PCCP View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PAPER
Cite this: DOI: 10.1039/c5cp02440d
View Journal
The HAlF4 superacid fragmentation induced by an excess electron attachment Marcin Czapla and Piotr Skurski* The excess electron attachment to the HAlF4 superacid molecule was studied by employing ab initio CCSD(T) and MP2 methods and a purposely suited aug-cc-pVTZ+4s4p3d basis set. The results indicate that the HAlF4 molecule, due to its polarity, may attract a distant excess electron and form a dipole-bound anionic state whose vertical electron binding energy is 1106 cm1. The initially formed (HAlF4) anion of a dipole-bound nature undergoes an immediate structural reorganization driven by the (AlF4) strongly-bound superhalogen anion formation. The potential energy surface analysis leads to the conclusion that the (HAlF4) - (AlF4) + H transformation should proceed spontaneously and involve
Received 27th April 2015, Accepted 17th June 2015
the simultaneous structure relaxation of the AlF4 moiety (in the direction approaching a tetrahedral geometry) and the excess electron density migration from the area outside the molecular framework to
DOI: 10.1039/c5cp02440d
the valence AlF4 region. The fragmentation of the HAlF4 superacid molecule is predicted to be the final effect of the excess electron attachment process. In addition, the important antenna role of the initially
www.rsc.org/pccp
formed (HAlF4) dipole-bound anionic state is discussed.
1. Introduction The enormously strong acidic behavior of species with a Hammett acidity function (H0) smaller than 121,2 has been extensively studied for the last four decades.3–8 The representative examples of such systems, termed superacids (and defined in the 1970s by Gillespie as any acidic structures stronger than 100% sulfuric acid1,2), include certain Brønsted (e.g., HSO3F) and Lewis (e.g., AsF5) acids. In fact, the term superacid appeared in the scientific literature much earlier, namely, in the article written by Hall and Conant in 1927 who provided a description of the salts produced by perchloric acid and sulfuric acid in glacial acetic acid reacting with weak bases.9 One important class of superacids consists of various combinations of strong Lewis and Brønsted acids (e.g., SbF5/HF or HSO3F/SbF5) whose acidic properties are also remarkable. In particular, SbF5/HF (i.e., HSbF6) is commonly considered as the strongest known liquid superacid (exhibiting a H0 of ca. 23).10–13 The theoretically estimated Gibbs free energies of the deprotonation reactions indicate, however, that even stronger acids may exist, such as F(SO3)4H or FSO3SbF5H, as their deprotonation in the gas phase is expected to be even more plausible.14,15 Recently,16 we proposed a few more compounds (i.e., HAl2F7, HAl3F10, and HAl4F13) whose Gibbs free deprotonation energies were found to be significant and comparable to the corresponding values characterizing the HTaF6 and HSbF5 ´sk, Wita Stwosza 63, 80-308, Gdan ´sk, Department of Chemistry, University of Gdan Poland. E-mail: [email protected]
This journal is © the Owner Societies 2015
superacids. In addition, we found out that the deprotonation energies of the HAlnF3n+1 acids (n = 1–4) were closely related to the electronic stabilities of their corresponding (AlnF3n+1) anions.16 Since the corresponding salts are typically more stable than their parent superacids (as we described elsewhere for HAlCl4 acid and its LiAlCl4, NaAlCl4, and KAlCl4 salts),17 their properties and susceptibility to an excess electron attachment were investigated.18,19 In particular, the LiBeX3 (X = F, Cl, Br) salts were found to be capable of forming stable anionic states of a dipole-bound nature and were characterized by relatively large vertical electronic stabilities (spanning the 0.54–0.89 eV range, which is rather untypical for dipole-bound anions and is likely caused by the significant polarity of the LiBeX3 salts).19 The possibility of an excess electron attachment to the superacids, however, has not been investigated thus far. As one may predict, some of the superacids are also polar enough to bind an extra electron, but the stability of such formed anions (exhibiting a dipole-bound nature) might be questionable. As it has been recognized and described in the literature, the dipole-bound states of anions exist primarily due to the longrange dipole potential that causes the density of the excess electron to be localized mainly on the positive side of a molecular dipole.20,21 Even though the static Coulomb stabilization is crucial for the existence of such states, it was found that it may not be the dominant component of the electron binding energy (instead, the dispersion contributions and other electron correlation effects are often responsible for binding an excess electron).20,22 In the last few decades, many dipole-bound
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
anions formed by various polar molecules have been found and investigated theoretically, mostly in the laboratories led by Adamowicz,23–26 Bartlett,27–29 Gutowski,20,22,30,31 Jordan,32–34 and Simons.21,35–37 On the other hand, much of the experimental work was produced in the Bowen,38,39 Brauman,40,41 Compton,42,43 Desfrançois,44,45 Johnson,46,47 and Lineberger48,49 groups. The most recent reports indicate that these theoretical and experimental efforts are being continued.50–55 Since the large electronic stability of superhalogen anions plays an important role in our discussion provided in the following sections, one needs to recall that such anions (whose existence and properties were first described by Gutsev and Boldyrev in 1981)56 are typically very strongly bound systems which is manifested by their vertical electron binding energies spanning the 3.6–13.9 eV range.57–69 Suffice it to say that the superhalogens MXk+1 and their anionic daughters (MXk+1) are usually composed of a central atom M (which is preferably metallic although semi-metals (e.g. B, Ge, As, Sb) or non-metals (e.g., H, P) are also allowed) decorated with k + 1 electronegative ligands (i.e., halogen atoms, halogenoids, electrophilic groups), where k stands for the maximal formal valence of the central atom M. However, the MXk+1 formula might be extended to also include polynuclear MnXnk+1 superhalogens and their corresponding (MnXnk+1) anions (where n stands for the number of central atoms, M). The representative examples of superhalogen anions that have been investigated theoretically and studied experimentally are (LiBr2) and (Na4Cl5), having a mononuclear and polynuclear structure, respectively.62,70 The connection between the superhalogen anions and superacids seems obvious, as the latter often contain a superhalogen fragment in their structure. For example, the HTaF6, HSbF5, or HAlF4 superacids might be viewed as being composed of a superhalogen subunit (TaF6, SbF5, or AlF4) and a hydrogen atom, or alternatively as consisting of the corresponding ionic fragments. The main goal of this work is to provide a description of the excess electron attachment to the HAlF4 superacid in the gas phase. As we demonstrate, the binding of an extra electron induces fragmentation of the system. The key role of both the dipolebound anionic state and the valence-bound anionic state (of a superhalogen nature) in this process is presented and discussed.
2. Methods The equilibrium geometries and the corresponding harmonic vibrational frequencies for the stationary points on the potential energy surface were calculated using the second-order Møller–Plesset (MP2) perturbational method whereas the electron binding energy of the initially formed dipole-bound (HAlF4) anionic state was estimated (by employing the supermolecular approach, i.e., by subtracting the energy of the anion from that of the neutral molecule) using the coupled-cluster method with single, double, and non-iterative triple excitations (CCSD(T)).71,72 While computing the correlation energies, all orbitals except the 1s orbitals of fluorine and the 1s2s2p orbitals of aluminum were included. The relaxed scan of the ground doublet state (HAlF4)
Phys. Chem. Chem. Phys.
PCCP
anionic potential energy surface was performed using the MP2 method. Since we used the methods based on an unrestricted Hartree–Fock (UHF) starting point it was important to make sure that little (if any) artificial spin contamination entered into the final wave functions. We computed the expectation value hS2i for the states studied in this work and found values not exceeding 0.7501 in the doublet anionic cases (at the UHF level). Hence we are certain that the spin contamination is not large enough to significantly affect our findings. As far as the basis sets are concerned, we decided to employ the aug-cc-pVTZ basis supplemented with an additional 4s4p3d set of diffuse functions. Our choice was dictated by the fact that we had to use a basis set which is appropriate for both the weakly dipole-bound anion and the strongly valence-bound superhalogen anion. Therefore, in order to properly describe the neutral molecular host, the aug-cc-pVTZ basis set was chosen, as its usefulness in describing dipole-bound anions has been demonstrated in the past and compared to other commonly used one-electron basis sets.73 Since the aug-ccpVTZ basis set was also found to be adequate for describing the equilibrium structures and electronic stabilities of strongly bound superhalogen anions,74 our choice seems to be appropriate. However, the diffuse character of the orbital describing the loosely bound electron (in a dipole-bound anionic state) necessitates the use of extra diffuse basis functions having very low exponents. Although we do realize that such an additional set of diffuse functions is not necessary to describe the strongly bound valence anionic state formed as the product of the process investigated, it is required to properly describe the dipole-bound anionic state that is initially formed during this process. Hence, while studying the properties of that initially formed dipole-bound anionic state of HAlF4 acid, we performed the calculations using the aug-cc-pVTZ basis set75 supplemented with an additional 4s4p3d set of diffuse functions centered on the hydrogen atom. The calculations for the remaining neutral and anionic states described in this work (including those examined while performing the relaxed potential energy surface scan) were carried out using the same aug-cc-pVTZ+4s4p3d basis set in order to maintain consistency. While studying the vertical electron binding energy of the dipole-bound (HAlF4) anionic state we verified that the inclusion of one additional diffuse 1s1p1d set (which led to the aug-ccpVTZ+5s5p4d basis set) increases the electron binding energy by less than 1 cm1 when calculated at the MP2 level. The extra diffuse functions do not share exponent values and we used even-tempered76 four-term s, four-term p, and three-term d basis sets. The geometric progression ratio was equal to 5.0,73 and for each symmetry we started to build up the exponents of the extra diffuse functions from the lowest exponent of the same symmetry included in the aug-cc-pVTZ basis set designed for hydrogen. As a consequence, we achieved the lowest exponents of 4.0416 105, 1.6320 104, and 1.9760 103 a.u. for the s, p, and d symmetries, respectively. The partial atomic charges were fitted to the electrostatic potential according to the Merz–Singh–Kollman scheme.77
This journal is © the Owner Societies 2015
View Article Online
PCCP
Paper
All calculations were performed with the Gaussian09 (Rev.A.02) software package.78 In order to avoid erroneous results from the default direct SCF calculations with the basis sets with large s, p, and d sets of diffuse functions, the keyword SCF = NoVarAcc was used and the two-electron integrals were evaluated (without prescreening) to a tolerance of 1020 a.u.
