has been selected as lowest-energy structure by the optimization scheme of (H2O)nH2SO4 (n = 3−6). The question of the relative stability of neutral versus ionic structures was addressed by the aforementioned DFT studies.47−51 In the case of (H2O)3H2SO4, as for the nature of the minimum-energy structure, this question appears to be strongly sensitive to computational details and no clear answer is given.47,49,51 In contrast, for (H2O)4H2SO4, (H2O)5H2SO4, and (H2O)6H2SO4, only ionic structures were proposed as lowest-energy configurations.49,51 At the SCC-DFTB level of theory, none of the reported (H2O)3H2SO4 isomers displays an ionic character. For (H2O)4H2SO4, only 4.2.1′.4−1 displays a proton transfer character between one water molecule and the HSO4− ion. However, this isomer is located ∼3 kcal·mol−1 higher in energy than the lowest-energy structure. Similarly, five ionic structures of (H2O)5H2SO4 were identified (see the SI), but they are found at least ∼2 kcal·mol−1 higher in energy than 5.3.2′.5−1. For (H2O)6H2SO4, lying ∼1 kcal·mol−1 higher in energy than the global minimum, two isomers (6.5.0′.6−1 and 6.5.0′.6−2) are deprotonated, i.e., display a (H2O)4(H5O2)HSO4-like structure in which the proton is in a Zundel-like environment. It is worth pointing out that these ionic structures, as well as the (H2O)4H2SO4 and (H2O)5H2SO4 ones, are characterized by a lone hydroxyl group of the H2SO4 molecule, whereas neutral forms are associated with a lone oxygen atom. These tendencies were also observed in the DFT studies of (H2O)nH2SO4 (n = 4−9) clusters.49,51 To ensure that the absence of deprotonated structures as SCC-DFTB lowest-energy isomers is not due to an inadequate exploration of the PES, MDPT explorations were performed starting from ionic structures, i.e., (H2O)n(H3O)HSO4 with n = 2−5. In all cases, this procedure leads to the structures presented in the SI, which demonstrates that the SCC-DFTB potential, although able to describe proton transfer processes, does not favor deprotonated structures for these particular sizes. Nevertheless, their appearance during our exploration of the PES demonstrates the ability of the SCC-DFTB potential to describe chemical bond-breaking and bond-forming in sulfate-containing aggregates at a cluster size that is rather close to what is observed at the DFT level of theory.49,51 Furthermore, as for (H2O)nSO42−, we present, in Table S5 of the SI, the binding energies of some selected (H2O)nH2SO4 isomers. These results show that SCC-DFTB only slightly overestimates binding energies with a mean absolute error of 1.72 and 1.49 kcal·mol−1 as compared to B3LYP/6-311+ +G(d,p) and M11-L/6-311++G(d,p) calculations, respectively. All these results demonstrate that the SCC-DFTB scheme provides a fairly accurate description of the complex potential energy landscapes of both small (H 2 O) n SO 4 2− and (H2O)nH2SO4 clusters. Indeed, although not strictly identical, the exploration of the SCC-DFTB PES leads to isomers similar to those previously reported at the DFT and wave function levels of theory. The lowest-energy minima obtained are often similar to the DFT ones, and we predict the appearance of water−water HB in (H2O)nSO42− aggregates at the cluster size previously reported. We also obtain low-energy minima with closed HB networks as reported in other theoretical studies and as observed experimentally.20,21,45 Furthermore, the SCCDFTB potential also behaves well for small (H2O)nH2SO4

