Stability of Superhalogen Anions in the Aqueous Phase - Inorganic

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Stability of Superhalogen Anions in the Aqueous Phase Iwona Anusiewicz, Sylwia Freza, and Piotr Skurski* Laboratory of Quantum Chemistry, Faculty of Chemistry, University of Gdańsk Wita Stwosza 63, 80-308 Gdańsk, Poland ABSTRACT: The issue of stability of superhalogen anions in an aqueous solution is investigated on the basis of theoretical calculations carried out at the CCSD(T)/6-311++G(d,p)//MP2/ 6-311++G(d,p) level for two representative negatively charged systems (NaF2− and AlF4−) whose fragmentation products differ in polarity. The presence of a water solvent is simulated independently by employing the polarized continuum solvation model and by involving eight H2O molecules explicitly to allow interactions at the molecular level. The best estimates of the Gibbs free energies characterizing the AlF4− and NaF2− fragmentation reactions in a water solvent are evaluated as equal to 33−34 and 12−14 kcal/mol, respectively (assuming the F− and AlF3/NaF products) or 14−15 and 26−28 kcal/mol, respectively (assuming the HF and AlF3OH−/NaFOH− products). The corresponding fragmentation routes are suggested to be nonoperative at T = 298.15 K. The conclusion concerning the thermodynamic stability of the AlF4− and NaF2− superhalogen anions in the aqueous phase is formulated and discussed.

1. INTRODUCTION Superhalogens and their corresponding anions have attracted growing attention since their first experimental identification in 1999.1 Even though the existence of such species was originally postulated by Gutsev and Boldyrev as early as 1981,2 the role that superhalogens might play in chemistry remained unrecognized for almost 2 decades. The original MXk+1 formula (where M corresponds to a metal atom of maximal formal valence k surrounded by k + 1 halogen ligands X) defining superhalogen systems3−8 as those expected to exceed the electron affinity of a chlorine atom (3.62 eV9) turned out to be much more general than it appeared. Namely, various functional groups (e.g., halogenoids,10 acidic functional groups,11 electrophilic substituents,12 or even superhalogens themselves13−16) were demonstrated to act as suitable ligands, whereas certain nonmetal atoms (e.g., silicon17−20 and hydrogen21,22) were found to be capable of playing the central atom role in both superhalogens and their daughter anions. Another important extension of the superhalogen formula led to the definition of the polynuclear MnXn(k+1) superhalogens and their corresponding (MnXn(k+1))− anions, such as Na4Cl5− and Li5F6−, whose promising properties are constantly being discovered.23−33 The role that superhalogens might play in chemistry (material chemistry in particular) includes their ability to act as strong oxidizing agents34−37 or superacid precursors.38−40 Clearly, the possibility of utilizing a given compound entails its stability in a certain environment. However, concerning both neutral and negatively charged superhalogens, the thermodynamic stability was usually verified regarding the gas phase only. Hence, we decided to take a closer look at the issue of the stability of superhalogen anions in water because one may preconceive certain fragmentation reactions (the MXk+1− → MXk + X− process in particular) to be thermodynamically favorable (and thus operative) in such a polar environment (especially when the MXk product is polar). © XXXX American Chemical Society

In this contribution, we provide a verification of the thermodynamic stability in the aqueous phase regarding two representative superhalogen anions. Our investigation is based on evaluating the Gibbs free energies characterizing most probable fragmentation paths that the superhalogen anions might be susceptible to. The presence of a water solvent is simulated either by employing the polarized continuum solvation model (PCM) or by involving H2O molecules explicitly to allow interactions at the molecular level.

2. METHODS The equilibrium geometries of the substrates and products of the following fragmentation processes leading to the formation of a solvated F− anion (for n = 0−8)

(H 2O)8 AlF4 − → (H 2O)8 − n AlF3 + (H 2O)n F−

(H 2O)8 NaF2− → (H 2O)8 − n NaF + (H 2O)n F− and the selected fragmentation reactions that lead to the formation of the solvated HF molecule (for n = 3 and 4) (H 2O)8 AlF4 − → (H 2O)7 − n HF + (H 2O)n AlF3OH−

(H 2O)8 NaF2− → (H 2O)7 − n HF + (H 2O)n NaFOH− were obtained by applying the second-order Møller−Plesset (MP2) perturbational method with the 6-311++G(d,p) basis set.41,42 The harmonic vibrational frequencies characterizing the stationary points were evaluated at the same MP2/6-311++G(d,p) theory level. The coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)]43−46 was then employed to refine the electronic energies [using the same 6-311++G(d,p) basis set]. The electronic and Gibbs free energies of the fragmentation reactions (labeled ΔEr and ΔGr298, respectively) were evaluated using the CCSD(T)/6-311++G(d,p) electronic energies and zero-pointReceived: June 3, 2016

