HF

10074

J. Phys. Chem. B 2000, 104, 10074-10079

Ab Initio Molecular Dynamics Study of the Superacid System SbF5/HF Solution Dongsup Kim* and Michael L. Klein Center for Molecular Modeling and Department of Chemistry, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6323 ReceiVed: July 24, 2000

We have investigated one of the strongest superacid systems, SbF5 in liquid HF, by ab initio molecular dynamics simulation. In dilute solution a barrierless, diffusion-limited fluorination reaction takes place to form the SbF6- anion and H2F+ cation. The initial contact ion pair evolves to become a fully separated ion pair by a series of stepwise, incoherent proton jumps. On average, the SbF6- anion had an octahedral structure with the average bond length of 1.9 Å. The cationic species is a protonated HF chain, which mediates the fast proton jump process.

I. Introduction Superacids are stronger than the conventional strong mineral Brønsted acids such as 100% sulfuric acid (H0 g -12). A solution of SbF5 in liquid HF (SbF5/HF) is considered the strongest liquid superacid, ∼109 times stronger than sulfuric acid (H0 ≈ -21).1,2 This property of SbF5/HF has been exploited for a variety of catalytic and synthetic applications.1,3-8 Despite the importance of this unique superacidic system, there have been few theoretical studies. One reason is the difficulty associated with handling the high atomic number of the Sb atom. Herein, we report an ab initio molecular dynamics simulation study on superacidic SbF5/HF, a hydrogen-bonded system, other than water, in which to study ion formation9-12 and proton transfer.13-17 Infrared and Raman spectroscopy,19F NMR spectroscopy, and conductance experiments18-22 on SbF5/HF generally support the following structural and dynamical features. First regarding the structural feature, in dilute solutions of up to about 10 mol %, SbF5 is almost exclusively fluorinated to form the hexasolvated [SbF6(HF)6]- anion and solvated H2F+ cation:

SbF5 + 2HF f SbF6- + H2F+ Early19 and recent21 19F NMR spectroscopy studies exhibit that at low concentration of SbF5 the spectrum showed only one broad line in addition to the HF line. This indicates that the only anionic species in the solution is SbF6- and that the ion is strongly interacting with the solvent HF molecules. Infrared20 and 1H NMR spectroscopy21 found that the cationic species in the solution is protonated HF chains, Hn+1Fn+, the length of which depends on the concentration of SbF5. Second, Hyman et al.18 and Gillespie and Moss19 found that the H2F+ ion, more precisely a proton solvated by HF, has an abnormally high mobility in the superacidic HF-SbF5 solution. The estimated molar conductivity of the cationic species is 350 Ω-1 cm2 mol-1, which is comparable with ionic conductivity for H3O+ in water. Moreover, they found that the electrical conductivity of SbF5/HF solutions showed a dramatic dependence on the SbF5 concentration. At a low concentration, the conductivity of the solution quickly rose with the addition of SbF5, reached its maximum at about 10 mol % of SbF5, and then sharply fell off. Further addition of SbF5 leads to the

formation of solvated polymeric SbnF5n+1- anions and the depolymerization of HF chains. These experimental findings and the well-known fact that in liquid HF the majority of HF molecules exist as hydrogenbonded chains23-27 strongly suggest that the proton in superacidic SbF5/HF solutions conducts by a “proton jump” mechanism.17 When SbF5 is added to liquid HF, it initially becomes fluorinated and forms an SbF6- anion, which is stabilized by the surrounding HF molecules through hydrogen bonds. The proton resulting from the fluorination reaction is transferred to a preexisting HF chain to form a protonated HF oligomer. When the concentration of SbF5 is low, the addition of SbF5 results in increasing conductivity, simply because of the increasing number of ionic species in the solution. However, as the concentration of SbF6- in solution further increases, more HF molecules are consumed to solvate SbF6- ions and depolymerization of the protonated HF chains takes place. This depolymerization destroys the chain structures, which are effective media for the proton jump process. In this paper, we report the results of the ab initio molecular dynamics studies on superacidic SbF5/HF. In section II, we describe the computational methods employed in this study. The detailed description on the Car-Parrinello ab initio molecular dynamics method28 is omitted. Instead, we cite several excellent reviews.29,30 Some details on how the pseudopotentials were constructed and the quality of those pseudopotentials, in particular for Sb atom, are given in section II. In section III, we summarize the computational results on SbF5+(HF)n clusters and make a comparison with our previous study on the weaker superacidic BF3+(HF)n clusters.42 Then, the main results on the solution are given in the second part of section III, where the structural and dynamic properties of the system are analyzed. II. Computational Methods To study the structural and dynamic properties of SbF5/HF, we have employed the Car-Parrinello ab initio molecular dynamics method,28 in which the interatomic forces are derived at each time step from ab initio electronic structure calculations based on density functional theory.31,32 Unlike conventional molecular dynamics, this method can describe bond making and breaking, which is an essential feature for the present study. Although nuclear quantum effects can be crucial for a system