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
3. Results and discussion 3.1.
The structure and stability of the neutral HAlF4 superacid
The gas phase equilibrium structure of the neutral HAlF4 molecule is well established, as it was investigated by Senger and Radom79 and was recently confirmed by our group.16 Briefly, the Cs-symmetry of the HAlF4 system (re-examined here at the MP2/aug-cc-pVTZ+4s4p3d level) is composed of a nearly planar AlF3 fragment with its three Al–F bonds of similar lengths (1.65–1.68 Å) and a H–F fragment tethered to it through an elongated (1.989 Å) Al–F bond (see Fig. 1, top). The structure is additionally stabilized by a H-bond formation between the AlF3 and HF subunits, whose length was predicted to be rather large (2.196 Å). The fact that HAlF4 might be considered as consisting of such two units implies that it might also be viewed as a HF molecule that has its F atom forming a dative bond with an underlying F3Al unit. Despite the presence of the elongated (ca. 2 Å) Al–F bond, the neutral HAlF4 system was
Fig. 1 The MP2/aug-cc-pVTZ+4s4p3d equilibrium structure of the neutral HAlF4 molecule in the gas phase (top) and the singly occupied molecular orbital holding an excess electron in the (HAlF4) dipolebound anion (bottom).
This journal is © the Owner Societies 2015
found to be stable towards HF molecule elimination (an elimination energy of 16.4 kcal mol1 and a Gibbs free energy of 7.1 kcal mol1 (at T = 298.15 K) for this process were established). In addition, the deprotonation energy (280 kcal mol1) and the Gibbs free deprotonation energy (269 kcal mol1, at T = 298.15) predicted for this compound indicated its very strong acidic character.16 Since a proper description of the HAlF4 neutral system is crucial for further discussion, the following statements need to be emphasized: (i) neutral HAlF4 is a closed shell singlet and it consists of the F3Al and HF subunits; (ii) the F atom of the HF unit forms a dative bond with an underlying F3Al unit; and (iii) the HF subunit also corresponds to a closed shell, whereas the F3Al unit is a singlet having a vacant 3p orbital on the Al atom that is used for the Al–F dative bond. As we explain in the following sections, this vacant 3p orbital plays an important role in the fragmentation process described in this contribution. 3.2.
Initial formation of a dipole-bound anion
Since the HAlF4 molecule is polar, an excess electron might be attracted to the positive pole of its molecular dipole. The polarity of the HAlF4 system manifests itself by having a dipole moment of 3.4 Debye, as we calculated for the Cs-symmetry equilibrium structure of the neutral species using the MP2 electron densities (the calculations utilizing the MP4(SDQ) and QCISD densities led to similar values of 3.425 and 3.424 D, respectively). Such a dipole moment is large enough to bind an extra electron (the polarity of the corresponding neutral molecule should be larger than 2.5 Debye to support a dipole-bound anionic state80), hence one may expect the HAlF4 system to form an electronically stable anion. It is well established (see ref. 20, 21, 32, 33 and 81) that the excess electron in a dipolebound anion is usually highly diffuse and localized at a relatively long distance away from the molecular framework, yet on the positive side of its dipole. Hence, one may expect such a distribution of an excess electron density also in the case of the (HAlF4) dipole-bound anion, as the polarity of the neutral HAlF4 parent is not large. Indeed, the singly occupied molecular orbital (SOMO) holding an extra electron resembles the typical SOMOs predicted for many other dipole-bound anions20–22 (see Fig. 1, bottom). Namely, it is diffused and localized outside the molecule, in the vicinity of the hydrogen atom (which corresponds to the positive dipole side). As observed for dipole-bound anions formed by other molecules of a similar polarity,20,22 the excess electron binding energy for this initially formed (HAlF4) dipole-bound state is not large. In particular, we established the vertical electron attachment energy (VAE) as being equal to 1106 cm1 at the CCSD(T)/augcc-pVTZ+4s4p3d level. It seems interesting that the electron correlation effects are responsible for more than 80% of this electron binding energy, as a VAE of only 187 cm1 was predicted at the Hartree–Fock level (at which only the electrostaticexchange and induction interactions are taken into account). Such a contribution coming from the electron correlation effects, albeit large, is not surprising concerning the nature of the system investigated (various dipole-bound anions whose
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
PCCP
electronic stabilities were dominated by the electron correlation contributions were described in the past,20,22,30,31,35–37 e.g., the p-chloroaniline anion82). We verified, however, that this initially formed (HAlF4) dipole-bound anion is not geometrically stable. Unlike what has been established for the majority of other dipole-bound anions investigated thus far (where a minor geometry relaxation upon excess electron attachment was observed),20–22 the (HAlF4) structure undergoes a significant reorganization. This process is associated with the evolution of the excess electron density distribution that finally leads to the hydrogen atom loss, as we explain in the following sections. Hence, we predict the described (HAlF4) dipole-bound anionic state to be a rather short-lived species, yet we consider its role in the overall electron attachment process to be very important. This is because the neutral HAlF4 superacid molecule has no other way of attracting a distant excess electron except through its dipole potential (playing an antenna role). Thus, we conclude that the dipole potential of the neutral HAlF4 molecule enables the long-range attraction of an extra electron which leads to the formation of a short-lived dipole-bound anionic state. The formation of this dipole-bound anion turns out to be the initial step that enables further processes to occur, including electron density evolution, structure relaxation, and finally the H–F bond homolytic cleavage. 3.3.
Dipole-bound to valence-bound anionic state evolution
Once the dipole-bound anionic state is formed, the excess electron is already attracted to the molecular framework of HAlF4 and thus might penetrate its valence region. Certainly, the evolution of the excess electron density distribution has to be caused by some influential factor. We believe that in the case considered, the possibility of the formation of a very strongly bound anionic state is the driving force. Namely, the (AlF4) superhalogen anion might be the final product of the (HAlF4) reorganization, if the hydrogen atom is detached. Even though such a process would require the H–F homolytic bond to rupture (whose energetic cost is about 135.1 0.3 kcal mol1 according to the HF dissociation energy),83 the formation of the (AlF4) anion would lower the energy by a much larger amount, as the excess electron binding energy of (AlF4) is 9.79 eV (226 kcal mol1).84 Hence, the energy profit and loss balance indicates that the dipole-bound to valence-bound anionic state evolution process should be favored (even if it is associated with the necessity of H–F bond cleavage). Indeed, we verified that the structural reorganization of the (HAlF4) system proceeds in this direction. In order to investigate it, we performed a relaxed scan of the ground doublet state anionic potential energy surface of (HAlF4) along the coordinate corresponding to the H–F separation (see Fig. 2 and Table 1). As stated above, the initial step of the overall process is the formation of the dipole-bound (HAlF4) anion (see the structure, SOMO and relative energy value depicted for the corresponding r(H–F) = 0.939 Å in Fig. 2). Recall that this data point represents in fact the energy of the (HAlF4) dipole-bound anion predicted at the equilibrium structure of its neutral parent.
Phys. Chem. Chem. Phys.
Fig. 2 The MP2/aug-cc-pVTZ+4s4p3d energy profile for (HAlF4) obtained by performing a relaxed ground doublet electronic state potential energy surface along the coordinate corresponding to the H–F distance. The molecular orbitals holding an excess electron for the arbitrarily chosen structures are depicted in black frames. The vicinity of the shallow minimum at r(H–F) = 2.790 Å is magnified.