variations, our results suggest that it occurs at the correct cluster size or really close to it at the SCC-DFTB level of theory. All these results thus demonstrate that the SCC-DFTB scheme provides a fairly accurate description of the various lowenergy isomers of small (H2O)nSO42− clusters. Indeed, we are able to locate most of the isomers previously reported in the literature,23,37,42,43 and to provide lowest-energy structures in agreement with these studies. Furthermore, in the cases where the SCC-DFTB and DFT lowest-energy conformations differ, the corresponding relative energies are always very small, less than 1 kcal·mol−1, which seems to indicate a satisfactory description of the energy landscape. It is worth pointing out that from n = 4, the energetic ordering of the low-energy conformations is strongly sensitive to the applied computational method, which leads to discrepancies even between DFT-based studies. SCC-DFTB thus displays an accuracy comparable to that of DFT schemes while displaying a significantly lower computational cost. This can be further confirmed by the comparisons presented in the SI between SCC-DFTB, DFT, and MP2 binding energies. The SCC-DFTB formalism makes it possible to study, a priori, different chemical species without any need of reparametrization as long as they are composed of the same chemical elements. In the present case, this allows for a direct comparison between the structural and energetics properties of (H2O)nH2SO4 and (H2O)nSO42− aggregates. So, following the same procedure as for the (H2O)nSO42− clusters, we present in Figure 3 the lowest-energy isomers found for each (H2O)nH2SO4 species as well as a number of relevant higher energy structures. A detailed discussion on all the reported isomers is provided in the SI. Even for the smallest species, clear differences appear with the structure of the corresponding (H2O)nSO42− aggregates. Indeed, the SCC-DFTB global minimum of (H2O)2H2SO4 is 2.1.1′.1−1, in agreement with Re et al. at the B3LYP/D95++(d,p) level of theory.49 However, neither 2.1.1′.1−1 nor the other (H2O)2H2SO4 isomers display only water molecules being HB donors, and there is always at least one HB involving one of the hydrogen of H2SO4. This feature leads to dangling hydrogen atoms originating from both the water molecules and H2SO4. For (H2O)3H2SO4 and larger clusters, the substitution of SO42− by H2SO4 clearly makes the PES flatter, with an energy ordering of the low-energy isomers that is strongly sensitive to the applied computational method (functional and basis set) and ZPE corrections, even at the DFT level of theory. This can be partly attributed to the weaker interaction of H2SO4 with H2O. Furthermore, in contrast to (H2O)nSO42− aggregates, a number of isomers display the same oxygen topology but a different HB network, which makes an exhaustive exploration of the PES more complex and hardly accessible to DFT and wave function approaches (see for instance in Figure 3 isomers 3.1.2′.2−1 and 3.1.2′.2−2). Consequently, most studies focused on a small number of selected isomers without applying a global optimization scheme,47−50 which leads to some discrepancies in the nature of the lowest-energy configurations, even for (H2O)3H2SO4. Thus, a clear picture of the spectrum of structures of these species at the DFT or higher level of theory is still missing. However, from these studies and our SCCDFTB exploration of the PES of (H2O)nH2SO4 in the range n = 3−6, a number of important features can be highlighted. First, in contrast with the structures of (H2O)nSO42−, the H2SO4 molecule is not surrounded by water molecules but lies 9093


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Figure 4. Selected low-energy isomers of (H2O)12SO42− and associated relative energies (in kcal·mol−1) without (bold) and with (italic) ZPE corrections. Other isomers are presented in the SI. The * symbol indicates structures previously reported by Thaunay et al.26

type isomers are similar to the W12−1 structures described by Thaunay and co-workers in which nine water molecules are in the first coordination sphere of SO42− and three are in the second. As highlighted by the authors, the isomers of this series display a similar oxygen atom topology but differ through their HB network. Hence, a number of topologically similar structures can be generated (Thaunay et al. presented four of them, whereas we obtained only two), but both studies suggest that the global minimum belongs to this particular series. This seems to support the idea that the W12-GL and W12-AN isomers predominantly discussed in other studies are not the lowest-energy conformations of (H2O)12SO42−.18,41 In particular, W12-AN, which belongs to the 12.12.12 series, is the lowest-energy structure reported in the basin-hopping exploration of Smeeton et al.45 but was not found in the present study. To ensure that this is not due to a limited MDPT exploration of the PES, we performed a SCC-DFTB local optimization starting from the W12-AN conformation of Smeeton et al. This leads to a structure 4.70 kcal·mol−1 higher in energy than 12.9.15−1. This result suggests that a nonpolarizable FF appears ill-suited to fully capture the complexity of the energy landscape of (H2O)nSO42− aggregates. In contrast, SCC-DFTB provides results in agreement with DFT data. At higher energy, isomers 12.12.12−1, 12.12.12−2, 12.9.15−1, and 12.10.14−2 are closely related to the W12−2, W12−5, W12−4, and W12− 6 previously reported structures, respectively. The other configurations presented in Figure 4 and in the SI were not previously reported although their oxygen atom topology is based on the same building blocks: water trimer, water tetramer, and cube-like motifs, which are, for instance, all present in 12.12.12−4. Overall, similarly to what is observed for small aggregates, the SCC-DFTB exploration of the PES leads

