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Dinuclear superhalogen anions containing two different central atoms
Journal of Fluorine Chemistry 199 (2017) 97–102
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Dinuclear superhalogen anions containing two different central atoms
MARK
Marcin Czapla Laboratory of Quantum Chemistry, Faculty of Chemistry, University of Gdańsk Wita Stwosza 63, 80-308 Gdańsk, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: Superhalogens Anions Calculations Vertical electron detachment energy
Novel dinuclear superhalogen anions containing two different central atoms (i.e., LiNaF3−, BeMgF5−, and AlBF7–) were investigated theoretically on the basis of ab initio MP2 and CCSD(T) calculations. Their vertical electron detachment energies, thermodynamic stability and the nature of doubly occupied highest molecular orbitals were examined and discussed. All the anions studied in this work were found stable against fragmentation processes and are characterized by significant VDE values (8.12–10.96 eV at the OVGF/6311+G(3df) level) comparable to those of their corresponding classical counterparts.
1. Introduction Originally described by Gutsev and Boldyrev in 1981 [1], strong electron acceptors called “superhalogens” are still fascinating objects of investigation for theoretical and experimental research groups from around the world. These unusual systems were initially defined as compounds matching simple general formula MXk+1 (mononuclear superhalogens) or MnXnk+1 (their polynuclear counterparts) [2–6]. In general, it means that the central metal atom M is surrounded by k+1 halogen ligands (k stands for the maximal formal valence of atom M), whereas n is the number of central atoms in the polynuclear systems. Due to their enormous values of the electron affinity (exceeding that of the chlorine atom − 3.62 eV [7]), superhalogens form very strongly bound and thermodynamically stable MXk+1− and MnXnk+1− superhalogen anions which are characterized by the extremely high values of the vertical electron detachment energies (VDEs) [8,9]. It should be stressed, that the very first experimental confirmation of superhalogens’ existence was provided almost 20 years after their primary theoretical prediction, when the Wang group published first photoelectron spectra of the selected triatomic superhalogen anions [10]. Since then, many other superhalogen systems (e.g. NakCl−k+1 (k = 1 − 4) anions) were investigated experimentally [11,12]. Additionally, the alternative superhalogens, in which non-metal atoms (e.g. silicone, hydrogen or even some noble gases) play the central atom role, were described [13–15]. It was also established that non-halogen ligands [16–18] or even non-modified superhalogens [19–21] could be utilized in designing novel strong electron acceptors. Recently, in addition to their numerous applications, the possible use of superhalogens as effective oxidizing agents (with respect to the molecules and nanoparticles characterized by the high ionization potentials) [22–26], LewisBrønsted superacids precursors [27,28] and steric shielding agents
E-mail address: [email protected]. http://dx.doi.org/10.1016/j.jfluchem.2017.05.003 Received 23 February 2017; Received in revised form 5 May 2017; Accepted 5 May 2017 Available online 08 May 2017 0022-1139/ © 2017 Elsevier B.V. All rights reserved.
(with respect to selected metal cations) [29] was presented. Moreover, some recent studies showed their novel applications in Li-ion batteries, hydrogen storage materials and solar cells [30–33]. Furthermore, it was shown that introducing various ligands into superhalogen anion reduces its electronic stability [34]. Among the six NaX2− anions investigated (X = F, Cl, Br), the highest vertical electron detachment energy was found for the NaF2− system as well as the strong excess electron binding energy dependence on the ligand type was observed. On the other hand, one may consider the opposite situation − i.e., introducing of two different central atoms from the same main group into one superhalogen structure. Hence, in this contribution we present a novel type of superhalogen systems − dinuclear superhalogen anions containing two various central atoms belonging to the 1st, 2nd and 13th groups of the Mendeleev periodic table (i.e., LiNaF3−, BeMgF5−, and AlBF7−) and we compare their properties and electronic stabilities to those of the corresponding classical dinuclear compounds (i.e., Li2F3−, Na2F3−, Be2F5−, Mg2F5−, B2F7−, and Al2F7− anions). To the best of our knowledge such mixed superhalogen anions (containing two different central atoms from the same group of the periodic table) have not been described in the literature thus far, so we believe that the results we provide in this work might be useful for experimental groups and will inspire further investigations in this direction. 2. Methods The equilibrium structures of all systems investigated in this work as well as the corresponding harmonic vibrational frequencies were obtained using the second order Møller-Plesset perturbation method (MP2) [35,36] together with the 6-311+G(d) basis set [37,38]. The electronic energies were calculated by employing the coupled-cluster
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method with single, double and non-iterative triple excitations (CCSD (T)) [39,40] and the 6–311+G(3df) basis set. The thermodynamic stability of novel LiNaF3−, BeMgF5−, and AlBF7− anions was verified through the analysis of the Gibbs free energies of the most probable fragmentation reactions. In the other words, we chose the fragmentation paths which lead to the most stable products. The Gibbs free energies were evaluated by applying the CCSD(T)/6-311+G(3df) electronic energies together with the zero-point energy corrections, thermal corrections (at T = 298.5 K) and entropy contributions calculated at the MP2/6–311+G(d) level. The vertical electron detachment energies of the anionic systems investigated were obtained by applying the direct scheme − outer valence Green function OVGF method (B approximation) [41–49] together with the 6-311+G(3df) basis set. It needs to be pointed out, that this level of theory has often been used for superhalogen anions before and resulted in an excellent agreement with the experimental results [11,50]. Because the OVGF method remains valid only for outer valence ionizations for which the pole strengths (PSs) are higher than 0.80–0.85 [51], we verified that the PS values were large enough to justify the usage of OVGF approximation (the smallest PS found for the states studied in this contribution is 0.92). All calculations were performed with the GAUSSIAN09 (Rev.E.01) package [52], whereas the three-dimensional plots of molecular orbitals were generated with the ChemCraft program.