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DOI: 10.1021/acs.inorgchem.6b01304 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry energy corrections, thermal corrections (at T = 298.15 K), and entropy contributions estimated with the MP2 method and 6-311++G(d,p) basis set. Because locating the global minimum of each substrate [(H2O)8AlF4− and (H2O)8NaF2−] and product [(H2O)8−nAlF3, (H2O)nF−, and (H2O)8−nNaF (for n = 0−8) and (H2O)nAlF3OH− and (H2O)nNaFOH− (for n = 3 and 4)] was not trivial (due to the conformational complexity of those weakly bound systems), we embedded our anions into the well-established structures of water (H2O)n oligomers (n = 2−8) retrieved from The Cambridge Cluster Database47 to obtain the initial structures for further geometry optimization. In addition, the random search was performed while the configuration space of each system was explored. Namely, various possibilities of surrounding either AlF4− or NaF2− by H2O molecules were examined by treating them as the starting structures during the independent geometry optimization procedures (various combinations of mutual interactions among the water systems were also taken into account). Alternatively, the effects of surrounding H2O molecules were approximated by employing the PCM48−50 within a self-consistentreaction-field treatment, as implemented in the Gaussian09 program (the default options for the PCM and the dielectric constant of 78.39 for water were used) regarding the AlF4− → AlF3 + F− and NaF2− → NaF + F− fragmentation reactions (the explicit presence of H2O molecules was not taken into account, while the PCM calculations were performed). The partial atomic charges were fitted to the electrostatic potential according to the Merz−Singh−Kollman scheme.51 In order to verify the reliability of the complexation energies calculated at the CCSD(T)/6-311++G(d,p)//MP2/6-311++G(d,p) level, we evaluated the fluoride-ion affinity (FIA) for the AlF3 system (117 kcal/mol) and compared this value to the CBS extrapolation of the CCSD(T) value (115 kcal/mol) available in the literature.52 Because the difference between these two FIA estimates is relatively small (2 kcal/mol), we believe that the theoretical level applied is adequate for reproducing such properties. The vertical electron detachment energies (VDEs) of the (H2O)8NaF2− and (H2O)8AlF4− anionic systems were calculated by applying the outer-valence Green function (OVGF) method (B approximation)53−61 together with the 6-311++G(3df,3pd) basis set. Analogous basis sets have been used for superhalogen anions before and provided excellent agreement with the experimentally measured VDE values.23,62 Because of the fact that the OVGF approximation remains valid only for outer-valence ionization for which the pole strengths (PSs) are greater than 0.80−0.85,63 we verified that the PS value obtained was sufficiently large to justify the use of the OVGF method (the smallest PS for the states studied in this work was equal to 0.93). All calculations were performed using the Gaussian09 (revision A.02) package.64

structurally simple systems, which makes the computational studies doable even in the presence of several H2O molecules. The presence of the water solvent was simulated by involving eight H2O molecules in the fragmentation process of each superhalogen anion considered. Such an approach might be justified by noting that the presence of eight H2O moieties is clearly sufficient to effectively surround either NaF2− or AlF4− (by which we mean the formation of hydrogen bonds between all fluorine ligands holding the excess partial negative charges and the hydrogen atoms). Moreover, we assumed that eight H2O molecules are enough to provide sufficient solvation of the fragmentation products (i.e., either a NaF or AlF3 neutral system and the F− anion). Because we limited our studies to the fragmentation paths that lead to the formation of either the neutral molecule (NaF or AlF3) and the F− anion or the HF molecule and the remaining (either NaFOH− or AlF3OH−) anion, it needs to be stressed that such routes clearly represent the most probable fragmentation channels because NaF, AlF3, and HF neutral systems are commonly known stable molecules, whereas the fluorine atom is expected to hold excess negative charge because of its significant electron affinity (3.4 eV).9 In order to address the possibility of hexacoordinate AlIII-ion formation, we considered two representative systems, i.e., Al(H2O)63+ and (H2O)12[Al(H2O)63+], each of which contains the central Al3+ cation solvated by a certain number of H2O molecules to mimic the coordination shell. The Al(H2O)63+ and (H2O)12[Al(H2O)63+] species were considered as possible products of the fragmentation of the solvated AlF4− anion, as explained in the next section. The presented discussion of the superhalogen anions’ stability against fragmentation in an aqueous solution is based on the Gibbs free energies of the reactions evaluated at T = 298.15 K. The substrates assumed for the fragmentation processes are NaF2− or AlF4− superhalogen anions surrounded by eight H2O molecules [labeled as (H2O)8NaF2− and (H2O)8AlF4−, respectively]. As explained in the preceding paragraphs, the NaF, AlF3, HF, AlF3OH−, NaFOH−, and F− fragmentation products were assumed, each of which solvated by various numbers of H2O molecules. In addition, the hexacoordinate AlIII-ion-containing systems, i.e., Al(H2O)63+ and (H 2 O) 12 [Al(H 2 O) 6 3+ ], were also assumed as the fragmentation products. 3.1. Stability of the AlF4− Anion against Fragmentation in an Aqueous Solution. We begin our discussion from the consideration of a very strongly electronically bound anion, i.e., AlF4−, whose vertical excess electron binding energy is remarkably large (9.79 eV).66 The equilibrium structure of the AlF4− anion interacting with eight H2O molecules is presented in Figure 1, whereas the selected geometrical parameters are collected in Table 1. This optimized structure represents the substrate for all fragmentation reactions considered, and because eight H2O molecules seem to be enough to surround the AlF4 moiety (i.e., to form its first coordination shell), the presented (H2O)8AlF4− structure is expected to mimic the real structure that the AlF4− anion adopts in the water phase. In order to verify the electronic stability of the (H2O)8AlF4− system, we calculated its excess VDE at the OVGF/6-311+ +G(3df,3pd) level. The resulting VDE value of 8.77 eV turned out to be significantly smaller (by 1.02 eV) than the corresponding value of 9.79 eV found previously for the isolated AlF4− anion in the gas phase.66