clusters without any need of reparametrization. This is a strength with respect to force-fields, all the more so as it is able to describe spontaneous proton transfers and therefore ionic structures. Properties of Large (H2O)nSO42− and (H2O)nH2SO4 Clusters. In this part, we apply the SCC-DFTB approach to characterize the low-energy isomers of large clusters with n ≥ 10. Some of these clusters have already been studied;18,25,26,33,39,41,45 however, only two of these studies achieved a global optimization search: Thaunay et al. used a hybrid approach combining an AMOEBA exploration of the PES with local optimizations performed at the DFT level on (H2O)12SO42− and (H2O)13SO42−,26 and Smeeton et al. performed a full exploration of (H2O)3−50SO42− PES using a FF potential.45 To the best of our knowledge, no such approach has been applied to (H2O)nH2SO4 aggregates. Thus, the moderate computational cost of the SCC-DFTB approach and its good performances for small clusters now provide an appealing opportunity to explore the PES of both large (H2O)nSO42− and (H2O)nH2SO4 clusters and to discuss their respective structural specificity. Nevertheless, the energy landscapes of these larger clusters are many-fold and complex, which makes exhaustive explorations rather tedious. Consequently, the presently reported structures have to be interpreted as good representative structures of the low-energy regions of the PES rather than true global minima. Properties of Large (H2O)nSO42− Clusters. (H2O)12SO42− and (H2O)13SO42− were first chosen to allow for a direct comparison with the recent study of Thaunay et al.26 Twelve among the whole of the (H2O)12SO42− low-energy isomers found with SCC-DFTB are reported in Figure 4. Other lowenergy isomers are provided in the SI Figure S13. The 12.9.159094


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Figure 5. Low-energy isomers of (H2O)13SO42− and associated relative energies (in kcal·mol−1) without (bold) and with (italic) ZPE corrections. Only isomers with a relative energy lower than 1 kcal·mol−1 from the global minimum are represented. Isomers with higher energy are presented in the SI.

co-workers,25 who suggested that the low temperature properties of (H2O)13SO42− originate from several isomers, even at the lowest temperatures. A proper understanding of this species would thus require an intensive exploration of its free energy surface by use of MD or Monte Carlo simulations. Such studies would be computationally expensive and hardly achievable using DFT but can be tackled with SCC-DFTB. Overall, as for (H2O)12SO42− and smaller sizes, the low-energy isomers of (H2O)13SO42− do not display any dangling hydrogen atom, which is in agreement with the experimental study by O’Brien et al.20 Consistently with the conclusion by Thaunay et al., the present SCC-DFTB results also suggest that the closure of the first hydration shell of SO42− has not yet occurred for 13 water molecules. The three aggregates (H2O)10SO42−, (H2O)15SO42−, and (H2O)20SO42− were also investigated in the present work. To the best of our knowledge, the only previous exploration of their PES was performed by Smeeton et al. using a FF approach. The present study is thus the first attempt of investigation at a quantum level of theory. Figure 6 shows the three identified lowest-energy minima obtained with and without considering ZPE corrections. Other low-energy configurations are presented in the SI Figures S15 to S17. For (H2O)10SO42−, the minimum energy structure without ZPE is a 10.10.10-type isomer derived from the structure of 6.7.5−1. It can be seen as two edge-fused cube-like motifs of

