Complexes of adamantane‐based group 13 Lewis acids and superacids: Bonding analysis and thermodynamics of hydrogen splitting

The electronic structure and chemical bonding in donor–acceptor complexes formed by group 13 element adamantane and perfluorinated adamantane derivatives EC9R′15 (E = B, Al; R′ = H, F) with Lewis bases XR3 and XC9H15 (X = N, P; R= H, CH3) have been studied using energy decomposition analysis at the BP86/TZ2P level of theory. Larger stability of complexes with perfluorinated adamantane derivatives is mainly due to better electrostatic and orbital interactions. Deformation energies of the fragments and Pauli repulsion are of less importance, with exception for the boron‐phosphorus complexes. The MO analysis reveals that LUMO energies of EC9R′15 significantly decrease upon fluorination (by 4.7 and 3.6 eV for E = B and Al, respectively) which results in an increase of orbital interaction energies by 27–38 (B) and 15–26 (Al) kcal mol−1. HOMO energies of XR3 increase in order PH3 < NH3 < PMe3 < PC9H15 < NMe3 < NC9H15. For the studied complexes, there is a linear correlation between the dissociation energy of the complex and the energy difference between HOMO of the donor and LUMO of the acceptor. The fluorination of the Lewis acid significantly reduces standard enthalpies of the heterolytic hydrogen splitting H2 + D + A = [HD]+ + [HA]−. Analysis of several types of the [HD]+···[HA]− ion pair formation in the gas phase reveals that structures with additional H···F interactions are energetically favorable. Taking into account the ion pair formation, hydrogen splitting is predicted to be highly exothermic in case of the perfluorinated derivatives both in the gas phase and in solution. Thus, fluorinated adamantane‐based Lewis superacids are attractive synthetic targets for the construction of the donor–acceptor cryptands. © 2016 Wiley Periodicals, Inc.


Introduction
The activation of H 2 molecule by frustrated Lewis pairs (FLPs) has attracted much attention over the past years. [1][2][3][4][5][6] Group 13-15 compounds, in particular, B-P FLP are very active in heterolytic hydrogen splitting. [7] Nitrogen-containing FLP are less common. [4][5][6] Nature of the Lewis acid is expected to play a significant role in energetics of the hydrogen splitting. Fluorination of group 13 element aryl derivatives significantly enhances their Lewis acidity. [8,9] However, the order of Lewis acidity remains controversial. Beckett et al. [10] reported that relative to OPEt 3 donor the Lewis acidity of B(C 6 F 5 ) 3 is weaker than BF 3 . On the other hand, Sakata and Fujimoto [11] reported that the electrophilic nature of the boron center is much stronger in B(C 6 F 5 ) 3 than in BF 3 . Small hydride donor ability of [HB(C 6 F 5 ) 3 ] 2 also indicates high Lewis acidity of B(C 6 F 5 ) 3 . [12] Computational studies [13][14][15] reveal importance of pyramidalized environment for the construction of group 13 Lewis superacids. In particular, it was shown that splitting of H 2 by donor-acceptor (DA) cryptands, featuring spatially separated donor and acceptor centers with pyramidalized environment, is highly exothermic. [13] On the other hand, cryptands designed and computationally considered in a previous work [13] served only as proof of the concept, since they are still experimentally unknown. A more practical approach should be based on the experimentally known pyramidal donor and acceptor molecules, for example adamantane derivatives. Several heteroatom derivatives of adamantane featuring nitrogen, boron, and silicon atoms have been prepared. [16][17][18] 1-Boraadamantane [19,20] and its complexes with N-containing donors [21] are known laboratory species. In addition, Bubnov et al. [22] reported that reaction of 1-boraadamantane with 1azaadamantane results in a DA complex (Scheme 1), which is stable toward atmospheric air and moisture. Synthesis of perfluorinated adamantane derivatives also seems viable due to success of the direct low temperature fluorination. [23] Thus, 1boroadamantane and its fully fluorinated derivatives emerge as viable building blocks for the construction of DA cryptands with pyramidalized group 13 environment. Analysis of the thermodynamics of the hydrogen splitting process is crucial for the correct choice of the Lewis acid-base combination.
In order to provide the best combination of donor and acceptor fragments for the construction of hydrogen splitting cryptands, in the present work we have undertaken a detailed computational study of donor-acceptor complexes formed by group 13 element adamantane and fully fluorinated adamantane derivatives EC 9 R 0 15 with nitrogen and phosphoruscontaining Lewis bases XR 3 and XC 9 H 15 (E 5 B, Al; R 0 5 H, F; X 5 N, P; R 5 H, CH 3 ) using the generalized gradient approximation (GGA) of density functional theory (DFT) in the form of BP86 functional with all electron TZ2P basis set.
We present a consistent set of structural data for the studied complexes and report thermodynamic characteristics for their   formation and reactions with molecular hydrogen. Results of energy decomposition analyses (EDA) and molecular orbital (MO) features of donor-acceptor complexes are presented. Finally, the influence of the donor and acceptor fragments on the thermodynamics of the heterolytic hydrogen splitting is also discussed. Obtained results can serve as a guideline for the construction of the DA cryptands for the heterolytic hydrogen splitting process.