Table 1 The r(H–F) and r(Al–FH) distances (in Å), the F–Al–F–F dihedral angles d (in degrees) and the vertical electron binding energies D (in eV) characterizing the data points plotted in Fig. 2. The last row (r(H–F) = N) corresponds to the isolated (AlF4) anion at its equilibrium Td-symmetry structure84
r(H–F)
r(Al–FH)
d
D
0.939 1.000 1.100 1.200 1.300 1.400 1.500 2.000 2.500 2.790 3.000 5.000 N
1.989 1.851 1.809 1.776 1.754 1.740 1.731 1.712 1.708 1.708 1.708 1.707 1.716
156.86 131.58 127.96 125.50 123.94 122.95 122.27 120.70 120.27 120.27 120.27 120.12 120.00
0.14 0.89 1.52 2.34 3.21 4.05 4.81 7.58 9.08 9.63 9.94 9.56 9.79
Since we were unable to find any (even shallow) minima on the anionic ground state potential energy surface in the vicinity of the lowest energy structure of the neutral HAlF4 molecule, we expect the structure reorganization process to proceed rather instantly. As the potential energy curve is repulsive, the structure further relaxes while the energy goes downhill. The two arbitrarily chosen representative structures on this path (with their corresponding molecular orbitals holding an excess electron) are presented in Fig. 2 (for r(H–F) = 1.50 Å and r(H–F) = 2.00 Å) whereas the detailed values characterizing: (i) the H–F separation, (ii) the Al–FH bond length, (iii) the F–Al–F–F dihedral angle (in the AlF3 subunit), and (iv) the vertical excess electron binding energy for all data points are gathered in Table 1. As it might be seen, the orbital holding an excess electron evolves
This journal is © the Owner Societies 2015
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PCCP
Paper
and eventually becomes localized in the valence region. In particular, it gradually delocalizes itself among the three remaining fluorine atoms while its anti-bonding H–F character escalates. This process is associated with the structure reorganization that progressively leads to the tetrahedral AlF4 moiety. Indeed, the previously elongated Al–FH bond shortens and the F–Al–F–F dihedral angle in the AlF3 subunit approaches 1201 when the H–F distance increases (see Table 1). Then, the flat region of the anionic potential energy surface is reached (at r(H–F) of ca. 2.5 Å), yet the energy keeps decreasing slowly until the shallow minimum is achieved at r(H–F) = 2.790 Å (see the magnified region shown in Fig. 2). Hence, our relaxed scan leads to the final system that corresponds to the AlF4 and H fragments separated by a large distance, with the excess electron localized on the former, which we discuss in the next section. In order to shed more light on this process, the following explanation might be utilized: in the beginning (i.e., when the excess electron is initially bound to the equilibrium structure of the neutral HAlF4 molecule) the system consists of the F3Al and FH subunits linked via the Al–F dative bond. This neutral species is in the singlet closed shell electronic state and its lowest unoccupied molecular orbital is a dipole orbital having a negative energy eigenvalue. The excess electron is initially described by this dipole orbital (see Fig. 1) which leads to the doublet anionic state. It is important to emphasize that the three electrons are crucial for the overall process, namely, the unpaired electron initially occupying the dipole orbital and the electron pair initially localized on the s(F–H) bonding orbital of the HF subunit (recall, that the fourth Al–F bond is not formed yet). As the r(H–F) distance increases (to 1.5 Å and 2.0 Å), the SOMO is evolving but the system remains a doublet electronic state. However, the fourth Al–F bond is being formed simultaneously and it contains two electrons, and as the F–H bond breaks it generates a hydrogen atom that contains one electron. Thus, the singly occupied molecular orbital at the end of the process corresponds to the H atom 1s orbital, whereas the highest doubly occupied molecular orbital (depicted in Fig. 2 for the final r(H–F) distance) is distributed among the ligands in the AlF4 anion. To summarize briefly, the three ‘‘active’’ electrons are localized in the following manner: at the beginning of the process, there are two electrons in a bonding s(F–H) orbital and one electron in the dipole orbital; at the end of the process, there are two electrons in the bonding s(Al–F) orbital and one electron in the departing H atom 1s orbital. Finally, one may notice that both the initial and final dominant electronic configurations are of the same symmetry (s1)2(s2)1, thus we do not have two configurations that cross; instead, there is one dominant configuration whose two orbitals smoothly evolve (one from s(F–H) to s(Al–F); the other from the dipole orbital to the H atom 1s orbital). 3.4.
minimum at r(H–F) = 2.790 Å is present (see Fig. 2), the fragmentation (i.e., the H atom detachment) is expected to proceed because the depth of this minimum does not exceed 0.7 kcal mol1. Thus the hydrogen atom detachment may progress almost freely, as the energy cost of surmounting the kinetic barrier is less than 1 kcal mol1. The Merz–Singh–Kollman population analysis for the resulting (AlF4 H) system depicted in Fig. 3 (i.e., the final product (having the stationary point characteristic) of the fragmentation process) leads to the following observations: (i) the partial atomic charge localized on the hydrogen atom is close to zero (0.01 a.u.); (ii) the partial atomic charges localized on the aluminum and fluorine atoms sum up to ca. 1 a.u. (0.99 a.u.); (iii) almost the entire (99.9%) unpaired spin
The final products of the excess electron attachment
The final structure achieved while performing a relaxed potential energy surface scan corresponds to the two separated species (AlF4 and H), as shown in Fig. 2 and 3. Although a shallow
This journal is © the Owner Societies 2015
Fig. 3 The MP2/aug-cc-pVTZ+4s4p3d equilibrium structure of the final (AlF4 H) product of an excess electron attachment to the HAlF4 superacid molecule. The corresponding orbital (holding an extra electron) is depicted at the bottom.
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
density is localized on the distant H atom. These findings clearly indicate that the resulting (AlF4 H) system consists of the (AlF4) closed shell anion weakly interacting with the escaping hydrogen atom, hence the overall process should be described by the following scheme: HAlF4 + e - (HAlF4) H + (AlF4). Recall that (HAlF4) represents the initially formed dipole-bound anion whereas (AlF4) corresponds to the valence-bound anion of a superhalogen nature. Indeed, the molecular orbital holding an excess electron in the final structure is localized entirely in the valence region of the AlF4 moiety, and almost evenly delocalized among the four fluorine atoms (as it was observed for the isolated (AlF4) superhalogen anion,84 see Fig. 3). In addition, the energy difference between the final (AlF4)/H system and its neutral parent (estimated for the anionic (AlF4)/H geometry and thus corresponding to the vertical electron detachment energy) is 9.63 eV (as calculated with the MP2 method, see Table 1), which is in agreement with the vertical electron detachment energy reported earlier for the isolated AlF4 anion (9.79 eV).84 Hence, we are confident that the superhalogen (AlF4) anion and the detached hydrogen atom are the final products of the process investigated.
4. Conclusions We studied the excess electron attachment to the HAlF4 superacid by employing ab initio quantum chemistry methods. The calculations performed with the CCSD(T) and MP2 methods and employing the aug-cc-pVTZ+4s4p3d basis set led us to the following conclusions: (i) the HAlF4 molecule is polar enough to attract a distant excess electron and form a dipole-bound anionic state (whose vertical electron binding energy is 1106 cm1); (ii) the initially formed (HAlF4) anion of a dipole-bound nature is not geometrically stable and it undergoes an immediate structural reorganization driven by the formation of the more stable (AlF4) valence-bound superhalogen anion; (iii) the (HAlF4) - (AlF4) + H transformation proceeds spontaneously and involves the simultaneous shortening of one Al–F bond, forming a tetrahedral AlF4 structure, the loss of the hydrogen atom, and the excess electron density migration (from the area outside the molecular framework to the valence region); (iv) the fragmentation of the HAlF4 superacid is expected to be the final effect of the excess electron attachment process, as the separated (AlF4) anion and the radical neutral hydrogen atom are identified as its end products; (v) the initially formed (HAlF4) dipole-bound anion, albeit only vertically electronically stable, plays an important antenna role in the overall process (it enables an excess electron attraction and opens the door to the further steps, including the valence region penetration). Even though this dissociative excess electron attachment discussed in this contribution was predicted for one superacid molecule, we anticipate that this behavior might be more general and typical for many similar compounds (due to the
Phys. Chem. Chem. Phys.
PCCP
large electronic stability of the superhalogen anions being the final products of such hypothetical reactions).
Acknowledgements This research was supported by the Polish Ministry of Science and Higher Education grant no. DS 530-8376-D499-14 (to P.S.) and partially by the Polish Ministry of Science and Higher Education grant no. BMN/538-8375-B666-14 and BMN/5388375-B666-15 (to M.C.). The calculations have been carried out using resources provided by the Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant no. 350 (to M.C.).
References 1 R. J. Gillespie and T. E. Peel, Adv. Phys. Org. Chem., 1971, 9, 1–24. 2 R. J. Gillespie and T. E. Peel, J. Am. Chem. Soc., 1973, 95, 5173–5178. 3 H. Hogeveen and A. F. Bickel, Recl. Trav. Chim. Pays-Bas, 1969, 88, 371–378. 4 H. Hogeveen and A. F. Bickel, J. Chem. Soc., Chem. Commun., 1967, 635–636. 5 A. F. Bickel, C. J. Gaasbeek, H. Hogeveen, J. M. Oelderik and J. C. Platteeuw, J. Chem. Soc., Chem. Commun., 1967, 634–635. 6 G. A. Olah and R. H. Schlosberg, J. Am. Chem. Soc., 1968, 90, 2726–2727. 7 G. A. Olah, Y. Halpern, J. Shen and Y. K. Mo, J. Am. Chem. Soc., 1971, 93, 1251–1256. 8 G. A. Olah and J. Lukas, J. Am. Chem. Soc., 1967, 89, 2227–2228. 9 N. F. Hall and J. B. Conant, J. Am. Chem. Soc., 1927, 49, 3047–3061. 10 D. Touiti, R. Jost and J. Sommer, J. Chem. Soc., Perkin Trans. 2, 1986, 1793–1797. 11 R. Jost and J. Sommer, Rev. Chem. Intermed., 1988, 9, 171–199. 12 G. A. Olah, G. K. Prakash and J. Sommer, Science, 1979, 206, 13–20. 13 G. A. Olah, G. K. Prakash and J. Sommer, Superacids, John Wiley and Sons, New York, 1985. 14 I. A. Koppel, P. Burk, I. Koppel, I. Leito, T. Sonoda and M. Mishima, J. Am. Chem. Soc., 2000, 122, 5114–5124. 15 A. H. Otto, T. Steiger and S. Schrader, Chem. Commun., 1998, 391–392. 16 M. Czapla and P. Skurski, Chem. Phys. Lett., 2015, 630, 1–5. 17 C. Sikorska, S. Freza and P. Skurski, J. Phys. Chem. A, 2010, 114, 2235–2239. 18 S.-H. Cui, Y. Li, F. F. Wang, D. Wu and Z.-R. Li, Phys. Chem. Chem. Phys., 2007, 9, 5721–5726. 19 J. Tong, Y. Li, D. Wu, S.-H. Cui, Z.-R. Li and X.-R. Huang, Chem. Phys. Lett., 2010, 496, 20–24.