to structures close to those previously reported at the DFT level.26 Of course, differences exist that could be assigned to a nonexhaustive exploration of the PES in either study. In a near future, the low computational cost of SCC-DFTB could allow to address this specific issue by performing more intensive PES explorations. Figure 5 presents 12 identified isomers of (H2O)13SO42−. Other low-energy conformations are reported in the SI Figures S14. As already mentioned by Thaunay and co-workers, the density of low-energy isomers is larger for (H2O)13SO42− than for (H2O)12SO42−. Thus, although we identified some identical isomers, significant differences appear in the nature of the reported structures. In particular, 13.12.14−1, 13.12.14−2, and 13.12.14−3 that constitute the lowest-energy isomers found in the present work were not previously reported. They are constructed from a cube-like motif on one side of SO42− and two fused tetramers on the other side. The lowest-energy minimum reported by Thaunay et al. displays a different oxygen atom topology, as a lone water molecule bridges a (H2O)12SO42− core. In the present study, isomers with such a bridging water molecule appear at higher energy, as seen in the SI. Similarly, the global minimum reported by Smeeton et al. lies 0.55 kcal·mol−1 higher in energy than the SCC-DFTB lowest-energy structure. These differences clearly highlight the complexity of the (H2O)13SO42− PES, displaying a large variety of structures. This is in line with the conclusions by Wan and 9095


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the structural arrangement of the water molecules. Furthermore, the strong HB acceptor character of SO42− leads to a clear directionality of the HB network toward the anion, which does not exist in pure and protonated water clusters. The lowest-energy structures without ZPE corrections for (H2O)15SO42− and (H2O)20SO42−, i.e. 15.11.19−1 and 20.12.28−1, are displayed in Figure 6. They are lower in energy than the minima reported by Smeeton et al. by 0.57 and 2.84 kcal·mol −1 for (H 2 O) 15SO4 2− and (H2 O) 20SO4 2−, respectively. When ZPE corrections are taken into account, the 15.12.18−2 isomer becomes the SCC-DFTB lowest-energy structure. This isomer displays the same oxygen atoms topology than the (H2O)15SO42− minimum reported by Smeeton et al. Apart from the arrangement of the water molecules, the key difference between 15.11.19−1 and 15.12.18−2 is the location of SO42− within the aggregate. Indeed, in 15.11.19−1, SO42− is at the surface with one face free of any water molecule while, in 15.12.18−2, it is well solvated at the center of the aggregate. Thus, for (H2O)15SO42−, the SO42− first solvation shell appears completed when ZPE corrections are taken into account although structures with SO42− at the surface are still close in energy (see Figure S16). 15.11.19−1 and 15.12.18−2 respectively display 5 and 3 water molecules not directly bonded to the anion and a closed HB network without dangling hydrogen atom. Similarly to (H2O)10SO42−, the structure of (H2O)15SO42− significantly differs from those of (H2O)16 and (H2O)16H+.97,98,101 This again highlights the strong influence of SO42− on the water structuration. Similar observations can be made for (H2O)20SO42−. Indeed, structures with SO42− at the surface and inside the aggregate are both found in the present study. The lowest-energy structure without ZPE displays a well solvated anion with a rather spherical structure, which is similar to the one of the wellknown protonated (H2O)21H+ clusters.101 However, the arrangement of the water molecules in 20.13.27−1 differs from the pentagonal dodecahedron arrangement of (H2O)21H+ that also displays a number of free hydrogen atoms. Properties of Large (H2O)nH2SO4 Clusters. The lowestenergy minima of (H2O)nH2SO4 (n = 10, 15, 20) with or without ZPE corrections are presented in Figure 7. Higherenergy isomers are presented in the SI. To the best of our knowledge, this is the first exploration of the PES of these species. In contrast with small (H2O)nH2SO4 clusters, all the reported isomers display a singly deprotonated molecule. The excess proton is exclusively found in a Zundel-like environment, i.e., H5O2+, located at the surface of the aggregate. Different structural arrangements are reported for the HSO42− ion. Indeed, in (H2O)10H2SO4 and (H2O)15H2SO4, HSO42− is always located on top of the water cluster with either the hydroxyl pointing outward (in that case it participates in the HB only as an acceptor), such as in the 10.6.0′.12 series, or being solvated (in that case the three other oxygen atoms are at the surface of the aggregate), such as in the 10.6.1′.11−1 isomer. For (H2O)10H2SO4, the lowest-energy structure without ZPE corrections has its hydroxyl group solvated, whereas it points outward when ZPE corrections are taken into account (see Figure 7). This reveals that for (H2O)10H2SO4, the two types of structural arrangements are very close in energy. Furthermore, the density of low-energy structures for this particular isomer is high, which makes difficult an accurate determination of its global minimum. In (H2O)15H2SO4, the present exploration suggests that configurations with a solvated hydroxyl group are more stable.