Table 1 The symmetry point groups, relative energies (REs) and vertical electron detachment energies (VDEs calculated at the OVGF/6–311+G(3df) level) of the isomers whose relative energies are not larger than 10 kcal/mol of all anions investigated in this work. Species
Symmetry
RE [kcal/mol]
VDE [eV]
Li2F3−(1) Li2F3− (2) LiNaF3−(1) LiNaF3− (2) Na2F3−(1) Na2F3− (2) Na2F3− (3) Be2F5−(1) Be2F5− (2) Be2F5− (3) BeMgF5−(1) BeMgF5− (2) Mg2F5−(1) B2F7− AlBF7− Al2F7−
D∞h C2v C∞v C3v D∞h D3h C2v C2v C2 D3h C2v C3v D3h C2 Cs D3d
0.0 9.3 0.0 8.1 0.0 2.6 4.7 0.0 0.5 3.2 0.0 0.9 0.0 – – –
8.51 7.12 8.12 7.18 8.09 7.31 6.88 9.44 10.29 9.86 9.39 9.92 10.03 10.63 10.96 11.36
mol are depicted in Fig. 1. The higher energy isomers characterized by the relative energies larger than 10 kcal/mol (i.e., Li2F3− (3), LiNaF3− (3), and LiNaF3− (4) structures) are presented in Supplementary data. The global energy minima are labeled 1, whereas the higher energy isomers are labeled 2, 3, and 4. The Li2F3− superhalogen anion was recently described by Wileńska and co-workers who concluded that preferred equilibrium geometries of the LinFn+1− anions (n = 2–5) correspond to the high-symmetry compact structures [53]. Indeed, the lowest energy structure of the Li2F3− anion is linear (D∞h-symmetry) with the LieF bond lengths equal to 1.68 and 1.74 Å (see Ref. [53], Fig. 1, and the Supplementary
3. Results and discussion 3.1. Dinuclear anions containing Li and Na as central atoms The equilibrium structures of dinuclear superhalogen anions containing lithium and sodium as central atoms (i.e., Li2F3−, Na2F3−, and LiNaF3− systems) whose relative energies (RE) do not exceed 10 kcal/
Fig. 1. The equilibrium structures of dinuclear superhalogen anions containing Li and Na as central atoms (the isomers whose relative energy does not exceed 10 kcal/mol). The relative energies (RE) of geometrical isomers are in kcal/mol, the interatomic distances are given in Å.
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data), whereas higher energy isomers Li2F3− (2) and Li2F3− (3) correspond to the C2v and D3h-symmetry structures, respectively. Since the relative energies (RE) of these 2 and 3 isomers are 9.3 and 14.2 kcal/mol (with respect to the lowest energy structure 1 of Li2F3−), one should not consider them as competitive at low temperatures. The vertical electron detachment energies (VDEs) calculated for all Li2F3− isomers using the OVGF method span the 7.12–8.51 eV range (see Table 1 and the Supplementary data). The largest VDE value was predicted for the lowest energy structure 1 of the Li2F3− anion. Superhalogen anions containing two sodium atoms (Na2F3−) are structurally similar to the Li2F3− isomers described above, however, the energetic order of isomers is slightly different. Namely, the global minimum, Na2F3− (1), is also characterized by a linear geometry with two different Na-F bond lengths (2.09 and 2.22 Å, see Fig. 1), but the order of two higher energy isomers 2 and 3 is alternated in comparison to the Li2F3− anionic structures (the Na2F3− (2) isomer corresponds to the D3h-symmetry structure, whereas the Na2F3− (3) isomer resembles a C2v-symmetry planar kite-like structure). The relative energies of the Na2F3− isomers (2.4 and 4.7 kcal/mol for 2 and 3, respectively) are smaller than the REs predicted for the corresponding 2 and 3 isomers of Li2F3−, hence, the formation of isomer 2 of Na2F3− seems to be plausible even at room temperature. The VDEs evaluated for the 1–3 Na2F3− anions are in the range of 6.88–8.09 eV which indicates their smaller electronic stability in comparison to the Li2F3− isomers (excluding the D3h-symmetry isomers for which the opposite situation is observed, see Table 1 and the Supplementary data). The lowest energy isomer of mixed LiNaF3− anion corresponds to the linear C∞v-symmetry structure with the F atom located in the center and connected to the LieF and NaeF fragments, see LiNaF3− (1) in Fig. 1. The distance between the central F atom and the Li atom is predicted to be 1.75 Å, whereas the analogical F-Na separation is much larger (2.27 Å). The lengths of the remaining LieF and NaeF bonds were found to be 1.68 and 2.09 Å, respectively. Three higher energy isomers were also found in the case of LiNaF3− anion: C3v-symmetry LiNaF3− (2) system (resembling the Li2F3− (3) and Na2F3− (2) isomers), and two kite-like C2v-symmetry LiNaF3− (3 and 4) structures that differ by the location of the Li and Na atoms, see Fig. 1 and the Supplementary data). However, the significant relative energies (8.1–33.4 kcal/mol) allow to exclude the possibility of spontaneous formation of the 2–4 isomers of LiNaF3− at low temperatures. The excess electron binding energies of the isomeric structures of the mixed (i.e., containing two different central atoms) LiNaF3− anion span the 6.62-8.12 eV range (see Table 1 and the Supplementary data for details) and the highest value of 8.12 eV was predicted for the global minimum structure (as it was the case for both Li2F3− and Na2F3− anions). Such significant VDE values confirm the superhalogen nature of the LiNaF3− anion, however, one may notice that in general the electronic stabilities of these novel mixed superhalogen anions (LiNaF3−) are slightly higher than those of the Na2F3− anions but definitely smaller than those of the Li2F3− systems.