10.1021/jp002619t CCC: $19.00 © 2000 American Chemical Society Published on Web 09/27/2000

Superacid System SbF5/HF Solution

J. Phys. Chem. B, Vol. 104, No. 43, 2000 10075 TABLE 1: Bond Lengths (d, Å) and Bond Angles (∠, deg) of Model Speciesg species HF Sb2 SbH3 SbF3 SbF5 (SbF5)3

SbF6Figure 1. Minimum energy structure of Sb-containing molecules calculated with CPMD: (a) SbF3, (b) SbF5, (c) (SbF5)3, and (d) SbF6-. Antimony and fluorine atoms are represented by large and small spheres, respectively.

in which hydrogenic motion plays a role, we initially treated the nuclear motions classically to avoid the enormous additional computational cost of quantizing the nuclear motion. Electron exchange and correlation were treated at the local density approximation with the gradient correction using the Becke (B) exchange33 and Lee, Yang, and Parr (LYP) correlation functionals,34 the combination commonly known as BLYP. The BLYP scheme has been shown to give a reasonably good description of hydrogen bonding. The valence electron wave functions are expanded in plane waves, and the interaction between the valence electrons and the ionic cores is described by the norm-conserving pseudopotentials. Specifically, for hydrogen a von Barth-Car type pseudopotential has been used, which is essentially a softened Coulomb potential with a cutoff radius rs ) 0.25a0. For fluorine, we generated a Troullier-Martins type pseudopotential35 in a separable form of Kleinman-Bylander (K-B)36 using the package fhi98PP.37 The cutoff radii for the s and p components, rs and rp, were chosen as rs ) rp ) 1.2a0. For antimony, the d component was also included. The cutoff radii were chosen as rs ) 2.23, rp ) 2.34, and rd ) 2.64a0. It should be noted that the K-B approximation scheme was not used for antimony. As discussed in many previous studies,36,38,39 the accuracy of the scheme strongly depends on the choice of the local part of the pseudopotential. Our test calculations with various choices of the local part with or without the K-B scheme indicate that this is also the case for Sb. We obtained the best agreement with experimental results when we chose the p component as a local part without using the K-B scheme. Because the system has only one Sb atom, we decided not to use the K-B scheme for Sb. The energy cutoff (Ec) for the plane wave basis set was 70 Ry. Although 70 Ry was somewhat small to achieve the convergence in the total energy calculations, we found that the relative energies and the minimum energy structures were reasonably converged at Ec ) 70 Ry. All calculations were done with the program CPMD.40 The quality of the pseudopotentials has been tested for several molecules and ions (HF, Sb2, SbH3, SbF3, SbF5, 3SbF5, and SbF6-) for which experimental results are available. The results are shown in Figure 1 and the important geometric parameters are collected in Table 1. Overall, the agreement with experimental results was quite satisfactory; for example, the bond length differences are within 0.05 Å.

geometry

CPMD

expt

d(H-F) d(Sb-Sb) d(Sb-H) ∠(H-Sb-H) ∠(Sb-F) ∠(F-Sb-F) d(Sb-Fe) d(Sb-Fa) d(Sb-Fe) d(Sb-Fa) d(Sb-Fb) ∠(Fa-Sb-Fa) ∠(Fe-Sb-Fe) ∠(Fb-Sb-Fb) ∠(Sb-Fb-Sb) d(Sb-F)

0.93 2.48 1.74 90.43 1.90 95.5 1.87 1.89 1.87 1.87 2.06 164.3 99.0 83.4 147.7 1.92

0.92a 2.49b 1.71c 91.42c 1.88d 95.1d 1.81e 1.81e 2.04e 161.6e 98.2e 81.5e 149.7e 1.87f

a See ref 47. b See ref 48. c See ref 49. d See ref 50. e See ref 51. The average bond length taken from the H5O2+SbF6- crystal structure. See ref 52. g See Figure 1 for the definition of bonds and angles.

f

Figure 2. Minimum energy structures of SbF5+(HF)1-3 clusters calculated with CPMD: (a) SbF5+(HF)1, (b) SbF5+(HF)2, and (c) SbF5+(HF)3. Hydrogen, antimony, and fluorine atoms are represented by light small spheres, dark large spheres, and dark small spheres, respectively. The numbers shown are the Sb-F bond lengths in Å.