Figure 6. Lowest-energy isomers reported for (H2O)nSO42− (n = 10, 15, 20) without (left) and with (right) ZPE corrections.

oxygen atoms, each one containing five water molecules and three oxygen atoms of the sulfate. The minimum reported by Smeeton et al. is different and belongs to the 10.9.11 series. It is constituted of an isolated water trimer capping one SO42− face and of two linked water trimer and tetramer capping two other faces. At the SCC-DFTB level of theory, this isomer lies 1.59 kcal·mol−1 higher in energy than 10.10.10−1. If one looks at the bunch of the low-energy isomers reported in the SI, two main structure-types can be observed: structures consisting of two cube-like motifs with SO42− at the center and structures displaying a lone water molecule hydrogen-bonded to two sulfate oxygen atoms, the other water molecules forming a tetramer and a cube-like motif on the other side of SO42−. If ZPE corrections are taken into account, the lowest energy structure, i.e., 10.11.9−1, belongs to this second structure-type. At this point, it is worth highlighting that the presence of SO42− within the aggregate completely modifies its structure as compared to the well-known pure and protonated water clusters. Indeed, the lowest-energy structure of (H2O)11 at the TIP5P97 and RHF/6-31G(d,p)98 levels of theory can be described as the stacking of one pentamer and one hexamer or two tetramers and one trimer of water molecules, respectively. Both structure displays a number of dangling hydrogen atoms. Describing (H2O)11H+ with the anisotropic site (ASP)99 and Kozack Jordan (KJ)100 potentials leads to a lowest-energy isomer corresponding to the stacking of two water pentamers and a bridging water molecule.101 These structures completely contrast with the present SCC-DFTB results for (H2O)10SO42−, which shows the strong impact of SO42− on 9096