This journal is © the Owner Societies 2015
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PCCP
20 M. Gutowski and P. Skurski, Recent Res. Dev. Phys. Chem., 1999, 3, 245–260. 21 J. Simons and P. Skurski, in Theoretical Prospects of Negative Ions, ed. J. Kalcher, Research Signpost, Trivandrum, 2002. 22 M. Gutowski, P. Skurski, A. I. Boldyrev, J. Simons and K. D. Jordan, Phys. Rev. A: At., Mol., Opt. Phys., 1996, 54, 1906–1909. 23 L. Adamowicz and E. A. McCullough Jr., Chem. Phys. Lett., 1984, 107, 72–76. 24 L. Adamowicz and E. A. McCullough, Jr., J. Phys. Chem., 1984, 88, 2045–2048. 25 N. A. Oyler and L. Adamowicz, J. Phys. Chem., 1993, 97, 11122–11123. 26 G. L. Gutsev and L. Adamowicz, Chem. Phys. Lett., 1995, 246, 245–250. 27 G. L. Gutsev, M. Nooijen and R. J. Bartlett, Chem. Phys. Lett., 1997, 267, 13–19. 28 G. L. Gutsev, M. Nooijen and R. J. Bartlett, Phys. Rev. A: At., Mol., Opt. Phys., 1998, 57, 1646–1651. 29 G. L. Gutsev and R. J. Bartlett, J. Chem. Phys., 1996, 105, 8785–8792. 30 M. Gutowski, K. D. Jordan and P. Skurski, J. Phys. Chem. A, 1998, 102, 2624–2633. 31 M. Gutowski and P. Skurski, J. Chem. Phys., 1997, 107, 2968–2973. 32 K. D. Jordan and W. Luken, J. Chem. Phys., 1976, 64, 2760–2766. 33 K. D. Jordan and J. J. Wendoloski, Chem. Phys., 1977, 21, 145–154. 34 Y. Yoshioka and K. D. Jordan, J. Chem. Phys., 1980, 73, 5899–5901. 35 P. Skurski, M. Gutowski and J. Simons, J. Chem. Phys., 1999, 110, 274–280. 36 M. Gutowski, P. Skurski and J. Simons, J. Am. Chem. Soc., 2000, 122, 10159–10162. 37 P. Skurski and J. Simons, J. Chem. Phys., 2001, 115, 8373–8380. 38 J. V. Coe, G. H. Lee, J. G. Eaton, S. T. Arnold, H. W. Sarkas, C. Ludewigt, H. Haberland, D. R. Worsnop and K. H. Bowen Jr., J. Chem. Phys., 1990, 92, 3980–3982. 39 A. W. Castelman Jr. and K. H. Bowen Jr., J. Phys. Chem., 1996, 100, 12911–12944. 40 D. M. Wetzel and J. I. Brauman, J. Chem. Phys., 1989, 90, 68–73. 41 B. C. Romer and J. I. Brauman, J. Am. Chem. Soc., 1997, 119, 2054–2055. 42 J. A. D. Stockdale, F. J. Davis, R. N. Compton and C. E. Klots, J. Chem. Phys., 1974, 60, 4279–4285. 43 R. N. Compton, P. W. Reinhardt and C. D. Cooper, J. Chem. Phys., 1978, 68, 4360–4367. 44 C. Desfrançois, H. Abdoul-Carime, C. P. Schulz and J. P. Schermann, Science, 1995, 269, 1707–1709. 45 C. Desfrançois, Phys. Rev. A: At., Mol., Opt. Phys., 1995, 51, 3667–3675. 46 C. E. H. Dessent, J. Kim and M. A. Johnson, J. Phys. Chem., 1996, 100, 12–24.
This journal is © the Owner Societies 2015
Paper
47 C. E. H. Dessent, J. Kim and M. A. Johnson, Acc. Chem. Res., 1998, 31, 527–534. 48 K. Yokoyama, G. W. Leach, J. B. Kim, W. C. Lineberger, A. I. Boldyrev and M. Gutowski, J. Chem. Phys., 1996, 105, 10706–10718. 49 J. Marks, J. I. Brauman, R. D. Mead, K. R. Lykke and W. C. Lineberger, J. Chem. Phys., 1988, 88, 6785–6792. 50 Q. K. Timerghazin, I. Rizvi and G. H. Peslherbe, J. Phys. Chem. A, 2011, 115, 13201–13209. 51 V. P. Vosotskiy, L. S. Cederbaum, T. Sommerfeld, V. K. Voora and K. D. Jordan, J. Chem. Theory Comput., 2012, 8, 893–900. 52 V. K. Voora, J. Ding, T. Sommerfeld and K. D. Jordan, J. Phys. Chem. B, 2013, 117, 4365–4370. 53 H.-T. Liu, C.-G. Ning, D.-L. Huang, P. D. Dau and L.-S. Wang, Angew. Chem., Int. Ed., 2013, 52, 8976–8979. 54 D. B. Dao and R. Mabbs, J. Chem. Phys., 2014, 141, 154304. 55 D.-L. Huang, G.-Z. Zhu and L.-S. Wang, J. Chem. Phys., 2015, 142, 091103. 56 G. L. Gutsev and A. I. Boldyrev, Chem. Phys., 1981, 56, 277–283. 57 G. L. Gutsev, R. J. Bartlett, A. I. Boldyrev and J. Simons, J. Chem. Phys., 1997, 107, 3867–3875. 58 M. K. Scheller and L. S. Cederbaum, J. Chem. Phys., 1994, 100, 8934–8942. 59 J. V. Ortiz, Chem. Phys. Lett., 1993, 214, 467–472. 60 J. V. Ortiz, J. Chem. Phys., 1993, 99, 6727–6731. 61 G. L. Gutsev, P. Jena and R. J. Bartlett, Chem. Phys. Lett., 1998, 292, 289–294. 62 X.-B. Wang, C.-F. Ding, L.-S. Wang, A. I. Boldyrev and J. Simons, J. Chem. Phys., 1999, 110, 4763–4771. ´ ska and P. Skurski, Chem. Phys. Lett., 2007, 443, 63 S. Smuczyn 190–193. 64 S. Freza and P. Skurski, Chem. Phys. Lett., 2010, 487, 19–23. ´ ska and P. Skurski, Inorg. Chem., 2009, 48, 65 S. Smuczyn 10231–10238. 66 I. Anusiewicz, J. Phys. Chem. A, 2009, 113, 6511–6516. 67 I. Anusiewicz, J. Phys. Chem. A, 2009, 113, 11429–11434. 68 C. Sikorska, S. Freza, P. Skurski and I. Anusiewicz, J. Phys. Chem. A, 2011, 115, 2077–2085. 69 B. Z. Child, S. Giri, S. Gronert and P. Jena, Chem. – Eur. J., 2014, 20, 4736–4745. 70 A. N. Alexandrova, A. I. Boldyrev, Y.-J. Fu, X. Yang, X.-B. Wang and L.-S. Wang, J. Chem. Phys., 2004, 121, 5709–5719. 71 G. D. Purvis III and R. J. Bartlett, J. Chem. Phys., 1982, 76, 1910–1918. 72 J. A. Pople, M. Head-Gordon and K. Raghavachari, J. Chem. Phys., 1987, 87, 5968–5975. 73 P. Skurski, M. Gutowski and J. Simons, Int. J. Quantum Chem., 2000, 80, 1024–1038. 74 C. Sikorska, D. Ignatowska, S. Freza and P. Skurski, J. Theor. Comput. Chem., 2011, 10, 93–110. 75 R. A. Kendall, T. H. Dunning Jr. and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796–6806. 76 M. W. Schmidt and K. Ruedenberg, J. Chem. Phys., 1979, 71, 3951–3962.
Phys. Chem. Chem. Phys.
View Article Online
Paper
81 J. Simons, J. Phys. Chem. A, 2008, 112, 6401–6511. ´ ska, I. Gwarda, I. Anusiewicz and P. Skurski, 82 S. Smuczyn J. Chem. Phys., 2009, 130, 124316. 83 J. W. C. Johns and R. F. Barrow, Proc. R. Soc. A, 1959, 251, 504–518. ´ ska, P. Skurski and I. Anusiewicz, 84 C. Sikorska, S. Smuczyn Inorg. Chem., 2008, 47, 7348–7354.
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
77 B. H. Besler, K. M. Merz Jr. and P. A. Kollman, J. Comput. Chem., 1990, 11, 431–439. 78 M. J. Frisch, et al., Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford, CT, 2009. 79 S. Senger and L. Radom, J. Phys. Chem. A, 2000, 104, 7375–7385. ´riquet, S. Carles, J. P. Schermann and 80 C. Desfrançois, V. Pe L. Adamowicz, Chem. Phys., 1998, 239, 475–483.