Computational Details
General procedures DFT calculations were performed with the Amsterdam Density Functional (ADF) program. [24,25] The molecular orbitals (MOs) were expanded in a large uncontracted set of Slater type orbitals (STOs) of triple-f quality for all atoms including two sets of polarization functions. [26] An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately for each SCF cycle. [27] Energies and gradients were computed using the local density approximation (Slater exchange and VWN correlation) [28] with non-local corrections for exchange (Becke88) [29] and correlation (Perdew86) [30] included self-consistently (i.e., BP86 functional). Analytical Hessians were computed to confirm that optimized geometries correspond to the true minima on the respective potential energy surfaces (PES). Standard enthalpies, entropies, and Gibbs energies were calculated from frequency computations using classical statistical-mechanics relationships for an ideal gas. [31] Solvent effects in toluene solution are treated with the COSMO model, [32] which takes into account the cavitation and dispersion contributions to the solvation free energy. BP86/TZ2P level of theory yields a mean absolute deviation (MAD) for proton affinities (at 298 K) of several neutral bases across the periodic table of 1.9 kcal mol 21 with respect to experiment. [33] For the best combination of Lewis acid BC 9 F 15 and Lewis base NC 9 H 15 we have compared standard enthalpies of the gas phase heterogeneous hydrogen splitting with formation of the isolated ions (process (4), vide infra). Values at BP86/TZ2P, M06-2X/6-311G**, and B3LYP/TZVP levels of theory are 4.27, 5.33, and 21.33 kcal mol 21 , respectively. Thus, values at BP86/TZ2P level are within 1 kcal mol 21 of M06-2X/6-311G** results and by 5 kcal mol 21 less exothermic than B3LYP/ TZVP results. Thus, our qualitative conclusions about the energetic favorability of the reactions are expected to be correct.

Bond energy decomposition analysis
An energy decomposition analysis (EDA) [34][35][36][37][38] has been carried out considering the process D 1 A ! DA that corresponds to the interaction of donor (D) fragment with acceptor (A) fragment. The complex formation energy (DE) can be written as a sum of two components [eq. (1)]: In this formula, the deformation energy DE def is the amount of energy required to deform the separated donor and acceptor fragments from their equilibrium structures to the geometry that they acquire in the complex. The interaction energy DE int corresponds to the energy change when the prepared (deformed) fragments are combined to form DA complex. It is analyzed in the framework of the Kohn-Sham MO model using a Morokuma-type decomposition of the interaction energy into electrostatic interaction, exchange (or Pauli) repulsion, and orbital interaction terms [eq. (2). [34,38] The term DV elstat is usually attractive. It corresponds to the classical electrostatic interaction between the unperturbed charge distribution of the prepared (deformed) fragments. The Pauli repulsion DE Pauli comprises the four-electron destabilizing interactions between occupied MOs. The orbital interaction DE oi term accounts for the charge transfer (i.e., donor-acceptor interactions between occupied orbitals on one fragment with unoccupied orbitals of the other, including the HOMO-LUMO interactions) and polarization (empty-occupied orbital mixing on one fragment due to the presence of another fragment).