the gas phase seems possible even at room temperature. The vertical electron detachment energies of all 1–3 isomers of Be2F3− span the 9.44–10.29 eV range, however, the lowest VDE value (9.44 eV) corresponds to the global minimum of the Be2F5− anion (in contrast to the anions containing Li and Na central atoms, see the preceding section). Dinuclear Mg2F5− superhalogen anion has already been described by Anusiewicz and Skurski [54] who found the D3h-symmetry structure (resembling the Be2F5− (3) isomer) to correspond to the global minimum. According to their results (confirmed in this contribution), the lowest energy structure of Mg2F5− (labeled 1 in Fig. 2) contains two magnesium atoms linked via three fluorine atoms which form a triangular ring (the Mg-F bond lengths in that ring are slightly elongated (1.98 Å) in comparison to two remaining MgeF bonds (1.83 Å)). The Mg2F5− (2) isomer was found to be higher in energy by 14.3 kcal/mol than the most stable Mg2F5− (1) structure and resembles the Be2F5− (1) C2v-symmetry species, whereas the third Mg2F5− (3) isomer is a D2d-symmetry system characterized by the relative energy of 24.1 kcal/mol with respect to the lowest energy isomer 1 (see Fig. 2, Ref. [54] and the Supplementary data for the detailed structures). The global minimum of dinuclear superhalogen anion containing two different central atoms from the 2nd group of the periodic table (BeMgF5−) corresponds to the C2v-symmetry structure which is similar to the Be2F5− (1) and Mg2F5− (2) isomers and resembles a planar kitelike fragment (with Mg, Be, and three F atoms located in the same plane) with two additional fluorine ligands connected to the magnesium atom via the Mg-F bonds whose lengths are equal to 1.84 Å. Somewhat larger MgeF separations were predicted in the kite-like fragment (2.06 Å), whereas the BeeF bond lengths were found to span the 1.44–1.52 Å range. In the case of the BeMgF5− anion, only one higher energy isomer was found, namely, the BeMgF5− (2) system characterized by very small relative energy of 0.9 kcal/mol. The structure of this isomer is of C3v-symmetry and resembles the global minimum of the Mg2F5− anion and the Be2F5− (3) structure, in which two central atoms are linked via three fluorine ligands. In this case, MgF bond lengths are equal to 1.82 and 1.98 Å, while the BeeF bonds are 1.46 and 1.66 Å. The electron binding energies calculated for the BeMgF5− isomers are rather substantial (9.39 eV for the global minimum 1 and 9.92 eV for the higher energy isomer 2). Such large values of excess electron binding energies confirm the superhalogen nature of the BeMgF5− anion, however, it needs to be stressed that the electronic stability of BeMgF5− (at its most stable geometry) is slightly smaller than that of the “classical” dinuclear superhalogen anions containing alkaline earth metals (i.e., Be2F5− and Mg2F5−, see the VDE values gathered in Table 1). On the other hand, if one considers the BeMgF5− (2) competitive isomer (RE = 0.9 kcal/mol) whose electronic stability is larger (9.92 eV), the VDE values are comparable to those of the Mg2F5− anion. 3.3. Dinuclear anions containing B and Al as central atoms
3.2. Dinuclear anions containing Be and Mg as central atoms The equilibrium geometries of dinuclear superhalogen anions containing B and Al atoms are depicted in Fig. 3. In each system investigated (i.e., B2F7−, AlBF7−, and Al2F7−) only one minimum energy structure was found. The polynuclear superhalogen anions consisting of aluminum central atoms and fluorine ligands were described in the past [55,56]. The equilibrium structure of the Al2F7− anion corresponds to D3dsymmetry structure in which two aluminum atoms are linked via one fluorine atom. The distances between center fluorine atom and aluminum atoms are equal to 1.80 Å, whereas the remaining Al-F bond lengths are slightly shorter (1.69 Å, see Fig. 3 and Refs. [55,56] for details). In contrast, the B2F7− superhalogen anion has never been described before. Its equilibrium structure resembles that of the Al2F7− anion, but the BeFeB fragment is clearly bent (the B-F-B valence angle
The global minima (labeled 1) and the higher energy isomers (labeled 2 and 3) of the dinuclear superhalogen anions containing Be and Mg atoms are presented in Fig. 2 and in the Supplementary data (the isomers whose relative energies are larger than 10 kcal/mol, i.e., Mg2F5− (2), and Mg2F5− (3) structures). The lowest energy structure of the Be2F5− anion (1) is of C2vsymmetry and resembles the planar kite-like molecular fragment (consisting of two Be and three F atoms) with two fluorine atoms located out of the kite plane, see Fig. 2. The BeeF separations in the BeeFeBe bridging fragments are in the range of 1.52–1.79 Å whereas the remaining BeeF bond lengths are shorter (1.44–1.47 Å). The 2 and 3 isomers of the Be2F3− anion are characterized by small relative energies (0.5 and 3.2 kcal/mol, respectively), hence their presence in 99
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Fig. 2. The equilibrium structures of dinuclear superhalogen anions containing Be and Mg as central atoms (the isomers whose relative energy does not exceed 10 kcal/mol). The relative energies (RE) of isomers are given in kcal/mol, the interatomic distances are provided in Å.