PCCP
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2015
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PAPER
Cite this: DOI: 10.1039/c5cp02440d
View Journal
The HAlF4 superacid fragmentation induced by an excess electron attachment Marcin Czapla and Piotr Skurski* The excess electron attachment to the HAlF4 superacid molecule was studied by employing ab initio CCSD(T) and MP2 methods and a purposely suited aug-cc-pVTZ+4s4p3d basis set. The results indicate that the HAlF4 molecule, due to its polarity, may attract a distant excess electron and form a dipole-bound anionic state whose vertical electron binding energy is 1106 cm1. The initially formed (HAlF4) anion of a dipole-bound nature undergoes an immediate structural reorganization driven by the (AlF4) strongly-bound superhalogen anion formation. The potential energy surface analysis leads to the conclusion that the (HAlF4) - (AlF4) + H transformation should proceed spontaneously and involve
Received 27th April 2015, Accepted 17th June 2015
the simultaneous structure relaxation of the AlF4 moiety (in the direction approaching a tetrahedral geometry) and the excess electron density migration from the area outside the molecular framework to
DOI: 10.1039/c5cp02440d
the valence AlF4 region. The fragmentation of the HAlF4 superacid molecule is predicted to be the final effect of the excess electron attachment process. In addition, the important antenna role of the initially
www.rsc.org/pccp
formed (HAlF4) dipole-bound anionic state is discussed.
1. Introduction The enormously strong acidic behavior of species with a Hammett acidity function (H0) smaller than 121,2 has been extensively studied for the last four decades.3–8 The representative examples of such systems, termed superacids (and defined in the 1970s by Gillespie as any acidic structures stronger than 100% sulfuric acid1,2), include certain Brønsted (e.g., HSO3F) and Lewis (e.g., AsF5) acids. In fact, the term superacid appeared in the scientific literature much earlier, namely, in the article written by Hall and Conant in 1927 who provided a description of the salts produced by perchloric acid and sulfuric acid in glacial acetic acid reacting with weak bases.9 One important class of superacids consists of various combinations of strong Lewis and Brønsted acids (e.g., SbF5/HF or HSO3F/SbF5) whose acidic properties are also remarkable. In particular, SbF5/HF (i.e., HSbF6) is commonly considered as the strongest known liquid superacid (exhibiting a H0 of ca. 23).10–13 The theoretically estimated Gibbs free energies of the deprotonation reactions indicate, however, that even stronger acids may exist, such as F(SO3)4H or FSO3SbF5H, as their deprotonation in the gas phase is expected to be even more plausible.14,15 Recently,16 we proposed a few more compounds (i.e., HAl2F7, HAl3F10, and HAl4F13) whose Gibbs free deprotonation energies were found to be significant and comparable to the corresponding values characterizing the HTaF6 and HSbF5 ´sk, Wita Stwosza 63, 80-308, Gdan ´sk, Department of Chemistry, University of Gdan Poland. E-mail: [email protected]
This journal is © the Owner Societies 2015
superacids. In addition, we found out that the deprotonation energies of the HAlnF3n+1 acids (n = 1–4) were closely related to the electronic stabilities of their corresponding (AlnF3n+1) anions.16 Since the corresponding salts are typically more stable than their parent superacids (as we described elsewhere for HAlCl4 acid and its LiAlCl4, NaAlCl4, and KAlCl4 salts),17 their properties and susceptibility to an excess electron attachment were investigated.18,19 In particular, the LiBeX3 (X = F, Cl, Br) salts were found to be capable of forming stable anionic states of a dipole-bound nature and were characterized by relatively large vertical electronic stabilities (spanning the 0.54–0.89 eV range, which is rather untypical for dipole-bound anions and is likely caused by the significant polarity of the LiBeX3 salts).19 The possibility of an excess electron attachment to the superacids, however, has not been investigated thus far. As one may predict, some of the superacids are also polar enough to bind an extra electron, but the stability of such formed anions (exhibiting a dipole-bound nature) might be questionable. As it has been recognized and described in the literature, the dipole-bound states of anions exist primarily due to the longrange dipole potential that causes the density of the excess electron to be localized mainly on the positive side of a molecular dipole.20,21 Even though the static Coulomb stabilization is crucial for the existence of such states, it was found that it may not be the dominant component of the electron binding energy (instead, the dispersion contributions and other electron correlation effects are often responsible for binding an excess electron).20,22 In the last few decades, many dipole-bound
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
anions formed by various polar molecules have been found and investigated theoretically, mostly in the laboratories led by Adamowicz,23–26 Bartlett,27–29 Gutowski,20,22,30,31 Jordan,32–34 and Simons.21,35–37 On the other hand, much of the experimental work was produced in the Bowen,38,39 Brauman,40,41 Compton,42,43 Desfrançois,44,45 Johnson,46,47 and Lineberger48,49 groups. The most recent reports indicate that these theoretical and experimental efforts are being continued.50–55 Since the large electronic stability of superhalogen anions plays an important role in our discussion provided in the following sections, one needs to recall that such anions (whose existence and properties were first described by Gutsev and Boldyrev in 1981)56 are typically very strongly bound systems which is manifested by their vertical electron binding energies spanning the 3.6–13.9 eV range.57–69 Suffice it to say that the superhalogens MXk+1 and their anionic daughters (MXk+1) are usually composed of a central atom M (which is preferably metallic although semi-metals (e.g. B, Ge, As, Sb) or non-metals (e.g., H, P) are also allowed) decorated with k + 1 electronegative ligands (i.e., halogen atoms, halogenoids, electrophilic groups), where k stands for the maximal formal valence of the central atom M. However, the MXk+1 formula might be extended to also include polynuclear MnXnk+1 superhalogens and their corresponding (MnXnk+1) anions (where n stands for the number of central atoms, M). The representative examples of superhalogen anions that have been investigated theoretically and studied experimentally are (LiBr2) and (Na4Cl5), having a mononuclear and polynuclear structure, respectively.62,70 The connection between the superhalogen anions and superacids seems obvious, as the latter often contain a superhalogen fragment in their structure. For example, the HTaF6, HSbF5, or HAlF4 superacids might be viewed as being composed of a superhalogen subunit (TaF6, SbF5, or AlF4) and a hydrogen atom, or alternatively as consisting of the corresponding ionic fragments. The main goal of this work is to provide a description of the excess electron attachment to the HAlF4 superacid in the gas phase. As we demonstrate, the binding of an extra electron induces fragmentation of the system. The key role of both the dipolebound anionic state and the valence-bound anionic state (of a superhalogen nature) in this process is presented and discussed.
2. Methods The equilibrium geometries and the corresponding harmonic vibrational frequencies for the stationary points on the potential energy surface were calculated using the second-order Møller–Plesset (MP2) perturbational method whereas the electron binding energy of the initially formed dipole-bound (HAlF4) anionic state was estimated (by employing the supermolecular approach, i.e., by subtracting the energy of the anion from that of the neutral molecule) using the coupled-cluster method with single, double, and non-iterative triple excitations (CCSD(T)).71,72 While computing the correlation energies, all orbitals except the 1s orbitals of fluorine and the 1s2s2p orbitals of aluminum were included. The relaxed scan of the ground doublet state (HAlF4)
Phys. Chem. Chem. Phys.
PCCP
anionic potential energy surface was performed using the MP2 method. Since we used the methods based on an unrestricted Hartree–Fock (UHF) starting point it was important to make sure that little (if any) artificial spin contamination entered into the final wave functions. We computed the expectation value hS2i for the states studied in this work and found values not exceeding 0.7501 in the doublet anionic cases (at the UHF level). Hence we are certain that the spin contamination is not large enough to significantly affect our findings. As far as the basis sets are concerned, we decided to employ the aug-cc-pVTZ basis supplemented with an additional 4s4p3d set of diffuse functions. Our choice was dictated by the fact that we had to use a basis set which is appropriate for both the weakly dipole-bound anion and the strongly valence-bound superhalogen anion. Therefore, in order to properly describe the neutral molecular host, the aug-cc-pVTZ basis set was chosen, as its usefulness in describing dipole-bound anions has been demonstrated in the past and compared to other commonly used one-electron basis sets.73 Since the aug-ccpVTZ basis set was also found to be adequate for describing the equilibrium structures and electronic stabilities of strongly bound superhalogen anions,74 our choice seems to be appropriate. However, the diffuse character of the orbital describing the loosely bound electron (in a dipole-bound anionic state) necessitates the use of extra diffuse basis functions having very low exponents. Although we do realize that such an additional set of diffuse functions is not necessary to describe the strongly bound valence anionic state formed as the product of the process investigated, it is required to properly describe the dipole-bound anionic state that is initially formed during this process. Hence, while studying the properties of that initially formed dipole-bound anionic state of HAlF4 acid, we performed the calculations using the aug-cc-pVTZ basis set75 supplemented with an additional 4s4p3d set of diffuse functions centered on the hydrogen atom. The calculations for the remaining neutral and anionic states described in this work (including those examined while performing the relaxed potential energy surface scan) were carried out using the same aug-cc-pVTZ+4s4p3d basis set in order to maintain consistency. While studying the vertical electron binding energy of the dipole-bound (HAlF4) anionic state we verified that the inclusion of one additional diffuse 1s1p1d set (which led to the aug-ccpVTZ+5s5p4d basis set) increases the electron binding energy by less than 1 cm1 when calculated at the MP2 level. The extra diffuse functions do not share exponent values and we used even-tempered76 four-term s, four-term p, and three-term d basis sets. The geometric progression ratio was equal to 5.0,73 and for each symmetry we started to build up the exponents of the extra diffuse functions from the lowest exponent of the same symmetry included in the aug-cc-pVTZ basis set designed for hydrogen. As a consequence, we achieved the lowest exponents of 4.0416 105, 1.6320 104, and 1.9760 103 a.u. for the s, p, and d symmetries, respectively. The partial atomic charges were fitted to the electrostatic potential according to the Merz–Singh–Kollman scheme.77
This journal is © the Owner Societies 2015
View Article Online
PCCP
Paper
All calculations were performed with the Gaussian09 (Rev.A.02) software package.78 In order to avoid erroneous results from the default direct SCF calculations with the basis sets with large s, p, and d sets of diffuse functions, the keyword SCF = NoVarAcc was used and the two-electron integrals were evaluated (without prescreening) to a tolerance of 1020 a.u.