3. RESULTS In order to address the issue of the stability of superhalogen anions in water, we have arbitrarily chosen two such species, i.e., NaF2− and AlF4−, whose structures, gas-phase stability against fragmentation, excess electron binding energies, and other properties were determined in the past.65,66 The choice of these two anionic systems was dictated by the following premises: (i) AlF4− is a good representative of a strongly electronically bound superhalogen anion (VDE = 9.79 eV),66 whereas NaF2− represents a less electronically stable system (VDE = 6.64 eV);65 (ii) possible F− loss (which both these systems might be susceptible to) leads to the nonpolar product (AlF3) in the case of AlF4− and to the polar molecule (NaF) in the case of NaF2−; hence, one may investigate the differences in the solvation effects when these two anions undergo fragmentation in a polar solvent; (iii) both anions are B


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sum up to −0.9 au); hence, one may consider the investigated (H2O)8AlF4− system as composed of a nearly intact AlF4− anion embedded in the cage of eight H2O molecules forming hydrogen bonds with its fluorine ligands and with one another. It is also important to stress that the minimum-energy structure of (H2O)8AlF4− shown in Figure 1 likely represents the global minimum of such a system because many attempts to achieve a structurally different local minimum either led to much higher energy configurations or resulted in convergence to the same global minimum. In particular, the attempts to obtain a local minimum where AlF3 and F− are separated by H2O molecules always led to the merging of these two species and thus the formation of AlF4− surrounded by H2O moieties. Keeping in mind that the system formed by AlF4− and eight H2O molecules seems geometrically stable as a whole and consists of a quasi-tetrahedral (i.e., only slightly perturbed) AlF4− anion interacting with H2O molecules (in the presence of mutual stabilizing interactions among the H2O molecules), we now move to the considerations regarding its susceptibility to fragmentation processes. First of all, one should realize that the most likely fragmentation paths for the AlF4− anion lead either to the neutral AlF3 molecule and the F− anion or to the neutral HF system and the remaining anion because these particular products correspond to very stable systems. Hence, if such processes are excluded (due to their palpably positive Gibbs free energies), then AlF4− might be considered thermodynamically stable. Because we verified that the AlF4− → AlF3 + F− process is not feasible in the gas phase (because ΔGr298 for this reaction was evaluated to be 107.4 kcal/mol at T = 298.15 K), we started our investigation from recalculating the Gibbs free energy of the same process but in the presence of surrounding solvent (water) molecules whose effect we approximated by employing the PCM within a self-consistent-reaction-field treatment. As a result, we obtained a ΔGr298 value of 77.7 kcal/mol, which indicates thermodynamic stability of the AlF4− anion in an aqueous solvent (at least when this solvent is approximated by such a simplified model). In order to provide more convincing evidence of the AlF4− thermodynamic stability in water (or lack thereof), we decided to consider H2O molecules explicitly. Hence, assuming the presence of eight H2O molecules (for the reasons explained in the beginning of this section), we considered the (H2O)8AlF4− system (whose equilibrium structure is presented in Figure 1 and characterized in Table 1) as the substrate in the following series of reactions (see also Figure 2). Clearly, the assumed treatment allows for various distributions of eight H2O molecules between both (AlF3 and F−) reaction products, which eliminates the possibility of an incorrect a priori assignment. The calculated values of the reaction energies (termed ΔEr) and Gibbs free reaction energies at T = 298.15 K (termed ΔGr298) are gathered in Table 2. Because all of the presented ΔEr and ΔGr298 values are positive and significant (i.e., exceeding 45 and 33 kcal/mol, respectively), we conclude that the fragmentation process considered is highly unlikely to be operative, no matter how the solvent molecules are distributed between the two products; see Table 2. In the case of each reaction (i.e., for any chosen n), ΔEr is larger than ΔGr298, which is clearly caused mostly by the inclusion of the entropy effects that act to favor the fragmentation process. In addition, one may analyze either the ΔEr or ΔGr298 dependence on the number of H2O molecules assigned to any of the products. Namely, the value of