turn indicates the thermodynamic stability of the LiNaF3−, BeMgF5−, and AlBF7− superhalogen anions. In addition, for the reason of completeness, we present the pictures of the highest occupied molecular orbitals (HOMO) of the lowest energy minima of all mixed anions investigated (see Fig. 4). As it can be seen, in each case the HOMO is almost entirely dominated by the contributions from the atomic orbitals (AO) of the F atom linked to the less electronegative central atom. In the case of the BeMgF5− anion, however, the additional contributions (yet almost negligible) from the two neighboring fluorine atoms are also visible. As a result, all the HOMOs exhibit a non-bonding character (with respect to the ligandcentral atom interactions) which was previously described for other classical superhalogen anions [1]. It should be stressed that the nonbonding character of doubly occupied highest molecular orbitals is broken when two different halogen atoms are used as ligands [34], however, as indicated by our findings, this phenomenon does not occur when two different central atoms are introduced into a superhalogen system. Due to the fact that the dinuclear superhalogen anions containing two different central atoms are almost as strongly bound as their corresponding classical counterparts (see Table 1), these systems might be useful for experimentalists (e.g., to design new materials involving strong electron acceptors). Moreover, our conclusion is also supported by the thermodynamic stability and the HOMOs’ non-bonding nature of all anions investigated. We believe that our structures and results presented in this paper will also be representative for other dinuclear superhalogen anions containing two various central atoms.
is 131.4°, while interatomic distances between boron and center fluorine atom are 1.58 Å) which results in C2-symmetry geometry with the remaining BeF bonds spanning the 1.37–1.38 Å range, see Fig. 3. The vertical electron detachment energies obtained for the Al2F7− and B2F7− anions are 11.36 and 10.63 eV, respectively, see Table 1. The equilibrium structure of the AlBF7− mixed anion is very similar to that of the B2F7− system and thus corresponds to the bent CSsymmetry geometry, see Fig. 3. Three AleF bonds are about 1.70 Å, whereas the Al-F bond involving the bridging fluorine atom is slightly elongated (1.79 Å). The same situation is observed for the BeF distances (three bonds are equal to 1.37 Å while the distance between boron and the bridging fluorine is 1.60 Å). The AleFeB valence angle is predicted to be 143.8° and the fluorine ligands are arranged in a staggered manner (as it is also the case for both B2F7− and Al2F7− anions (see Fig. 3 for details). As far as the electronic stability is concerned, the VDE values obtained for the mixed AlBF7− anion clearly indicate its superhalogen nature (the electron binding energy estimated by applying the OVGF scheme is 10.96 eV). Having such predicted VDEs at hand, one may conclude that the AlBF7− superhalogen anion is more strongly bound than the classical B2F7− system, yet its electronic stability is slightly smaller (by 0.4 eV) than that of the Al2F7− anion, see Table 1. 3.4. Thermodynamic stability and highest occupied molecular orbitals of dinuclear anions containing two different central atoms In order to verify the thermodynamic stability of the global minima of mixed superhalogen anions investigated (i.e., LiNaF3− (1), BeMgF5− (1), and AlBF7− systems) we chose the most probable (leading to the most stable products) fragmentation paths and then we estimated the Gibbs free energies (ΔG) of such fragmentation reactions which are gathered in Table 2. The ΔG values obtained for such selected fragmentation routes span the 14.0–113.6 kcal/mol range which in
4. Conclusions On the basis of our ab initio calculations performed at the CCSD(T)/ 6-311+G(3df)//MP2/6-311+G(d) and OVGF/6-311+G(3df))//MP2/ 100
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Fig. 4. Highest occupied molecular orbitals of the lowest energy isomers of the mixed superhalogen anions.
for the BeMgF5− molecule (RE = 0.9 kcal/mol, which indicates the possible existence of both isomers in the gas phase). (iii) The electronic stability of novel dinuclear anions containing two different central atoms (LiNaF3−, BeMgF5− and AlBF7− systems) is similar to that of their corresponding classical superhalogen anions (Li2F3−, Na2F3−, Be2F5−, Mg2F5−, B2F7− and Al2F7−). (iv) All the negatively charged mixed anions investigated are thermodynamically stable systems with respect to the most probable fragmentation reactions (the corresponding Gibbs free energies of the reactions were predicted to span the 14.0–113.6 kcal/mol range). (v) The highest occupied molecular orbitals of the anions containing two different central atoms are dominated by the contributions from the terminal fluorine ligand connected with the less electronegative central atom. All the HOMOs are characterized by the non-bonding nature (with respect to the ligand-central atom interactions).
Fig. 3. The equilibrium structures of dinuclear superhalogen anions containing B and Al as central atoms. The interatomic distances are given in Å. Table 2 Gibbs free energies of selected fragmentation reactions (ΔG in kcal/mol) calculated at the CCSD(T)/6-311+G(3df)//MP2/6-311+G(d) level (at T = 298.15 K). Fragmentation reaction
ΔG [kcal/mol]
LiNaF3− → LiF2− + NaF LiNaF3− → LiF + NaF2− LiNaF3− → LiNaF2 + F− BeMgF5− → BeF3− + MgF2 BeMgF5− → BeF2 + MgF3− BeMgF5− → BeMgF4 + F− AlBF7− → AlF4− + BF3 AlBF7− → AlF3 + BF4− AlBF7− → AlBF6 + F−
34.5 45.3 47.5 53.2 50.7 94.4 14.0 47.5 113.6
Acknowledgements 6-311+G(d) theory levels for novel mixed dinuclear superhalogen anions containing two different central atoms (LiNaF3−, BeMgF5−, and AlBF7− systems), we conclude the following:
This work was supported by the Polish Ministry of Science and Higher Education [grant number DS 530-8375-D499-16]. The calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant no. 350.