Results and Discussion
Structural and energetic features of the donor-acceptor complexes The optimized geometries of the closed-shell singlet ground state of donor-acceptor complexes are shown in Figure 1.
All complexes are C 3v symmetric. Table 1 summarizes selected geometric parameters of the compounds. The Table 1. Selected geometrical parameters of studied complexes (bond lengths d and r in Å and angles a in degrees) [a] , standard dissociation enthalpies D diss H8 298 in kcal mol 21 and standard dissociation entropies D diss S8 298 (in cal mol 21 K 21 ), and dipole moments l (in Debye). Cartesian coordinates of all studied complexes are provided in the Supporting Information (Table S1). Thermodynamic parameters (standard dissociation enthalpies and entropies) are also given in Table 1, together with dipole moments. As can be seen from Table 1, dissociation enthalpies of complexes with BC 9 H 15 are in the range 8.6-20.8 kcal mol 21 . These values can be compared with experimental gas phase dissociation enthalpies of 1-Quinuclidine-BMe 3 and 1-pyridine-1boraadamantane complexes (19.9 6 1 kcal mol 21 and 22.7 6 0.7 kcal mol 21 , respectively). [39,40] The fluorination of the acceptor moiety does not affect much the standard dissociation entropies, which are in range 28-54 cal mol 21 K 21 for the non fluorinated and 34-55 cal mol 21 K 21 for fluorinated compounds. Computed dipole moments of 1-boraadamantane complexes ( Table 1) are comparable with experimental values of dipole moments in benzene solution for 1-boraadamantane-pyridine (6.0 6 0.15 D) and 1-boraadamantane-quinuclidine (6.2 6 0.2 D). [41] The fluorination of the acceptor moiety dramatically increases the dissociation enthalpy of the boron-containing complexes (by about 40-48 kcal mol 21 ). For aluminumcontaining compounds fluorination effect is smaller than for boron analogues (dissociation enthalpies increase by about 22-31 kcal mol 21 ). Note that complexes with BC 9 F 15 have larger dissociation energies compared to those with AlC 9 F 15 , which reflects higher Lewis acidity of fluorinated boron-containing pyramidalized Lewis acids. [42] Trends in bond dissociation enthalpies for phosphorus-containing complexes are similar to those of nitrogen analogues. Thus, perfluorinated group 13 adamantane derivatives form the most stable complexes with large dissociation energies and large dipole moments. Since dissociation enthalpies of complexes of EC 9 F 15 are much larger than that of AlCl 3 , [43] perfluorinated adamantane derivatives are Lewis superacids in terms of Olah's definition. [44]   Due to high Lewis acidity, perfluorinated group 13 adamantane derivatives would be extremely difficult to isolate as free compounds, but synthesis of their complexes seems reliable. On the basis of bond angle 2 bond distance 2 bond energy relationship, [42,43] decrease of the C -E 2 C angle upon complex formation has been previously used as a quantitative indicator for the strength of the unstrained group 13 Lewis acids. However, for the rigid pyramidalized adamantane-type Lewis acids studied in the present work, the structural changes upon complex formation are very small. Fluorination of the acceptor moiety also has little effect on the structural parameters. Upon fluorination, B-X bond distances shorten by 0.066-0.068 Å with the only exception of the P(CH 3 ) 3 donor, B-C bond lengths increase by 0.003-0.027 Å , and C -B 2 C angles decrease by about 1.6-3.58. For aluminum analogues, upon fluorination Al-X bond distances shorten by 0.085-0.116 Å , Al-C bond distances increase by 0.033-0.042 Å , and C 2 Al 2 C angles decrease by 4.8-5.38.