Figure 1. Equilibrium structures of the (H2O)8AlF4− (top) and (H2O)8NaF2− (bottom) negatively charged systems.

Table 1. Selected Geometrical Parameters (Bond Lengths r in Angstroms and Valence and Dihedral Angles in Degrees) of the (H2O)8AlF4− and (H2O)8NaF2− Equilibrium Structures Depicted in Figure 1 species

geometrical parameters

(H2O)8AlF4−

r(AlF1) = 1.715 Å r(AlF2) = 1.723 Å r(AlF3) = 1.714 Å r(AlF4) = 1.705 Å α(F1AlF2) = 107.10° α(F1AlF3) = 110.21° α(F1AlF4) = 111.57° α(F3AlF4) = 108.30° α(F3AlF2) = 108.39° α(F2AlF4) = 111.23° β(F4AlF2F3) = 118.95° β(F3AlF2F1) = 118.89° r(NaF1) = 2.474 Å r(NaF2) = 2.646 Å α(F1NaF2) = 112.56°

(H2O)8NaF2−

Clearly, AlF4− seems to preserve its nearly tetrahedral structure, which is characteristic for the isolated anion in the gas phase.66 Certainly, the interactions with the surrounding H2O molecules cause the Td symmetry to be broken; however, the Al−F bond lengths are nearly equivalent (1.705−1.723 Å; see Table 1) and similar to the Al−F bond length predicted earlier for the isolated AlF4− (1.716 Å).66 Moreover, the valence (107.1−111.6°) and dihedral (118.9−119.0°) angles are close to the 109.47° and 120.00° values, respectively, which are typical for the perfect Td-symmetry molecule; see Table 1. Each fluorine atom is involved in the formation of two hydrogen bonds; see Figure 1. The fact that the global minimum for the (H2O)8AlF4− system corresponds to the almost unperturbed AlF4 moiety surrounded by H2O molecules indicates its possible stability (at least locally) in the aqueous phase. In addition, population analysis leads to the conclusion that almost the entire excess negative charge in (H2O)8AlF4− is delocalized among the fluorine atoms of the AlF4 subunit (the partial atomic charges on the aluminum and four fluorine atoms C


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while the F− anion is not solvated, and for n = 1−2, the F− solvation remains insufficient. (ii) For n = 3−4, the solvation of both reaction products seems adequate (because F− tends to form hydrogen bonds with three or four H2O molecules, while AlF3 may still form two H2O → Al(3p) dative bonds and preserve its three electronegative fluorine ligands involved in hydrogen-bond formation; see Figure 2). (iii) For n = 5, the solvation of F− remains sufficient, whereas the solvation of AlF3 does not (one fluorine ligand is not involved in hydrogen-bond formation, and only one H2O → Al(3p) dative bond is present, which, in turn, causes AlF3 structure deformation from planarity); however, the overall effect (in ΔGr298 terms) is similar to that observed for n = 4, likely because of the formation of a larger number of hydrogen bonds by the molecules surrounding F−, which provides additional stabilization. (iv) For n = 6−8, the F− product stays fully solvated, whereas solvation of the AlF3 molecule is clearly insufficient; see Figure 2. Certainly, in each case, the insufficient solvation experienced by any of the two fragmentation products causes an increase of the corresponding ΔGr298 value that the process is characterized with (this behavior is most visible for n = 0 and 8). Because such an increase should be treated as artificial because it is the result of nonrealistic insufficient solvation, one should consider the results (ΔEr and ΔGr298) obtained for n = 3−4 as the most reliable. Therefore, we conclude that the Gibbs free energy of the AlF4− fragmentation, leading to AlF3 and F− and modeled in the presence of eight H2O molecules, is equal to ca. 33−34 kcal/mol. Even though this value is substantially smaller than the value of 77.7 kcal/mol predicted for the same process without any H2O molecules explicitly present but with the effect of a water solvent approximated by employing the PCM, we consider the former result (i.e., 33−34 kcal/mol) as much more reliable because it takes into account the interactions at the molecular level. Needless to say, the positive Gibbs free reaction energies resulting from these two general approaches clearly indicate the stability of the AlF4− anion in the aqueous phase. In addition, we considered an alternative fragmentation path that leads to formation of the HF molecule and the remaining AlF3OH− anion (both solvated by H2O molecules). Because we have already verified (while investigating the fragmentation channels leading to the F− and AlF3 systems) that the most energetically favorable distribution of H2O molecules between the products should enable the solvation of both resulting species, we limited our computations to the two routes