(i) The vertical electron detachment energies estimated for the lowest energy isomers of LiNaF3−, BeMgF5−, and AlBF7− anions are 8.12 eV, 9.39 eV, 10.96 eV (at the OVGF/6–311 + G(3df) level), respectively. These results clearly confirm the superhalogen nature of the LiNaF3−, BeMgF5−, and AlBF7− systems. (ii) For the LiNaF3− anion three higher energy isomers characterized by significantly large relative energies (RE = 8.1-33.4 kcal/mol) were found, whereas only one higher energy structure was found
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jfluchem.2017.05.003. 101
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Dinuclear superhalogen anions containing two different central atoms
MARK
Marcin Czapla Laboratory of Quantum Chemistry, Faculty of Chemistry, University of Gdańsk Wita Stwosza 63, 80-308 Gdańsk, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: Superhalogens Anions Calculations Vertical electron detachment energy
Novel dinuclear superhalogen anions containing two different central atoms (i.e., LiNaF3−, BeMgF5−, and AlBF7–) were investigated theoretically on the basis of ab initio MP2 and CCSD(T) calculations. Their vertical electron detachment energies, thermodynamic stability and the nature of doubly occupied highest molecular orbitals were examined and discussed. All the anions studied in this work were found stable against fragmentation processes and are characterized by significant VDE values (8.12–10.96 eV at the OVGF/6311+G(3df) level) comparable to those of their corresponding classical counterparts.
1. Introduction Originally described by Gutsev and Boldyrev in 1981 [1], strong electron acceptors called “superhalogens” are still fascinating objects of investigation for theoretical and experimental research groups from around the world. These unusual systems were initially defined as compounds matching simple general formula MXk+1 (mononuclear superhalogens) or MnXnk+1 (their polynuclear counterparts) [2–6]. In general, it means that the central metal atom M is surrounded by k+1 halogen ligands (k stands for the maximal formal valence of atom M), whereas n is the number of central atoms in the polynuclear systems. Due to their enormous values of the electron affinity (exceeding that of the chlorine atom − 3.62 eV [7]), superhalogens form very strongly bound and thermodynamically stable MXk+1− and MnXnk+1− superhalogen anions which are characterized by the extremely high values of the vertical electron detachment energies (VDEs) [8,9]. It should be stressed, that the very first experimental confirmation of superhalogens’ existence was provided almost 20 years after their primary theoretical prediction, when the Wang group published first photoelectron spectra of the selected triatomic superhalogen anions [10]. Since then, many other superhalogen systems (e.g. NakCl−k+1 (k = 1 − 4) anions) were investigated experimentally [11,12]. Additionally, the alternative superhalogens, in which non-metal atoms (e.g. silicone, hydrogen or even some noble gases) play the central atom role, were described [13–15]. It was also established that non-halogen ligands [16–18] or even non-modified superhalogens [19–21] could be utilized in designing novel strong electron acceptors. Recently, in addition to their numerous applications, the possible use of superhalogens as effective oxidizing agents (with respect to the molecules and nanoparticles characterized by the high ionization potentials) [22–26], LewisBrønsted superacids precursors [27,28] and steric shielding agents
E-mail address: [email protected]. http://dx.doi.org/10.1016/j.jfluchem.2017.05.003 Received 23 February 2017; Received in revised form 5 May 2017; Accepted 5 May 2017 Available online 08 May 2017 0022-1139/ © 2017 Elsevier B.V. All rights reserved.
(with respect to selected metal cations) [29] was presented. Moreover, some recent studies showed their novel applications in Li-ion batteries, hydrogen storage materials and solar cells [30–33]. Furthermore, it was shown that introducing various ligands into superhalogen anion reduces its electronic stability [34]. Among the six NaX2− anions investigated (X = F, Cl, Br), the highest vertical electron detachment energy was found for the NaF2− system as well as the strong excess electron binding energy dependence on the ligand type was observed. On the other hand, one may consider the opposite situation − i.e., introducing of two different central atoms from the same main group into one superhalogen structure. Hence, in this contribution we present a novel type of superhalogen systems − dinuclear superhalogen anions containing two various central atoms belonging to the 1st, 2nd and 13th groups of the Mendeleev periodic table (i.e., LiNaF3−, BeMgF5−, and AlBF7−) and we compare their properties and electronic stabilities to those of the corresponding classical dinuclear compounds (i.e., Li2F3−, Na2F3−, Be2F5−, Mg2F5−, B2F7−, and Al2F7− anions). To the best of our knowledge such mixed superhalogen anions (containing two different central atoms from the same group of the periodic table) have not been described in the literature thus far, so we believe that the results we provide in this work might be useful for experimental groups and will inspire further investigations in this direction. 2. Methods The equilibrium structures of all systems investigated in this work as well as the corresponding harmonic vibrational frequencies were obtained using the second order Møller-Plesset perturbation method (MP2) [35,36] together with the 6-311+G(d) basis set [37,38]. The electronic energies were calculated by employing the coupled-cluster
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method with single, double and non-iterative triple excitations (CCSD (T)) [39,40] and the 6–311+G(3df) basis set. The thermodynamic stability of novel LiNaF3−, BeMgF5−, and AlBF7− anions was verified through the analysis of the Gibbs free energies of the most probable fragmentation reactions. In the other words, we chose the fragmentation paths which lead to the most stable products. The Gibbs free energies were evaluated by applying the CCSD(T)/6-311+G(3df) electronic energies together with the zero-point energy corrections, thermal corrections (at T = 298.5 K) and entropy contributions calculated at the MP2/6–311+G(d) level. The vertical electron detachment energies of the anionic systems investigated were obtained by applying the direct scheme − outer valence Green function OVGF method (B approximation) [41–49] together with the 6-311+G(3df) basis set. It needs to be pointed out, that this level of theory has often been used for superhalogen anions before and resulted in an excellent agreement with the experimental results [11,50]. Because the OVGF method remains valid only for outer valence ionizations for which the pole strengths (PSs) are higher than 0.80–0.85 [51], we verified that the PS values were large enough to justify the usage of OVGF approximation (the smallest PS found for the states studied in this contribution is 0.92). All calculations were performed with the GAUSSIAN09 (Rev.E.01) package [52], whereas the three-dimensional plots of molecular orbitals were generated with the ChemCraft program.