Bonding analysis
In order to understand the origin of the higher stability of complexes of group 13 fluorinated adamantane derivatives we have undertaken an energy decomposition analysis (EDA) of the complexes in their closed shell ground state with respect to isolated fragments (Tables 2 and 3). The total bonding energies (DE) for complexes with fluorinated acceptors are by 40.6-50.8 kcal mol 21 larger compared to non-fluorinated. This difference mainly comes from the interaction energy (DE int ), as deforma-tion energies (DE def ) favor hydrogen-substituted complexes (a maximum difference 7.4 kcal mol 21 ). On the other hand, aluminum complexes present the same trends, but with smaller differences (Table 3). DE differences are in the range 20.7-32.2 kcal mol 21 , and DE def also favor hydrogenated systems with a maximum difference of 4.5 kcal mol 21 . Thus, we must go into the decomposition of DE int into Pauli, electrostatic and orbital interaction terms in order to get an explanation for the larger strength of the bond formed in fluorinated complexes. Pauli repulsion does not give a clear trend, thus disfavoring fluorinated complexes with the exception of all B-P complexes and NH 3 ÁBC 9 H 15 . For the same geometry, fluorinated compounds should have larger Pauli repulsion because they have more electrons. Lower Pauli repulsion for fluorinated compounds is attributed to their smaller a(C-B-C) angles. In the cases that DE Pauli favors the hydrogenated compounds, the contribution of this term to DE int is minor, being up to 8.7 and 11.9 kcal mol 21 for B and Al containing complexes, respectively.
Furthermore, in all these cases, both DV elstat and DE oi terms cause the largest contribution to the higher strength observed in fluorinated compounds. Only for B-P bonded compounds the decrease of Pauli repulsion upon fluorination makes this term more decisive than DV elstat . Therefore, we can state that stabilization of boron complexes with perfluorinated derivatives is mainly due to the orbital interaction term. On the other hand, as compared to boron analogues, aluminum-   containing complexes show a significant decrease of the absolute values of DE oi , DV elstat , and DE Pauli due to the lengthening of Al-X bond and the lower electronegativity of Al. In general, stabilization of aluminum complexes with perfluorinated derivatives is due to a combination of more favorable DV elstat and DE oi terms.
With the aim to understand the orbital interactions referred above, the MO diagram for the complex NC 9 H 15 ÁBC 9 H 15 is shown in Figure 2. The MO diagrams for the other complexes are very similar (See HOMO and LUMO energies in Supporting Information, Table S4). As expected, the interaction between HOMO (24.49 eV) of the donor fragment NC 9 H 15 and LUMO (21.23 eV) of the acceptor fragment BC 9 H 15 leads to the formation of r-bonding and r-antibonding orbitals. Fluorination of the acceptor significantly decreases the energy of the LUMO (by 4.62 eV, from 21.23 to 25.85 eV), which enhances the stability of the complex.
Energy differences between the HOMO of the donor and the LUMO of the acceptor for Al containing compounds are smaller than for B containing ones (Table 4); the stabilization effect caused by fluorination is also noticeable. Thus, such stabilization of the LUMO by fluorination is translated into the larger orbital interactions observed above.
For all studied complexes there is a linear correlation between the energy difference of the HOMO of the donor E HOMO (D) and the LUMO of the acceptor E LUMO (A) (in eV) and the dissociation energy of the complex DE diss [eq. (3), Fig. 3 Importance of the frontier orbitals on the dissociation energy has been emphasized by Fleming, [45,46] however, the quantitative correlations for the donor-acceptor compounds like eq. (3) have not been reported.