Figure 2. Equilibrium structures of the products for the (H2O)8AlF4− → (H2O)8−nAlF3 + (H2O)nF− reactions.

Table 2. Reaction Energies (ΔEr in kcal/mol) and Gibbs Free Reaction Energies (ΔGr298 at T = 298.15 K in kcal/mol) Evaluated for Various Fragmentation Processes Regarding the (H2O)8AlF4− System process −

(H2O)8AlF4 (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4− (H2O)8AlF4−

→ → → → → → → → → → →

−

(H2O)8AlF3 + F (H2O)7AlF3 + (H2O)F− (H2O)6AlF3 + (H2O)2F− (H2O)5AlF3 + (H2O)3F− (H2O)4AlF3 + (H2O)4F− (H2O)3AlF3 + (H2O)5F− (H2O)2AlF3 + (H2O)6F− (H2O)AlF3+ (H2O)7F− AlF3 + (H2O)8F− (H2O)3HF + (H2O)4(AlF3OH)− (H2O)4HF + (H2O)3(AlF3OH)−

ΔEr

ΔGr

79.8 63.9 54.5 48.1 45.6 45.8 46.6 49.7 69.4 27.3 27.6

74.8 56.0 42.9 34.3 33.7 33.6 36.8 41.6 62.4 14.7 14.9

(H 2O)8 AlF4 − → (H 2O)3 HF + (H 2O)4 (AlF3OH)−

(H 2O)8 AlF4 − → (H 2O)4 HF + (H 2O)3 (AlF3OH)−

because they are expected to correspond to the lowest Gibbs free energies characterizing the fragmentation reactions (because of the even distribution of solvent molecules between the products). The predicted ΔG r298 values for these fragmentation paths (14−15 kcal/mol; see Table 2) turned out to be smaller than those evaluated for the reactions leading to the F− formation yet large enough to ensure thermodynamic stability of the AlF4− anion in the aqueous phase. Finally, we considered the possibility of hexacoordinate AlIIIion formation by examining the energy effects of two representative processes:

the Gibbs free energy (which we consider more related to the experimental conditions than ΔEr) rapidly decreases (from 74.8 to 34.3 kcal/mol) for n developing from 0 to 3, then remains approximately the same (in the 33.6−34.3 kcal/mol range) for n increasing from 3 to 5, and finally grows for n developing from 6 to 8 (ΔGr298 = 62.4 kcal/mol is achieved for n = 8); see Table 2. Such a dependence may be easily explained by noticing the following: (i) For n = 0, the AlF3 molecule is fully solvated

(H 2O)18 AlF4 − → Al(H 2O)6 3 + + 4(H 2O)3 F− D


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Inorganic Chemistry (H 2O)30 AlF4 − → (H 2O)12 Al(H 2O)6 3 + + 4(H 2O)3 F−

The Al(H2O)63+ and (H2O)12Al(H2O)63+ systems represent the Al3+ cation surrounded by various numbers of H2O molecules (assuming a coordination number of 6), and their B3LYP/6-311++G(d,p) equilibrium structures are presented in Figure 3. In order to balance the overall reaction charge, we

Figure 4. Equilibrium structures of the solvated AlF4− anions: (H2O)18AlF4− (top) and (H2O)30AlF4− (bottom) representing the substrates of the (H2O)18AlF4− → Al(H2O)63+ + 4(H2O)3F− and (H2O)30AlF4− → (H2O)12Al(H2O)63+ + 4(H2O)3F− reactions.