III. Results and Discussion A. Gas Phase. For the calculations of the gas-phase molecules and clusters, a cubic supercell was used with cell lengths chosen to be large enough to prevent the interactions between the periodic images. Depending on the size of the system, the unit cell length varied between 20a0 and 30a0. The effects of the unit cell length were checked. The minimum energy structures of SbF5+(HF)1-3 are shown in Figure 2. The fact that SbF5/HF is the strongest superacid implies that the interaction between SbF5 and HF is strong. Our previous study on one of the weakest superacids,42 BF3/HF, indicates that the interaction between BF3 and HF is weak, so that the BF3+HF dimer is essentially a van der Waals complex. In contrast to BF3+(HF)1-7 clusters, the interaction strength between Sb and F in the SbF5+HF dimer is indeed high, which is indicated by the short Sb-F distance and large dimerization energy. The Sb-F distance is calculated to be 2.25 Å, which is far less than the sum of the van der Waals radii43 of Sb (2.2 Å) and F (1.35 Å). The estimated binding energy is 14.8 kcal/mol, which is quite large compared to that of the BF3+HF dimer (1.3 kcal/mol from CPMD/BLYP, 3-4 kcal/mol from the experiment).44 Similar to BF3/HF clusters, SbF5+(HF)2 and SbF5+(HF)3 have shorter Sb-F distances (2.14 and 2.02 Å, respectively) than SbF5+(HF)1, which indicates that the cooperative nature of multiple hydrogen bonds significantly increases the interaction strength. In the case of SbF5+(HF)3, the F atom is almost completely transferred from HF to SbF5 and the cluster has an ionized form, SbF6-‚H3F2+. In the SbF6- subunit, there are two different Sb-F bond types: two longer Sb-F bonds that are directly connected to H3F2+, the protonated subunit, and four

10076 J. Phys. Chem. B, Vol. 104, No. 43, 2000

Kim and Klein

Figure 3. Three representative configurations of SbF5/HF: (a) neutral initial state with the trigonal bipyramidal geometry, (b) contact ion pair, and (c) fully separated ion pair. The large red, yellow, and blue spheres represent an Sb atom, the excess proton (H+), and the special F atom (F*), respectively. The normal H and F atoms are drawn as small green and brown spheres, respectively.

shorter Sb-F bonds that are not. The Sb-F bond lengths are 2.02 Å for the former group and 1.89 Å for the latter group. The bond length of 1.89 Å is similar to the F-Sb bond length of the SbF6- anion (1.92 Å), which indicates that SbF5+(HF)3 is stable in a fully ionized form. B. Solution. For the SbF5/HF solution, the simulation system comprising 25 HF molecules and one SbF5, which was contained in a 18.67a0 × 18.67a0 × 18.67a0 periodic cubic box, was prepared as follows. First, well-equilibrated neutral liquid HF at 290 K was generated following the procedure employed in earlier studies.27,41 Then, two HF molecules were replaced by one SbF5 molecule, and the volume was adjusted to the value interpolated from the densities of the liquid SbF5 and HF at ambient condition. With the SbF5 molecule constrained at gasphase geometry, we continued the simulation for ∼0.6 ps to obtain the initial configuration shown in Figure 3a. Next, after removing the constraint, we let the system evolve for ∼1.5 ps, while maintaining the temperature at ∼290 K by scaling the nuclear velocities occasionally. After another equilibration for ∼1.5 ps, data were sampled for ∼3.5 ps. Almost immediately after the constraints were removed, the expected fluorination reaction took place in the solution:

SbF5 + 2HF f SbF6- + H2F+ where H2F+ and SbF6- specify the liquid HF with an excess proton and a counteranion, respectively. The exact nature of the SbF6- and H2F+ ions is one of the main objects of this work. In Figure 3, three representative configurations are shown: (a) initial neutral state, (b) contact ion pair, and (c) fully separated ion pair. The states b and c are distinguished by the relative location of the H2F+ ion, more precisely a solvated excess proton, and the SbF6- counteranion. For this purpose, the excess proton should be unambiguously identified. As in our earlier study,41 the excess proton (H+) and special F atom (F*), which compose H2F+, are defined by a H or F atom whose bond distances to the two nearby F or H atoms are most alike. Then, the contact ion pair state can be defined as the state in which the H2F+ and SbF6- ions are in contact with each other.

However, ambiguity still remains because it is rather difficult to define the exact form of the cations. As discussed in our earlier study,41 the excess proton in liquid HF exists essentially as a dynamic mixture of H2F+ and H3F2+ ions, and sometimes it is difficult to distinguish the two species. For the same reason, it is even more ambiguous to define a “solvent-separated ion pair”, the intermediate state between the contact ion pair and the fully separated ion pair. In this paper, we define the fully separated ion pair (state c) as the state in which the excess proton (H+) and SbF6- ion are separated by at least two HF molecules and the contact ion pair (state b) as the state in which the excess proton (H+) and SbF6- ion are closer to each other than in state c. The reaction from state a to b is a barrierless, diffusion-limited reaction. Various quantities (temperature, potential energy, Sb-F bond distances, and H-F bond distance of the incoming HF molecule) that can signify the progress during the early stage of the fluorination reaction are shown in Figure 4. The reaction begins with one of the solvent HF molecules approaching SbF5 (see Figure 4b) between two F atoms at the equatorial site. After around 0.35 ps, when the incoming HF molecule and SbF5 get closer than ∼3 Å, a new bond starts to form between the F atom of the incoming HF molecule and Sb, and simultaneously the SbF5 molecule starts to unfold like an umbrella to assume an octahedral shape. We ran several simulations with different initial configurations. Depending on the surrounding solvent configurations, the time for the initial fluorination reaction ranges from