Table 1 The symmetry point groups, relative energies (REs) and vertical electron detachment energies (VDEs calculated at the OVGF/6–311+G(3df) level) of the isomers whose relative energies are not larger than 10 kcal/mol of all anions investigated in this work. Species
Symmetry
RE [kcal/mol]
VDE [eV]
Li2F3−(1) Li2F3− (2) LiNaF3−(1) LiNaF3− (2) Na2F3−(1) Na2F3− (2) Na2F3− (3) Be2F5−(1) Be2F5− (2) Be2F5− (3) BeMgF5−(1) BeMgF5− (2) Mg2F5−(1) B2F7− AlBF7− Al2F7−
D∞h C2v C∞v C3v D∞h D3h C2v C2v C2 D3h C2v C3v D3h C2 Cs D3d
0.0 9.3 0.0 8.1 0.0 2.6 4.7 0.0 0.5 3.2 0.0 0.9 0.0 – – –
8.51 7.12 8.12 7.18 8.09 7.31 6.88 9.44 10.29 9.86 9.39 9.92 10.03 10.63 10.96 11.36
mol are depicted in Fig. 1. The higher energy isomers characterized by the relative energies larger than 10 kcal/mol (i.e., Li2F3− (3), LiNaF3− (3), and LiNaF3− (4) structures) are presented in Supplementary data. The global energy minima are labeled 1, whereas the higher energy isomers are labeled 2, 3, and 4. The Li2F3− superhalogen anion was recently described by Wileńska and co-workers who concluded that preferred equilibrium geometries of the LinFn+1− anions (n = 2–5) correspond to the high-symmetry compact structures [53]. Indeed, the lowest energy structure of the Li2F3− anion is linear (D∞h-symmetry) with the LieF bond lengths equal to 1.68 and 1.74 Å (see Ref. [53], Fig. 1, and the Supplementary
3. Results and discussion 3.1. Dinuclear anions containing Li and Na as central atoms The equilibrium structures of dinuclear superhalogen anions containing lithium and sodium as central atoms (i.e., Li2F3−, Na2F3−, and LiNaF3− systems) whose relative energies (RE) do not exceed 10 kcal/
Fig. 1. The equilibrium structures of dinuclear superhalogen anions containing Li and Na as central atoms (the isomers whose relative energy does not exceed 10 kcal/mol). The relative energies (RE) of geometrical isomers are in kcal/mol, the interatomic distances are given in Å.
98
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data), whereas higher energy isomers Li2F3− (2) and Li2F3− (3) correspond to the C2v and D3h-symmetry structures, respectively. Since the relative energies (RE) of these 2 and 3 isomers are 9.3 and 14.2 kcal/mol (with respect to the lowest energy structure 1 of Li2F3−), one should not consider them as competitive at low temperatures. The vertical electron detachment energies (VDEs) calculated for all Li2F3− isomers using the OVGF method span the 7.12–8.51 eV range (see Table 1 and the Supplementary data). The largest VDE value was predicted for the lowest energy structure 1 of the Li2F3− anion. Superhalogen anions containing two sodium atoms (Na2F3−) are structurally similar to the Li2F3− isomers described above, however, the energetic order of isomers is slightly different. Namely, the global minimum, Na2F3− (1), is also characterized by a linear geometry with two different Na-F bond lengths (2.09 and 2.22 Å, see Fig. 1), but the order of two higher energy isomers 2 and 3 is alternated in comparison to the Li2F3− anionic structures (the Na2F3− (2) isomer corresponds to the D3h-symmetry structure, whereas the Na2F3− (3) isomer resembles a C2v-symmetry planar kite-like structure). The relative energies of the Na2F3− isomers (2.4 and 4.7 kcal/mol for 2 and 3, respectively) are smaller than the REs predicted for the corresponding 2 and 3 isomers of Li2F3−, hence, the formation of isomer 2 of Na2F3− seems to be plausible even at room temperature. The VDEs evaluated for the 1–3 Na2F3− anions are in the range of 6.88–8.09 eV which indicates their smaller electronic stability in comparison to the Li2F3− isomers (excluding the D3h-symmetry isomers for which the opposite situation is observed, see Table 1 and the Supplementary data). The lowest energy isomer of mixed LiNaF3− anion corresponds to the linear C∞v-symmetry structure with the F atom located in the center and connected to the LieF and NaeF fragments, see LiNaF3− (1) in Fig. 1. The distance between the central F atom and the Li atom is predicted to be 1.75 Å, whereas the analogical F-Na separation is much larger (2.27 Å). The lengths of the remaining LieF and NaeF bonds were found to be 1.68 and 2.09 Å, respectively. Three higher energy isomers were also found in the case of LiNaF3− anion: C3v-symmetry LiNaF3− (2) system (resembling the Li2F3− (3) and Na2F3− (2) isomers), and two kite-like C2v-symmetry LiNaF3− (3 and 4) structures that differ by the location of the Li and Na atoms, see Fig. 1 and the Supplementary data). However, the significant relative energies (8.1–33.4 kcal/mol) allow to exclude the possibility of spontaneous formation of the 2–4 isomers of LiNaF3− at low temperatures. The excess electron binding energies of the isomeric structures of the mixed (i.e., containing two different central atoms) LiNaF3− anion span the 6.62-8.12 eV range (see Table 1 and the Supplementary data for details) and the highest value of 8.12 eV was predicted for the global minimum structure (as it was the case for both Li2F3− and Na2F3− anions). Such significant VDE values confirm the superhalogen nature of the LiNaF3− anion, however, one may notice that in general the electronic stabilities of these novel mixed superhalogen anions (LiNaF3−) are slightly higher than those of the Na2F3− anions but definitely smaller than those of the Li2F3− systems.