that of AlF4− (9.79 eV).66 Hence, we chose NaF2− as our second representative superhalogen anion, while investigating the stability of those species in an aqueous solution. Our choice was also motivated by the fact that fragmentation of NaF2−, unlike that of AlF4−, leads to the polar product NaF. The equilibrium structure of the NaF2− anion interacting with eight H2O molecules [i.e., (H2O)8NaF2−] is demonstrated in Figure 1 (the values of the Na−F bond lengths and the F− Na−F valence angle are gathered in Table 1). As was the case for the (H2O)8AlF4− structure, the (H2O)8NaF2−-optimized structure was assumed as the substrate for all fragmentation reactions considered. The structure of the NaF2− fragment assembled into the (H2O)8NaF2− system is bent [α(F−Na−F) = 112.6°], and both Na−F bonds seem elongated (see Table 1) compared to the D∞h-symmetry (linear) gas-phase equilibrium structure of the isolated NaF2− anion.65 Such a deformation of the NaF2− structure is likely caused by the hydrogen-bond interactions with surrounding H2O molecules that both fluorine atoms are involved in (see Figure 1) and the presence of a lowenergy (113 cm−1) vibrational scissors mode of πu symmetry (predicted for the isolated NaF2− anion).65 Because our attempts of achieving structurally different local minima (pursued by starting the geometry optimization procedures using various initial structures) either led to higher-energy (although qualitatively analogous) local minima or converged to the same lowest energy (H2O)8NaF2− structure, we conclude that the (H2O)8NaF2− system presented in Figure 1 most likely represents the global minimum structure of this compound. We

Figure 3. Equilibrium structures of the solvated AlIII ion: Al(H2O)63+ (top) and (H2O)12Al(H2O)63+ (bottom) representing the products of the (H2O)18AlF4− → Al(H2O)63+ + 4(H2O)3F− and (H2O)30AlF4− → (H2O)12Al(H2O)63+ + 4(H2O)3F− reactions.

assumed the formation of four F− anions in each case (each of which was solvated by three H2O molecules). Such an assumption enforced the choice of (H2 O)18AlF4− and (H2O)30AlF4− as the reaction substrates. The equilibrium structures of the (H2O)18AlF4− and (H2O)30AlF4− anions [obtained at the B3LYP/6-311++G(d,p) level] are depicted in Figure 4. Because the reaction energies predicted for these two processes [(H2O)18AlF4− → Al(H2O)63+ + 4(H2O)3F− and (H2O)30AlF4− → (H2O)12Al(H2O)63+ + 4(H2O)3F−] were found to be positive and relatively significant at the B3LYP/6311++G(d,p) level with inclusion of the PCM model, i.e., 136.1 and 99.6 kcal/mol, respectively, we conclude that the spontaneous evolution of the solvated AlF4− anion [represented here by either (H2O)18AlF4− or (H2O)30AlF4−] to the hexacoordinate AlIII system [represented here by either Al(H2O)63+ or (H2O)12Al(H2O)63+] should not be considered likely, which, in turn, provides another argument that confirms the stability of the AlF4− anion in the aqueous phase. 3.2. Stability of the NaF2− Anion against Fragmentation in an Aqueous Solution. The VDE of the NaF2− anion, albeit relatively large (6.64 eV),65 is substantially smaller than E


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Inorganic Chemistry also need to point out that, similar to the (H2O)8AlF4− system described in the preceding section, our attempts to obtain a local minimum containing NaF and F− separated by H2O molecules always led to the merging of these two fragments and thus the formation of NaF2− surrounded by the H2O moieties, as shown in Figure 1. The results of the Merz−Singh−Kollman population analysis performed for the (H2O)8NaF2− system indicate that the partial atomic charges on the sodium and two fluorine atoms sum up to −0.7 au, which, in turn, suggests that the majority of the excess negative charge is localized on the NaF2 fragment. Hence, one may consider the investigated (H2O)8NaF2− system as composed of a significantly structurally deformed NaF2− anion trapped in the cage of eight H2O molecules. In order to confirm the electronic stability of the (H2O)8NaF2− system, we evaluated its excess VDE at the OVGF/6-311++G(3df,3pd) level. The predicted VDE value of 8.30 eV was found to be significantly larger (by 1.66 eV) than the corresponding value of 6.64 eV found previously for the isolated NaF2− anion in the gas phase.65 Having discussed the structure of the (H2O)8NaF2− system (in which the integrity of the NaF2 negatively charged fragment is preserved, at least to a significant extent), we stress that the existence of such a minimum-energy structure proves the geometrical stability thereof. At this point of our discussion, we move to the considerations regarding the susceptibility of (H2O)8NaF2− to fragmentation processes. Similar to the previously described (H2O)8AlF4− case, we assumed that the most likely fragmentation paths for the NaF2− anion lead to either the neutral NaF molecule and the F− anion or to the HF molecule and the remaining anion (because these particular products represent the most stable systems that the NaF2− anion could be divided into). Therefore, the exclusion of such processes (based on their positive Gibbs free energies) would allow one to consider NaF2− as a thermodynamically stable system. We verified that the NaF2− → NaF + F− process is not expected to be operative in the gas phase because the ΔGr298 for this reaction was found to be 53.8 kcal/mol at a temperature of 298.15 K. After confirming the NaF2− thermodynamic stability in the gas phase, we calculated the Gibbs free energy for the same reaction but in the presence of a surrounding water solvent, whose effect was approximated by employing the PCM. The resulting ΔGr298 value of 12.5 kcal/mol indicates the thermodynamic stability of the NaF2− anion in an aqueous solvent (approximated by the PCM). Another verification of the NaF2− thermodynamic stability in water was done by considering the explicit presence of H2O molecules. By doing so, we followed exactly the same route that we utilized while investigating the stability of the AlF4− anion (see the preceding section). Namely, we considered the (H2O)8NaF2− system (shown in Figure 1) as the substrate in the following series of reactions (see also Figure 5, where the equilibrium structures of all products are presented): The calculated reaction energies (ΔEr) and Gibbs free reaction energies at T = 298.15 K (ΔGr298) are collected in Table 3. First of all, we notice that all of the evaluated ΔEr and ΔGr298 values are positive and exceed 34 and 12 kcal/mol, respectively. Therefore, it can be concluded that the fragmentation process considered is not expected to proceed spontaneously, irrespective of the distribution of solvent molecules between the two products (see Table 3). Performing the calculations for