Thermodynamics of hydrogen splitting
Enthalpies and Gibbs energies of the heterolytic hydrogen splitting in the gas phase (process (4)) are summarized in Table 5.
Optimized geometries of ionic products of hydrogen splitting are provided in the Supporting Information (Table S1).
The fluorination of the Lewis acid results in a dramatic decrease of the hydrogen splitting enthalpy by 90.9 and 68.3 kcal mol 21 (Gibbs energies by 90.3 and 68.1 kcal mol 21 ) for compounds containing boron and aluminum, respectively. The influence of group 15 Lewis base is weaker but still pronounced. Thus, substitution of XH 3 by X(CH 3 ) 3 or XC 9 H 15 results in a decrease of the endothermicity of process (4) by 21.1 and 32.5 kcal mol 21 (Gibbs energies by 22.0 and 33.2 kcal mol 21 ) for X 5 N, and by 41.9 and 44.6 kcal mol 21 (Gibbs energies by 42.7 and 45.1 kcal mol 21 ) for X 5 P. Therefore, the enthalpy of the gas phase heterogeneous hydrogen splitting with formation of the isolated ions is endothermic by only 4.3 kcal mol 21 for the best combination of Lewis acid BC 9 F 15 and Lewis base NC 9 H 15 .
In order to take into account ion pair interaction, several possible orientations have been considered for each ion pair (see Supporting information for details).
For the non-fluorinated compounds the most stable is the structure featuring dihydrogen bond [47] (Fig. 4a). In the case of fluorinated derivatives, the ion pair in which terminal fluorine atoms are involved in intermolecular HÁÁÁF interactions (Fig. 4b) is the most stable. Energetics of the hydrogen splitting with contact ion pair formation (process (5)) in the gas phase and in toluene solution are given in Table 6.
It should be noted that for weaker Lewis acids EC 9 H 15 , in several cases, optimization of the contact ion pairs converged to the H 2 molecule, indicating favorability of hydrogen evolution. In contrast, for the perfluorinated group 13 adamantane derivatives the process (5) is highly exothermic. The solvent makes the hydrogen splitting reaction slightly more exothermic (by about 2-6 kcal mol 21 ). Our results indicate that the splitting of H 2 in gas-phase becomes energetically favorable if ion pair formation is taken into account.
Reaction energies DE8 0 for heterolytic hydrogen splitting starting from the donor-acceptor complexes (process (6)) in the gas phase and in toluene solution are given in Table 7.
The reaction energies for the process (6) are endothermic except for complexes of BC 9 F 15 with N(CH 3 ) 3 and NC 9 H 15 . The toluene makes the reactions slightly less endothermic (by about 7 kcal mol 21 ). Due to the large size of the ion pair complexes, which precluded the calculation of Hessian matrix, we limited our study on the reaction energies DE8 0 .
Both processes (5) and (6) are disfavorable by entropy, but due to large exothermicity the process (5) is expected to be exergonic.
From the obtained results, B-N system is predicted to be the most promising candidate for the construction of DA cryptands for the hydrogen splitting.

Conclusions
A comparative computational study of the structural properties, stability and reactivity of adamantane-based Lewis acids and their donor-acceptor complexes has been carried out. Fluorination dramatically decreases the LUMO energy of the acceptor and increases the Lewis acidity, making group 13 perfluorinated adamantane derivatives Lewis superacids. EDA results show that stronger orbital interactions are responsible for the larger stability of boron complexes with fluorinated acceptors. In the case of aluminum complexes, the higher stability of Table 6. Reaction energies DE8 0 (kcal mol 21 ) for the process (5)   the perfluorinated compounds is attributed to a combination of more favorable electrostatic and orbital interaction terms. For all studied complexes there is a linear correlation between the energy difference of HOMO of the donor and LUMO of the acceptor molecule and the dissociation energy of the complex. Finally, our results demonstrate that the fluorination of the Lewis acid has tremendous effect on the hydrogen splitting process. Perfluorinated 1-boroadamantane in combination with Ncontaining donors is predicted to exothermically split molecular hydrogen with the formation of the contact ion pairs. Thus, perfluorinated 1-boroadamantane appears to be an attractive synthetic target as Lewis superacid and a good candidate for the construction of spatially separated donor-acceptor cryptands.

Acknowledgments
Excellent service of the Centre de Serveis Cient ıfics i Acadèmics de Catalunya (CESCA) and computer cluster at St. Petersburg State University provided by Resource Center "Computer Center of SPbSU" are gratefully acknowledged. The authors declare no competing financial interest.