the gas phase seems possible even at room temperature. The vertical electron detachment energies of all 1–3 isomers of Be2F3− span the 9.44–10.29 eV range, however, the lowest VDE value (9.44 eV) corresponds to the global minimum of the Be2F5− anion (in contrast to the anions containing Li and Na central atoms, see the preceding section). Dinuclear Mg2F5− superhalogen anion has already been described by Anusiewicz and Skurski [54] who found the D3h-symmetry structure (resembling the Be2F5− (3) isomer) to correspond to the global minimum. According to their results (confirmed in this contribution), the lowest energy structure of Mg2F5− (labeled 1 in Fig. 2) contains two magnesium atoms linked via three fluorine atoms which form a triangular ring (the Mg-F bond lengths in that ring are slightly elongated (1.98 Å) in comparison to two remaining MgeF bonds (1.83 Å)). The Mg2F5− (2) isomer was found to be higher in energy by 14.3 kcal/mol than the most stable Mg2F5− (1) structure and resembles the Be2F5− (1) C2v-symmetry species, whereas the third Mg2F5− (3) isomer is a D2d-symmetry system characterized by the relative energy of 24.1 kcal/mol with respect to the lowest energy isomer 1 (see Fig. 2, Ref. [54] and the Supplementary data for the detailed structures). The global minimum of dinuclear superhalogen anion containing two different central atoms from the 2nd group of the periodic table (BeMgF5−) corresponds to the C2v-symmetry structure which is similar to the Be2F5− (1) and Mg2F5− (2) isomers and resembles a planar kitelike fragment (with Mg, Be, and three F atoms located in the same plane) with two additional fluorine ligands connected to the magnesium atom via the Mg-F bonds whose lengths are equal to 1.84 Å. Somewhat larger MgeF separations were predicted in the kite-like fragment (2.06 Å), whereas the BeeF bond lengths were found to span the 1.44–1.52 Å range. In the case of the BeMgF5− anion, only one higher energy isomer was found, namely, the BeMgF5− (2) system characterized by very small relative energy of 0.9 kcal/mol. The structure of this isomer is of C3v-symmetry and resembles the global minimum of the Mg2F5− anion and the Be2F5− (3) structure, in which two central atoms are linked via three fluorine ligands. In this case, MgF bond lengths are equal to 1.82 and 1.98 Å, while the BeeF bonds are 1.46 and 1.66 Å. The electron binding energies calculated for the BeMgF5− isomers are rather substantial (9.39 eV for the global minimum 1 and 9.92 eV for the higher energy isomer 2). Such large values of excess electron binding energies confirm the superhalogen nature of the BeMgF5− anion, however, it needs to be stressed that the electronic stability of BeMgF5− (at its most stable geometry) is slightly smaller than that of the “classical” dinuclear superhalogen anions containing alkaline earth metals (i.e., Be2F5− and Mg2F5−, see the VDE values gathered in Table 1). On the other hand, if one considers the BeMgF5− (2) competitive isomer (RE = 0.9 kcal/mol) whose electronic stability is larger (9.92 eV), the VDE values are comparable to those of the Mg2F5− anion. 3.3. Dinuclear anions containing B and Al as central atoms
3.2. Dinuclear anions containing Be and Mg as central atoms The equilibrium geometries of dinuclear superhalogen anions containing B and Al atoms are depicted in Fig. 3. In each system investigated (i.e., B2F7−, AlBF7−, and Al2F7−) only one minimum energy structure was found. The polynuclear superhalogen anions consisting of aluminum central atoms and fluorine ligands were described in the past [55,56]. The equilibrium structure of the Al2F7− anion corresponds to D3dsymmetry structure in which two aluminum atoms are linked via one fluorine atom. The distances between center fluorine atom and aluminum atoms are equal to 1.80 Å, whereas the remaining Al-F bond lengths are slightly shorter (1.69 Å, see Fig. 3 and Refs. [55,56] for details). In contrast, the B2F7− superhalogen anion has never been described before. Its equilibrium structure resembles that of the Al2F7− anion, but the BeFeB fragment is clearly bent (the B-F-B valence angle
The global minima (labeled 1) and the higher energy isomers (labeled 2 and 3) of the dinuclear superhalogen anions containing Be and Mg atoms are presented in Fig. 2 and in the Supplementary data (the isomers whose relative energies are larger than 10 kcal/mol, i.e., Mg2F5− (2), and Mg2F5− (3) structures). The lowest energy structure of the Be2F5− anion (1) is of C2vsymmetry and resembles the planar kite-like molecular fragment (consisting of two Be and three F atoms) with two fluorine atoms located out of the kite plane, see Fig. 2. The BeeF separations in the BeeFeBe bridging fragments are in the range of 1.52–1.79 Å whereas the remaining BeeF bond lengths are shorter (1.44–1.47 Å). The 2 and 3 isomers of the Be2F3− anion are characterized by small relative energies (0.5 and 3.2 kcal/mol, respectively), hence their presence in 99
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Fig. 2. The equilibrium structures of dinuclear superhalogen anions containing Be and Mg as central atoms (the isomers whose relative energy does not exceed 10 kcal/mol). The relative energies (RE) of isomers are given in kcal/mol, the interatomic distances are provided in Å.