Figure 5. Equilibrium structures of the products for the (H2O)8NaF2− → (H2O)8−nNaF + (H2O)nF− reactions.

Table 3. Reaction Energies (ΔEr in kcal/mol) and Gibbs Free Reaction Energies (ΔGr298 at T = 298.15 K in kcal/mol) Evaluated for Various Fragmentation Processes Regarding the (H2O)8NaF2− System process

ΔEr298

ΔGr298

(H2O)8NaF2−→ (H2O)8NaF + F− (H2O)8NaF2−→ (H2O)7NaF + (H2O)F− (H2O)8NaF2−→ (H2O)6NaF + (H2O)2F− (H2O)8NaF2−→ (H2O)5NaF + (H2O)3F− (H2O)8NaF2−→ (H2O)4NaF + (H2O)4F− (H2O)8NaF2−→ (H2O)3NaF + (H2O)5F− (H2O)8NaF2−→ (H2O)2NaF + (H2O)6F− (H2O)8NaF2−→ (H2O)NaF + (H2O)7F− (H2O)8NaF2−→ NaF + (H2O)8F− (H2O)8NaF2− → (H2O)3HF + (H2O)4(NaFOH)− (H2O)8NaF2− → (H2O)4HF + (H2O)3(NaFOH)−

65.6 51.7 38.3 36.5 34.4 34.6 37.6 44.0 53.8 48.9 55.6

54.8 32.8 21.6 12.2 13.7 16.0 19.1 29.8 42.1 26.5 27.4

various values of n (which stands for the number of H2O molecules surrounding the F− product) allows one to analyze the ΔGr298 dependence on the number of H2O molecules assigned to any of the two products, as was done for the AlF4− anion. Namely, the value of Gibbs free energy gradually decreases from 54.8 to 12.2 kcal/mol for n developing from 0 F


Article

Inorganic Chemistry

(i) The Gibbs free energy of the AlF4− → AlF3 + F− process was 77.7 kcal/mol when evaluated by approximating the solvent effects using the PCM, whereas the corresponding value characterizing the NaF2− → NaF + F− process was found to be 12.5 kcal/mol (at T = 298.15 K). (ii) The Gibbs free energies calculated for the (H2O)8AlF4− → (H2O)8−nAlF3 + (H2O)nF− reactions (allowing the explicit presence of eight H2O molecules) indicate that values of 33−34 kcal/mol should be assumed for this process at T = 298.15 K (because they apply to the most effective solvation of both products). (iii) The Gibbs free energies evaluated for the (H2O)8NaF2− → (H2O)8−nNaF + (H2O)nF− reactions (i.e., with the eight H2O molecules explicitly present) indicate that values of 12−14 kcal/mol should be assumed for this process at T = 298.15 K (as they apply to the most effective solvation of both products). (iv) The Gibbs free energies calculated for the (H2O)8AlF4− → (H2O)7−nHF + (H2O)nAlF3OH− (14−15 kcal/mol) and (H2O)8NaF2− → (H2O)7−nHF + (H2O)nNaFOH− (26−28 kcal/mol) reactions (for n = 3 and 4) indicate the stability of the superhalogen anions (i.e., AlF4− and NaF2−) against the fragmentation processes that lead to the HF formation in the aqueous phase. We suggest to consider the Gibbs free energy of 77.7 kcal/ mol, which corresponds to the AlF4− fragmentation (leading to the F− anion) when evaluated using the PCM as artificially overestimated due to the inability of reproducing a certain stabilizing effect at the molecular level (i.e., dative bonds formed between the neutral AlF3 and H2O molecules). Because such an inability is not a problem in the NaF2− case (because solvation of the NaF product is reasonably well reproduced because of its polar character), the Gibbs free energy of the NaF2− fragmentation evaluated using the PCM is in good agreement with the corresponding value obtained from the calculations that involve the H2O molecules explicitly. Finally, we conclude that our best estimates of the Gibbs free energies characterizing the AlF4− and NaF2− fragmentation reactions in a water solvent are equal to (i) 33−34 and 12−14 kcal/mol, respectively (when the process leading to the F− formation is considered) and (ii) 14−15 and 26−28 kcal/mol, respectively (when the fragmentation leading to the HF formation is considered). Therefore, the corresponding fragmentation routes should be regarded as nonoperative at T = 298.15 K, which, in turn, implies thermodynamic stability of the AlF4− and NaF2− superhalogen anions in the aqueous phase. In the case of the AlF4− anion, its stability against the spontaneous formation of the hexacoordinate AlIII ions was also confirmed.