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
3. Results and discussion 3.1.
The structure and stability of the neutral HAlF4 superacid
The gas phase equilibrium structure of the neutral HAlF4 molecule is well established, as it was investigated by Senger and Radom79 and was recently confirmed by our group.16 Briefly, the Cs-symmetry of the HAlF4 system (re-examined here at the MP2/aug-cc-pVTZ+4s4p3d level) is composed of a nearly planar AlF3 fragment with its three Al–F bonds of similar lengths (1.65–1.68 Å) and a H–F fragment tethered to it through an elongated (1.989 Å) Al–F bond (see Fig. 1, top). The structure is additionally stabilized by a H-bond formation between the AlF3 and HF subunits, whose length was predicted to be rather large (2.196 Å). The fact that HAlF4 might be considered as consisting of such two units implies that it might also be viewed as a HF molecule that has its F atom forming a dative bond with an underlying F3Al unit. Despite the presence of the elongated (ca. 2 Å) Al–F bond, the neutral HAlF4 system was
Fig. 1 The MP2/aug-cc-pVTZ+4s4p3d equilibrium structure of the neutral HAlF4 molecule in the gas phase (top) and the singly occupied molecular orbital holding an excess electron in the (HAlF4) dipolebound anion (bottom).
This journal is © the Owner Societies 2015
found to be stable towards HF molecule elimination (an elimination energy of 16.4 kcal mol1 and a Gibbs free energy of 7.1 kcal mol1 (at T = 298.15 K) for this process were established). In addition, the deprotonation energy (280 kcal mol1) and the Gibbs free deprotonation energy (269 kcal mol1, at T = 298.15) predicted for this compound indicated its very strong acidic character.16 Since a proper description of the HAlF4 neutral system is crucial for further discussion, the following statements need to be emphasized: (i) neutral HAlF4 is a closed shell singlet and it consists of the F3Al and HF subunits; (ii) the F atom of the HF unit forms a dative bond with an underlying F3Al unit; and (iii) the HF subunit also corresponds to a closed shell, whereas the F3Al unit is a singlet having a vacant 3p orbital on the Al atom that is used for the Al–F dative bond. As we explain in the following sections, this vacant 3p orbital plays an important role in the fragmentation process described in this contribution. 3.2.
Initial formation of a dipole-bound anion
Since the HAlF4 molecule is polar, an excess electron might be attracted to the positive pole of its molecular dipole. The polarity of the HAlF4 system manifests itself by having a dipole moment of 3.4 Debye, as we calculated for the Cs-symmetry equilibrium structure of the neutral species using the MP2 electron densities (the calculations utilizing the MP4(SDQ) and QCISD densities led to similar values of 3.425 and 3.424 D, respectively). Such a dipole moment is large enough to bind an extra electron (the polarity of the corresponding neutral molecule should be larger than 2.5 Debye to support a dipole-bound anionic state80), hence one may expect the HAlF4 system to form an electronically stable anion. It is well established (see ref. 20, 21, 32, 33 and 81) that the excess electron in a dipolebound anion is usually highly diffuse and localized at a relatively long distance away from the molecular framework, yet on the positive side of its dipole. Hence, one may expect such a distribution of an excess electron density also in the case of the (HAlF4) dipole-bound anion, as the polarity of the neutral HAlF4 parent is not large. Indeed, the singly occupied molecular orbital (SOMO) holding an extra electron resembles the typical SOMOs predicted for many other dipole-bound anions20–22 (see Fig. 1, bottom). Namely, it is diffused and localized outside the molecule, in the vicinity of the hydrogen atom (which corresponds to the positive dipole side). As observed for dipole-bound anions formed by other molecules of a similar polarity,20,22 the excess electron binding energy for this initially formed (HAlF4) dipole-bound state is not large. In particular, we established the vertical electron attachment energy (VAE) as being equal to 1106 cm1 at the CCSD(T)/augcc-pVTZ+4s4p3d level. It seems interesting that the electron correlation effects are responsible for more than 80% of this electron binding energy, as a VAE of only 187 cm1 was predicted at the Hartree–Fock level (at which only the electrostaticexchange and induction interactions are taken into account). Such a contribution coming from the electron correlation effects, albeit large, is not surprising concerning the nature of the system investigated (various dipole-bound anions whose
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
PCCP
electronic stabilities were dominated by the electron correlation contributions were described in the past,20,22,30,31,35–37 e.g., the p-chloroaniline anion82). We verified, however, that this initially formed (HAlF4) dipole-bound anion is not geometrically stable. Unlike what has been established for the majority of other dipole-bound anions investigated thus far (where a minor geometry relaxation upon excess electron attachment was observed),20–22 the (HAlF4) structure undergoes a significant reorganization. This process is associated with the evolution of the excess electron density distribution that finally leads to the hydrogen atom loss, as we explain in the following sections. Hence, we predict the described (HAlF4) dipole-bound anionic state to be a rather short-lived species, yet we consider its role in the overall electron attachment process to be very important. This is because the neutral HAlF4 superacid molecule has no other way of attracting a distant excess electron except through its dipole potential (playing an antenna role). Thus, we conclude that the dipole potential of the neutral HAlF4 molecule enables the long-range attraction of an extra electron which leads to the formation of a short-lived dipole-bound anionic state. The formation of this dipole-bound anion turns out to be the initial step that enables further processes to occur, including electron density evolution, structure relaxation, and finally the H–F bond homolytic cleavage. 3.3.
Dipole-bound to valence-bound anionic state evolution
Once the dipole-bound anionic state is formed, the excess electron is already attracted to the molecular framework of HAlF4 and thus might penetrate its valence region. Certainly, the evolution of the excess electron density distribution has to be caused by some influential factor. We believe that in the case considered, the possibility of the formation of a very strongly bound anionic state is the driving force. Namely, the (AlF4) superhalogen anion might be the final product of the (HAlF4) reorganization, if the hydrogen atom is detached. Even though such a process would require the H–F homolytic bond to rupture (whose energetic cost is about 135.1 0.3 kcal mol1 according to the HF dissociation energy),83 the formation of the (AlF4) anion would lower the energy by a much larger amount, as the excess electron binding energy of (AlF4) is 9.79 eV (226 kcal mol1).84 Hence, the energy profit and loss balance indicates that the dipole-bound to valence-bound anionic state evolution process should be favored (even if it is associated with the necessity of H–F bond cleavage). Indeed, we verified that the structural reorganization of the (HAlF4) system proceeds in this direction. In order to investigate it, we performed a relaxed scan of the ground doublet state anionic potential energy surface of (HAlF4) along the coordinate corresponding to the H–F separation (see Fig. 2 and Table 1). As stated above, the initial step of the overall process is the formation of the dipole-bound (HAlF4) anion (see the structure, SOMO and relative energy value depicted for the corresponding r(H–F) = 0.939 Å in Fig. 2). Recall that this data point represents in fact the energy of the (HAlF4) dipole-bound anion predicted at the equilibrium structure of its neutral parent.
Phys. Chem. Chem. Phys.
Fig. 2 The MP2/aug-cc-pVTZ+4s4p3d energy profile for (HAlF4) obtained by performing a relaxed ground doublet electronic state potential energy surface along the coordinate corresponding to the H–F distance. The molecular orbitals holding an excess electron for the arbitrarily chosen structures are depicted in black frames. The vicinity of the shallow minimum at r(H–F) = 2.790 Å is magnified.