turn indicates the thermodynamic stability of the LiNaF3−, BeMgF5−, and AlBF7− superhalogen anions. In addition, for the reason of completeness, we present the pictures of the highest occupied molecular orbitals (HOMO) of the lowest energy minima of all mixed anions investigated (see Fig. 4). As it can be seen, in each case the HOMO is almost entirely dominated by the contributions from the atomic orbitals (AO) of the F atom linked to the less electronegative central atom. In the case of the BeMgF5− anion, however, the additional contributions (yet almost negligible) from the two neighboring fluorine atoms are also visible. As a result, all the HOMOs exhibit a non-bonding character (with respect to the ligandcentral atom interactions) which was previously described for other classical superhalogen anions [1]. It should be stressed that the nonbonding character of doubly occupied highest molecular orbitals is broken when two different halogen atoms are used as ligands [34], however, as indicated by our findings, this phenomenon does not occur when two different central atoms are introduced into a superhalogen system. Due to the fact that the dinuclear superhalogen anions containing two different central atoms are almost as strongly bound as their corresponding classical counterparts (see Table 1), these systems might be useful for experimentalists (e.g., to design new materials involving strong electron acceptors). Moreover, our conclusion is also supported by the thermodynamic stability and the HOMOs’ non-bonding nature of all anions investigated. We believe that our structures and results presented in this paper will also be representative for other dinuclear superhalogen anions containing two various central atoms.
is 131.4°, while interatomic distances between boron and center fluorine atom are 1.58 Å) which results in C2-symmetry geometry with the remaining BeF bonds spanning the 1.37–1.38 Å range, see Fig. 3. The vertical electron detachment energies obtained for the Al2F7− and B2F7− anions are 11.36 and 10.63 eV, respectively, see Table 1. The equilibrium structure of the AlBF7− mixed anion is very similar to that of the B2F7− system and thus corresponds to the bent CSsymmetry geometry, see Fig. 3. Three AleF bonds are about 1.70 Å, whereas the Al-F bond involving the bridging fluorine atom is slightly elongated (1.79 Å). The same situation is observed for the BeF distances (three bonds are equal to 1.37 Å while the distance between boron and the bridging fluorine is 1.60 Å). The AleFeB valence angle is predicted to be 143.8° and the fluorine ligands are arranged in a staggered manner (as it is also the case for both B2F7− and Al2F7− anions (see Fig. 3 for details). As far as the electronic stability is concerned, the VDE values obtained for the mixed AlBF7− anion clearly indicate its superhalogen nature (the electron binding energy estimated by applying the OVGF scheme is 10.96 eV). Having such predicted VDEs at hand, one may conclude that the AlBF7− superhalogen anion is more strongly bound than the classical B2F7− system, yet its electronic stability is slightly smaller (by 0.4 eV) than that of the Al2F7− anion, see Table 1. 3.4. Thermodynamic stability and highest occupied molecular orbitals of dinuclear anions containing two different central atoms In order to verify the thermodynamic stability of the global minima of mixed superhalogen anions investigated (i.e., LiNaF3− (1), BeMgF5− (1), and AlBF7− systems) we chose the most probable (leading to the most stable products) fragmentation paths and then we estimated the Gibbs free energies (ΔG) of such fragmentation reactions which are gathered in Table 2. The ΔG values obtained for such selected fragmentation routes span the 14.0–113.6 kcal/mol range which in
4. Conclusions On the basis of our ab initio calculations performed at the CCSD(T)/ 6-311+G(3df)//MP2/6-311+G(d) and OVGF/6-311+G(3df))//MP2/ 100
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Fig. 4. Highest occupied molecular orbitals of the lowest energy isomers of the mixed superhalogen anions.
for the BeMgF5− molecule (RE = 0.9 kcal/mol, which indicates the possible existence of both isomers in the gas phase). (iii) The electronic stability of novel dinuclear anions containing two different central atoms (LiNaF3−, BeMgF5− and AlBF7− systems) is similar to that of their corresponding classical superhalogen anions (Li2F3−, Na2F3−, Be2F5−, Mg2F5−, B2F7− and Al2F7−). (iv) All the negatively charged mixed anions investigated are thermodynamically stable systems with respect to the most probable fragmentation reactions (the corresponding Gibbs free energies of the reactions were predicted to span the 14.0–113.6 kcal/mol range). (v) The highest occupied molecular orbitals of the anions containing two different central atoms are dominated by the contributions from the terminal fluorine ligand connected with the less electronegative central atom. All the HOMOs are characterized by the non-bonding nature (with respect to the ligand-central atom interactions).
Fig. 3. The equilibrium structures of dinuclear superhalogen anions containing B and Al as central atoms. The interatomic distances are given in Å. Table 2 Gibbs free energies of selected fragmentation reactions (ΔG in kcal/mol) calculated at the CCSD(T)/6-311+G(3df)//MP2/6-311+G(d) level (at T = 298.15 K). Fragmentation reaction
ΔG [kcal/mol]
LiNaF3− → LiF2− + NaF LiNaF3− → LiF + NaF2− LiNaF3− → LiNaF2 + F− BeMgF5− → BeF3− + MgF2 BeMgF5− → BeF2 + MgF3− BeMgF5− → BeMgF4 + F− AlBF7− → AlF4− + BF3 AlBF7− → AlF3 + BF4− AlBF7− → AlBF6 + F−
34.5 45.3 47.5 53.2 50.7 94.4 14.0 47.5 113.6
Acknowledgements 6-311+G(d) theory levels for novel mixed dinuclear superhalogen anions containing two different central atoms (LiNaF3−, BeMgF5−, and AlBF7− systems), we conclude the following:
This work was supported by the Polish Ministry of Science and Higher Education [grant number DS 530-8375-D499-16]. The calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant no. 350.
(i) The vertical electron detachment energies estimated for the lowest energy isomers of LiNaF3−, BeMgF5−, and AlBF7− anions are 8.12 eV, 9.39 eV, 10.96 eV (at the OVGF/6–311 + G(3df) level), respectively. These results clearly confirm the superhalogen nature of the LiNaF3−, BeMgF5−, and AlBF7− systems. (ii) For the LiNaF3− anion three higher energy isomers characterized by significantly large relative energies (RE = 8.1-33.4 kcal/mol) were found, whereas only one higher energy structure was found
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jfluchem.2017.05.003. 101
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