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have been investigated within a systematic search based on parallel tempering molecular dynamics and periodic quenching. The energy and the energy gradients necessary for the dynamics and optimizations were obtained using the SCCDFTB approach. For small (H2O)nSO42− and (H2O)nH2SO4 clusters, comparisons of the results with MP2 and DFT calculations as well as with literature data show that SCCDFTB provides a reliable description of their configurations and relative and binding energies. In the case of (H2O)nH2SO4, the SCC-DFTB approach is able to describe deprotonated structure, which is hardly achievable with common force-fields. In terms of structural characteristics, a significant difference between nanodroplets containing SO42− versus H2SO4 was found. For all SO42− clusters, water molecules form a network of strong HB around the ion. Thereby, the sulfate anion is well solvated and the water cluster exhibits an ordered structure with no dangling hydrogen atoms. In contrast, in the case of H2SO4-containing aggregates, a very different picture is observed. First of all, we show that the deprotonation of H2SO4 occurs for clusters containing five or more water molecules. Besides, the sulfate fragment is mainly located at the surface of the water clusters for small and middle-size clusters. This leads to an arrangement of the water molecules that is amorphous-like, with a large number of dangling hydrogen atoms. Hence, the present SCC-DFTB scheme is shown to be flexible enough to capture the various kinds of interactions in sulfur-containing species yielding a complex landscape and a large variety of conformers. Considering that SCC-DFTB is computationally less demanding than ab initio methods, the present results open the way to future studies of middle and large size sulfurcontaining water aggregates with extensive finite-temperature simulation schemes. For the small species, this should also allow to fingerprint the structural changes with temperature and in particular the isomer interconversion mechanisms. For the largest species, SCC-DFTB simulations may provide a tool to investigate their thermodynamical properties, in particular the role of the sulfate impurities on the phase transitions of water nanodroplets. This would allow to tackle various questions of interest in the context of atmospheric chemistry in which the structure and dynamical behavior of charged water nanodroplets is of primary importance. Finally, the use of classical Born−Oppenheimer dynamics could allow for the simulation of finite-temperature anharmonic infrared spectra to relate structural properties to specific spectroscopic features experimentally accessible.

Figure 7. Lowest-energy isomers reported for (H2O)nH2SO4 (n = 10, 15, 20) without (left) and with (right) ZPE corrections. For (H2O)20H2SO4, the lowest-energy structure is the same with or without ZPE corrections.

(H2O) 20H2SO4 behaves somewhat differently, as the hydroxyl group is always involved in a HB, either as a donor or as an acceptor (in five isomers out of the six presented, it acts as both a donor and acceptor), and the remaining oxygen atoms may be found at the surface or solvated inside the aggregate. More importantly, the lowest-energy minimum displays a significantly higher stability as compared to the other isomers. Indeed, its energy difference with the second lowest-energy isomer is 3.63 and 4.38 kcal·mol−1 when ZPE corrections are and are not taken into account, respectively. It has a well-defined spherical cage-like structure with the hydroxyl group at the center and three HSO4− oxygen atoms at the surface. Although the cage is made of square, pentagon, and hexagon of water molecules, this rather well-ordered structure has some similarities with that of (H2O)21H+. Consequently, this particular structure may also suggest a peculiar thermodynamical behavior of (H2O)20H2SO4 as can be found in (H2O)21H+, for instance.102 As expected, whatever the size of the aggregate, there is always a number of dangling HB directed outside of the aggregate. This is another strong difference with the large (H2O)nSO42− aggregates, that overall display few common features with the (H2O)nH2SO4 clusters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b08251. Description of the equilibrium geometry of SO42− and H2SO4 obtained at the SCC-DFTB, DFT, and MP2 levels of theory. Detailed discussion and comparison between all the low-energy structures obtained for the small (H2O)nSO42− and (H2O)nH2SO4 aggregates (n = 2−6). Binding energies of a selected number of isomers calculated using various computational methods for comparison with the SCC-DFTB results. Additional low-energy structures for (H2O)12SO42−, (H2O)13SO42−, (H 2 O) 1 0 SO 4 2 − , (H 2 O) 1 5 SO 4 2 − , (H 2 O) 2 0 SO 4 2 − ,

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CONCLUSIONS The structural characteristics of (H2O)nSO42− (n = 1−6, 10, 12, 13, 15, 20) and (H2O)nH2SO4 (n = 1−6, 10, 15, 20) clusters 9097


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(H2O)10H2SO4, (H2O)15H2SO4, and (H2O)20H2SO4 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33 (0) 561556836. Fax: +33 (0) 561556065. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the supercomputing facility of CALMIP for generous allocation of computer resources (projects P1320 and P0059). This work was supported by the French ANR grant ANR-13-BS08-0005 PARCS “Polycyclic Aromatic Hydrocarbons Reactivity in Cryogenic Solids” and by the GDR Groupement de Recherche 533 EMIE “Edifices Moléculaires Isolés et Environnés”.

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Structural Characterization of Sulfur-Containing Water Clusters

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