Table 1 The r(H–F) and r(Al–FH) distances (in Å), the F–Al–F–F dihedral angles d (in degrees) and the vertical electron binding energies D (in eV) characterizing the data points plotted in Fig. 2. The last row (r(H–F) = N) corresponds to the isolated (AlF4) anion at its equilibrium Td-symmetry structure84
r(H–F)
r(Al–FH)
d
D
0.939 1.000 1.100 1.200 1.300 1.400 1.500 2.000 2.500 2.790 3.000 5.000 N
1.989 1.851 1.809 1.776 1.754 1.740 1.731 1.712 1.708 1.708 1.708 1.707 1.716
156.86 131.58 127.96 125.50 123.94 122.95 122.27 120.70 120.27 120.27 120.27 120.12 120.00
0.14 0.89 1.52 2.34 3.21 4.05 4.81 7.58 9.08 9.63 9.94 9.56 9.79
Since we were unable to find any (even shallow) minima on the anionic ground state potential energy surface in the vicinity of the lowest energy structure of the neutral HAlF4 molecule, we expect the structure reorganization process to proceed rather instantly. As the potential energy curve is repulsive, the structure further relaxes while the energy goes downhill. The two arbitrarily chosen representative structures on this path (with their corresponding molecular orbitals holding an excess electron) are presented in Fig. 2 (for r(H–F) = 1.50 Å and r(H–F) = 2.00 Å) whereas the detailed values characterizing: (i) the H–F separation, (ii) the Al–FH bond length, (iii) the F–Al–F–F dihedral angle (in the AlF3 subunit), and (iv) the vertical excess electron binding energy for all data points are gathered in Table 1. As it might be seen, the orbital holding an excess electron evolves
This journal is © the Owner Societies 2015
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PCCP
Paper
and eventually becomes localized in the valence region. In particular, it gradually delocalizes itself among the three remaining fluorine atoms while its anti-bonding H–F character escalates. This process is associated with the structure reorganization that progressively leads to the tetrahedral AlF4 moiety. Indeed, the previously elongated Al–FH bond shortens and the F–Al–F–F dihedral angle in the AlF3 subunit approaches 1201 when the H–F distance increases (see Table 1). Then, the flat region of the anionic potential energy surface is reached (at r(H–F) of ca. 2.5 Å), yet the energy keeps decreasing slowly until the shallow minimum is achieved at r(H–F) = 2.790 Å (see the magnified region shown in Fig. 2). Hence, our relaxed scan leads to the final system that corresponds to the AlF4 and H fragments separated by a large distance, with the excess electron localized on the former, which we discuss in the next section. In order to shed more light on this process, the following explanation might be utilized: in the beginning (i.e., when the excess electron is initially bound to the equilibrium structure of the neutral HAlF4 molecule) the system consists of the F3Al and FH subunits linked via the Al–F dative bond. This neutral species is in the singlet closed shell electronic state and its lowest unoccupied molecular orbital is a dipole orbital having a negative energy eigenvalue. The excess electron is initially described by this dipole orbital (see Fig. 1) which leads to the doublet anionic state. It is important to emphasize that the three electrons are crucial for the overall process, namely, the unpaired electron initially occupying the dipole orbital and the electron pair initially localized on the s(F–H) bonding orbital of the HF subunit (recall, that the fourth Al–F bond is not formed yet). As the r(H–F) distance increases (to 1.5 Å and 2.0 Å), the SOMO is evolving but the system remains a doublet electronic state. However, the fourth Al–F bond is being formed simultaneously and it contains two electrons, and as the F–H bond breaks it generates a hydrogen atom that contains one electron. Thus, the singly occupied molecular orbital at the end of the process corresponds to the H atom 1s orbital, whereas the highest doubly occupied molecular orbital (depicted in Fig. 2 for the final r(H–F) distance) is distributed among the ligands in the AlF4 anion. To summarize briefly, the three ‘‘active’’ electrons are localized in the following manner: at the beginning of the process, there are two electrons in a bonding s(F–H) orbital and one electron in the dipole orbital; at the end of the process, there are two electrons in the bonding s(Al–F) orbital and one electron in the departing H atom 1s orbital. Finally, one may notice that both the initial and final dominant electronic configurations are of the same symmetry (s1)2(s2)1, thus we do not have two configurations that cross; instead, there is one dominant configuration whose two orbitals smoothly evolve (one from s(F–H) to s(Al–F); the other from the dipole orbital to the H atom 1s orbital). 3.4.
minimum at r(H–F) = 2.790 Å is present (see Fig. 2), the fragmentation (i.e., the H atom detachment) is expected to proceed because the depth of this minimum does not exceed 0.7 kcal mol1. Thus the hydrogen atom detachment may progress almost freely, as the energy cost of surmounting the kinetic barrier is less than 1 kcal mol1. The Merz–Singh–Kollman population analysis for the resulting (AlF4 H) system depicted in Fig. 3 (i.e., the final product (having the stationary point characteristic) of the fragmentation process) leads to the following observations: (i) the partial atomic charge localized on the hydrogen atom is close to zero (0.01 a.u.); (ii) the partial atomic charges localized on the aluminum and fluorine atoms sum up to ca. 1 a.u. (0.99 a.u.); (iii) almost the entire (99.9%) unpaired spin
The final products of the excess electron attachment
The final structure achieved while performing a relaxed potential energy surface scan corresponds to the two separated species (AlF4 and H), as shown in Fig. 2 and 3. Although a shallow
This journal is © the Owner Societies 2015
Fig. 3 The MP2/aug-cc-pVTZ+4s4p3d equilibrium structure of the final (AlF4 H) product of an excess electron attachment to the HAlF4 superacid molecule. The corresponding orbital (holding an extra electron) is depicted at the bottom.
Phys. Chem. Chem. Phys.
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
Paper
density is localized on the distant H atom. These findings clearly indicate that the resulting (AlF4 H) system consists of the (AlF4) closed shell anion weakly interacting with the escaping hydrogen atom, hence the overall process should be described by the following scheme: HAlF4 + e - (HAlF4) H + (AlF4). Recall that (HAlF4) represents the initially formed dipole-bound anion whereas (AlF4) corresponds to the valence-bound anion of a superhalogen nature. Indeed, the molecular orbital holding an excess electron in the final structure is localized entirely in the valence region of the AlF4 moiety, and almost evenly delocalized among the four fluorine atoms (as it was observed for the isolated (AlF4) superhalogen anion,84 see Fig. 3). In addition, the energy difference between the final (AlF4)/H system and its neutral parent (estimated for the anionic (AlF4)/H geometry and thus corresponding to the vertical electron detachment energy) is 9.63 eV (as calculated with the MP2 method, see Table 1), which is in agreement with the vertical electron detachment energy reported earlier for the isolated AlF4 anion (9.79 eV).84 Hence, we are confident that the superhalogen (AlF4) anion and the detached hydrogen atom are the final products of the process investigated.
4. Conclusions We studied the excess electron attachment to the HAlF4 superacid by employing ab initio quantum chemistry methods. The calculations performed with the CCSD(T) and MP2 methods and employing the aug-cc-pVTZ+4s4p3d basis set led us to the following conclusions: (i) the HAlF4 molecule is polar enough to attract a distant excess electron and form a dipole-bound anionic state (whose vertical electron binding energy is 1106 cm1); (ii) the initially formed (HAlF4) anion of a dipole-bound nature is not geometrically stable and it undergoes an immediate structural reorganization driven by the formation of the more stable (AlF4) valence-bound superhalogen anion; (iii) the (HAlF4) - (AlF4) + H transformation proceeds spontaneously and involves the simultaneous shortening of one Al–F bond, forming a tetrahedral AlF4 structure, the loss of the hydrogen atom, and the excess electron density migration (from the area outside the molecular framework to the valence region); (iv) the fragmentation of the HAlF4 superacid is expected to be the final effect of the excess electron attachment process, as the separated (AlF4) anion and the radical neutral hydrogen atom are identified as its end products; (v) the initially formed (HAlF4) dipole-bound anion, albeit only vertically electronically stable, plays an important antenna role in the overall process (it enables an excess electron attraction and opens the door to the further steps, including the valence region penetration). Even though this dissociative excess electron attachment discussed in this contribution was predicted for one superacid molecule, we anticipate that this behavior might be more general and typical for many similar compounds (due to the
Phys. Chem. Chem. Phys.
PCCP
large electronic stability of the superhalogen anions being the final products of such hypothetical reactions).
Acknowledgements This research was supported by the Polish Ministry of Science and Higher Education grant no. DS 530-8376-D499-14 (to P.S.) and partially by the Polish Ministry of Science and Higher Education grant no. BMN/538-8375-B666-14 and BMN/5388375-B666-15 (to M.C.). The calculations have been carried out using resources provided by the Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant no. 350 (to M.C.).
References 1 R. J. Gillespie and T. E. Peel, Adv. Phys. Org. Chem., 1971, 9, 1–24. 2 R. J. Gillespie and T. E. Peel, J. Am. Chem. Soc., 1973, 95, 5173–5178. 3 H. Hogeveen and A. F. Bickel, Recl. Trav. Chim. Pays-Bas, 1969, 88, 371–378. 4 H. Hogeveen and A. F. Bickel, J. Chem. Soc., Chem. Commun., 1967, 635–636. 5 A. F. Bickel, C. J. Gaasbeek, H. Hogeveen, J. M. Oelderik and J. C. Platteeuw, J. Chem. Soc., Chem. Commun., 1967, 634–635. 6 G. A. Olah and R. H. Schlosberg, J. Am. Chem. Soc., 1968, 90, 2726–2727. 7 G. A. Olah, Y. Halpern, J. Shen and Y. K. Mo, J. Am. Chem. Soc., 1971, 93, 1251–1256. 8 G. A. Olah and J. Lukas, J. Am. Chem. Soc., 1967, 89, 2227–2228. 9 N. F. Hall and J. B. Conant, J. Am. Chem. Soc., 1927, 49, 3047–3061. 10 D. Touiti, R. Jost and J. Sommer, J. Chem. Soc., Perkin Trans. 2, 1986, 1793–1797. 11 R. Jost and J. Sommer, Rev. Chem. Intermed., 1988, 9, 171–199. 12 G. A. Olah, G. K. Prakash and J. Sommer, Science, 1979, 206, 13–20. 13 G. A. Olah, G. K. Prakash and J. Sommer, Superacids, John Wiley and Sons, New York, 1985. 14 I. A. Koppel, P. Burk, I. Koppel, I. Leito, T. Sonoda and M. Mishima, J. Am. Chem. Soc., 2000, 122, 5114–5124. 15 A. H. Otto, T. Steiger and S. Schrader, Chem. Commun., 1998, 391–392. 16 M. Czapla and P. Skurski, Chem. Phys. Lett., 2015, 630, 1–5. 17 C. Sikorska, S. Freza and P. Skurski, J. Phys. Chem. A, 2010, 114, 2235–2239. 18 S.-H. Cui, Y. Li, F. F. Wang, D. Wu and Z.-R. Li, Phys. Chem. Chem. Phys., 2007, 9, 5721–5726. 19 J. Tong, Y. Li, D. Wu, S.-H. Cui, Z.-R. Li and X.-R. Huang, Chem. Phys. Lett., 2010, 496, 20–24.