to 3, which is clearly caused by the increase in the number of H2O molecules surrounding the F− anion; see Table 3. In fact, the solvation surroundings for n = 3 (i.e., three H2O molecules assigned to F− and five H2O molecules interacting with NaF) seem optimal, for both structural reasons (see Figure 3) and energy requirements. For n increasing from 3 to 6, ΔGr298 slowly increases to achieve the value of 19.1 kcal/mol for n = 6; see Table 3, which is likely caused by a weakening of the stabilizing solvation effects regarding the polar NaF product (whereas the solvation of F− remains sufficient). Consistently, for n developing from 6 to 8, the solvation of NaF becomes more and more insufficient, which results in simultaneously increasing ΔGr298 values (29.8 and 42.1 kcal/mol for n = 7 and 8, respectively). Clearly, in the case of each process considered (i.e., for each n), the insufficient solvation experienced by any of the two fragmentation products causes an increase of the corresponding ΔGr298 value, which is most evidently for the n = 0 and 8 cases. Similar to the previously discussed series of (H2O)8AlF4− fragmentation reactions (see the preceding section), we consider such a ΔGr298 increase artificial as a result of nonrealistic insufficient solvation. Hence, we suggest to consider the results (ΔEr and ΔGr298 values) obtained for n = 3−4 as the most reliable also in the (H2O)8NaF2− case. Therefore, we conclude that the Gibbs free energy of the NaF2− fragmentation process leading to NaF and F− and modeled in the presence of eight H2O molecules is equal to ca. 12−14 kcal/mol. Taking into account that this value is approximately the same as the value of 12.5 kcal/mol evaluated using the PCM (i.e., in the absence of H2O molecules and with the effect of the water solvent approximated by employing the PCM), we consider our result (i.e., 12−14 kcal/mol) as reliable enough to support the conclusion about the thermodynamic stability of the NaF2− anion in the aqueous phase. In addition, we investigated an alternative fragmentation route that leads to the formation of the HF molecule and the remaining NaFOH− anion (both solvated by H2O molecules). As explained in the previous section, the most energetically favorable distribution of the H2O molecules between the products should enable the proper solvation of both resulting species; hence, we limited our computations to the two paths (H 2O)8 NaF2− → (H 2O)3 HF + (H 2O)4 (NaFOH)− (H 2O)8 NaF2− → (H 2O)4 HF + (H 2O)3 (NaFOH)−

because they correspond to the even distribution of solvent molecules between the products, which should result in the lowest Gibbs free energies characterizing the fragmentation reactions. The calculated ΔGr298 values for these fragmentation paths (26−28 kcal/mol; see Table 3) turned out to be even larger than those evaluated for the reactions leading to the F− formation. Therefore, we conclude that the NaF2− anion should be stable in the aqueous phase also against this fragmentation process.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

4. CONCLUSIONS On the basis of our quantum-chemical calculations performed at the CCSD(T)/6-311++G(d,p)//MP2/6-311++G(d,p) level, we positively verified the thermodynamic stability of two representative superhalogen anions (i.e., AlF4− and NaF2−) in the aqueous phase. The consideration of most probable fragmentation processes (that lead either to the F− and AlF3/ NaF products or to the HF and AlF3OH−/NaFOH− systems) revealed the following:

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Polish Ministry of Science and Higher Education Grants 538-8375-B030-15 and 5388375-B030-16 to S.F. and by the Polish Ministry of Science and Higher Education Grant DS-530-8375-D499-16 to P.S. G


Article

Inorganic Chemistry

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Stability of Superhalogen Anions in the Aqueous Phase - Inorganic

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