This journal is © the Owner Societies 2015
View Article Online
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
PCCP
20 M. Gutowski and P. Skurski, Recent Res. Dev. Phys. Chem., 1999, 3, 245–260. 21 J. Simons and P. Skurski, in Theoretical Prospects of Negative Ions, ed. J. Kalcher, Research Signpost, Trivandrum, 2002. 22 M. Gutowski, P. Skurski, A. I. Boldyrev, J. Simons and K. D. Jordan, Phys. Rev. A: At., Mol., Opt. Phys., 1996, 54, 1906–1909. 23 L. Adamowicz and E. A. McCullough Jr., Chem. Phys. Lett., 1984, 107, 72–76. 24 L. Adamowicz and E. A. McCullough, Jr., J. Phys. Chem., 1984, 88, 2045–2048. 25 N. A. Oyler and L. Adamowicz, J. Phys. Chem., 1993, 97, 11122–11123. 26 G. L. Gutsev and L. Adamowicz, Chem. Phys. Lett., 1995, 246, 245–250. 27 G. L. Gutsev, M. Nooijen and R. J. Bartlett, Chem. Phys. Lett., 1997, 267, 13–19. 28 G. L. Gutsev, M. Nooijen and R. J. Bartlett, Phys. Rev. A: At., Mol., Opt. Phys., 1998, 57, 1646–1651. 29 G. L. Gutsev and R. J. Bartlett, J. Chem. Phys., 1996, 105, 8785–8792. 30 M. Gutowski, K. D. Jordan and P. Skurski, J. Phys. Chem. A, 1998, 102, 2624–2633. 31 M. Gutowski and P. Skurski, J. Chem. Phys., 1997, 107, 2968–2973. 32 K. D. Jordan and W. Luken, J. Chem. Phys., 1976, 64, 2760–2766. 33 K. D. Jordan and J. J. Wendoloski, Chem. Phys., 1977, 21, 145–154. 34 Y. Yoshioka and K. D. Jordan, J. Chem. Phys., 1980, 73, 5899–5901. 35 P. Skurski, M. Gutowski and J. Simons, J. Chem. Phys., 1999, 110, 274–280. 36 M. Gutowski, P. Skurski and J. Simons, J. Am. Chem. Soc., 2000, 122, 10159–10162. 37 P. Skurski and J. Simons, J. Chem. Phys., 2001, 115, 8373–8380. 38 J. V. Coe, G. H. Lee, J. G. Eaton, S. T. Arnold, H. W. Sarkas, C. Ludewigt, H. Haberland, D. R. Worsnop and K. H. Bowen Jr., J. Chem. Phys., 1990, 92, 3980–3982. 39 A. W. Castelman Jr. and K. H. Bowen Jr., J. Phys. Chem., 1996, 100, 12911–12944. 40 D. M. Wetzel and J. I. Brauman, J. Chem. Phys., 1989, 90, 68–73. 41 B. C. Romer and J. I. Brauman, J. Am. Chem. Soc., 1997, 119, 2054–2055. 42 J. A. D. Stockdale, F. J. Davis, R. N. Compton and C. E. Klots, J. Chem. Phys., 1974, 60, 4279–4285. 43 R. N. Compton, P. W. Reinhardt and C. D. Cooper, J. Chem. Phys., 1978, 68, 4360–4367. 44 C. Desfrançois, H. Abdoul-Carime, C. P. Schulz and J. P. Schermann, Science, 1995, 269, 1707–1709. 45 C. Desfrançois, Phys. Rev. A: At., Mol., Opt. Phys., 1995, 51, 3667–3675. 46 C. E. H. Dessent, J. Kim and M. A. Johnson, J. Phys. Chem., 1996, 100, 12–24.
This journal is © the Owner Societies 2015
Paper
47 C. E. H. Dessent, J. Kim and M. A. Johnson, Acc. Chem. Res., 1998, 31, 527–534. 48 K. Yokoyama, G. W. Leach, J. B. Kim, W. C. Lineberger, A. I. Boldyrev and M. Gutowski, J. Chem. Phys., 1996, 105, 10706–10718. 49 J. Marks, J. I. Brauman, R. D. Mead, K. R. Lykke and W. C. Lineberger, J. Chem. Phys., 1988, 88, 6785–6792. 50 Q. K. Timerghazin, I. Rizvi and G. H. Peslherbe, J. Phys. Chem. A, 2011, 115, 13201–13209. 51 V. P. Vosotskiy, L. S. Cederbaum, T. Sommerfeld, V. K. Voora and K. D. Jordan, J. Chem. Theory Comput., 2012, 8, 893–900. 52 V. K. Voora, J. Ding, T. Sommerfeld and K. D. Jordan, J. Phys. Chem. B, 2013, 117, 4365–4370. 53 H.-T. Liu, C.-G. Ning, D.-L. Huang, P. D. Dau and L.-S. Wang, Angew. Chem., Int. Ed., 2013, 52, 8976–8979. 54 D. B. Dao and R. Mabbs, J. Chem. Phys., 2014, 141, 154304. 55 D.-L. Huang, G.-Z. Zhu and L.-S. Wang, J. Chem. Phys., 2015, 142, 091103. 56 G. L. Gutsev and A. I. Boldyrev, Chem. Phys., 1981, 56, 277–283. 57 G. L. Gutsev, R. J. Bartlett, A. I. Boldyrev and J. Simons, J. Chem. Phys., 1997, 107, 3867–3875. 58 M. K. Scheller and L. S. Cederbaum, J. Chem. Phys., 1994, 100, 8934–8942. 59 J. V. Ortiz, Chem. Phys. Lett., 1993, 214, 467–472. 60 J. V. Ortiz, J. Chem. Phys., 1993, 99, 6727–6731. 61 G. L. Gutsev, P. Jena and R. J. Bartlett, Chem. Phys. Lett., 1998, 292, 289–294. 62 X.-B. Wang, C.-F. Ding, L.-S. Wang, A. I. Boldyrev and J. Simons, J. Chem. Phys., 1999, 110, 4763–4771. ´ ska and P. Skurski, Chem. Phys. Lett., 2007, 443, 63 S. Smuczyn 190–193. 64 S. Freza and P. Skurski, Chem. Phys. Lett., 2010, 487, 19–23. ´ ska and P. Skurski, Inorg. Chem., 2009, 48, 65 S. Smuczyn 10231–10238. 66 I. Anusiewicz, J. Phys. Chem. A, 2009, 113, 6511–6516. 67 I. Anusiewicz, J. Phys. Chem. A, 2009, 113, 11429–11434. 68 C. Sikorska, S. Freza, P. Skurski and I. Anusiewicz, J. Phys. Chem. A, 2011, 115, 2077–2085. 69 B. Z. Child, S. Giri, S. Gronert and P. Jena, Chem. – Eur. J., 2014, 20, 4736–4745. 70 A. N. Alexandrova, A. I. Boldyrev, Y.-J. Fu, X. Yang, X.-B. Wang and L.-S. Wang, J. Chem. Phys., 2004, 121, 5709–5719. 71 G. D. Purvis III and R. J. Bartlett, J. Chem. Phys., 1982, 76, 1910–1918. 72 J. A. Pople, M. Head-Gordon and K. Raghavachari, J. Chem. Phys., 1987, 87, 5968–5975. 73 P. Skurski, M. Gutowski and J. Simons, Int. J. Quantum Chem., 2000, 80, 1024–1038. 74 C. Sikorska, D. Ignatowska, S. Freza and P. Skurski, J. Theor. Comput. Chem., 2011, 10, 93–110. 75 R. A. Kendall, T. H. Dunning Jr. and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796–6806. 76 M. W. Schmidt and K. Ruedenberg, J. Chem. Phys., 1979, 71, 3951–3962.
Phys. Chem. Chem. Phys.
View Article Online
Paper
81 J. Simons, J. Phys. Chem. A, 2008, 112, 6401–6511. ´ ska, I. Gwarda, I. Anusiewicz and P. Skurski, 82 S. Smuczyn J. Chem. Phys., 2009, 130, 124316. 83 J. W. C. Johns and R. F. Barrow, Proc. R. Soc. A, 1959, 251, 504–518. ´ ska, P. Skurski and I. Anusiewicz, 84 C. Sikorska, S. Smuczyn Inorg. Chem., 2008, 47, 7348–7354.
Published on 17 June 2015. Downloaded by Freie Universitaet Berlin on 03/07/2015 20:17:07.
77 B. H. Besler, K. M. Merz Jr. and P. A. Kollman, J. Comput. Chem., 1990, 11, 431–439. 78 M. J. Frisch, et al., Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford, CT, 2009. 79 S. Senger and L. Radom, J. Phys. Chem. A, 2000, 104, 7375–7385. ´riquet, S. Carles, J. P. Schermann and 80 C. Desfrançois, V. Pe L. Adamowicz, Chem. Phys., 1998, 239, 475–483.
PCCP
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2015
