Complexes Between Adamantane Analogues B4X6 -X = {CH2, NH, O ; SiH2, PH, S} - and Dihydrogen, B4X6:nH2 (n = 1-4).

In this work, we study the interactions between adamantane-like structures B4X6 with X = {CH2, NH, O ; SiH2, PH, S} and dihydrogen molecules above the Boron atom, with ab initio methods based on perturbation theory (MP2/aug-cc-pVDZ). Molecular electrostatic potentials (MESP) for optimized B4X6 systems, optimized geometries, and binding energies are reported for all B4X6:nH2 (n = 1–4) complexes. All B4X6:nH2 (n = 1–4) complexes show attractive patterns, with B4O6:nH2 systems showing remarkable behavior with larger binding energies and smaller B···H2 distances as compared to the other structures with different X.


Introduction
Hydrogen storage is becoming an important issue regarding the energetic needs of our modern world [1,2]. Different methods are designed for hydrogen storage [3][4][5], including cryogenics, high pressures, and chemical compounds that reversibly release dihydrogen upon heating [6]. Among the different systems described in the literature, the metal organic frameworks (MOF) have been the most successful ones as hydrogen storage [7][8][9][10][11].
Related to the computational study in the chemical trapping of dihydrogen, noncovalent interactions must be taken into account [12], given the relatively weak attracting force-mostly dispersive-derived from two neutral molecules, leading to general complexes with formula Z:nH 2 , where Z is a neutral molecule and n is the number of H 2 molecules attached to the Z neutral system. A number of theoretical articles have been devoted to the interaction of dihydrogen with metallic systems [13][14][15][16][17][18][19][20][21][22].
For the study of dihydrogen complexes, we propose the use of adamantane analog systems where each CH tetrahedral vertex in adamantane is substituted by a Boron atom, and the remaining CH 2 moieties is substituted by divalent X groups, with X = {CH 2 , NH, O; SiH 2 , PH, S} thus leading to B 4 X 6 tetrahedral molecules, as shown in Scheme 1.
(a) (b) Scheme 1. Substitution of CH and CH2 groups by B and X respectively in (a) adamantane leading to the (b) B4X6 systems studied in this work. One of the four equivalent local Ĉ3 rotation axis is also shown.
The B4X6:nH2 complexes (n = 1-4) could be formed by approaching H2 molecules towards the B atom centered vertically along the four equivalent local Ĉ3 rotation axis. The existence of adamantane analogs B4X6 is not known, except for the 1-boraadamantane, where only one tetrahedral CH vertex is substituted by a B atom [41], with the remaining structure unaltered; this system has also been the target for a computational study for complex formation [42] with Lewis acids and superacids. Further substitutions of B atoms in tetrahedral sites have been studied from a theoretical point of view only [43]. Directly related to this work is the concept of the, -hole, proposed by Politzer and Murray [44][45][46], which refers to the electron-deficient outer lobe of a p orbital involved in a covalent bond, especially when one of the atoms is highly electronegative, that present positive values for the electrostatic potential [47,48]. On the other hand, when the deficient outer lobe of a p orbital involved in a covalent bond is perpendicular or axially oriented with respect of the molecular frame, the electrostatic nature of the interactions considered between B atoms in B4X6 systems and H2 molecules can be rationalized in terms of -holes [49]. We should emphasize the relation between the Lewis acidity of trivalent B centers and the (non)planarity of the structure surrounding the B atom [50].

Molecular Electrostatic Potential (MESP) and -Holes in B4X6 Systems
As stated above, we can rationalize the electrostatic nature of the interaction between B4X6 and H2 molecules in terms of -holes, namely regions of positive electrostatic potential perpendicular or axially-oriented (as in the adamantane structure) with respect to a portion of the molecular framework, as shown in Figure 1. The empty/electron-deficient p lobe of Boron pointing outwards in the B4X6 systems is an electron (or surplus charge density) attractor, as shown by the positive values of the -holes.
Scheme 1. Substitution of CH and CH 2 groups by B and X respectively in (a) adamantane leading to the (b) B 4 X 6 systems studied in this work. One of the four equivalent localĈ 3 rotation axis is also shown.
The B 4 X 6 :nH 2 complexes (n = 1-4) could be formed by approaching H 2 molecules towards the B atom centered vertically along the four equivalent localĈ 3 rotation axis. The existence of adamantane analogs B 4 X 6 is not known, except for the 1-boraadamantane, where only one tetrahedral CH vertex is substituted by a B atom [41], with the remaining structure unaltered; this system has also been the target for a computational study for complex formation [42] with Lewis acids and superacids. Further substitutions of B atoms in tetrahedral sites have been studied from a theoretical point of view only [43]. Directly related to this work is the concept of the, σ-hole, proposed by Politzer and Murray [44][45][46], which refers to the electron-deficient outer lobe of a p orbital involved in a covalent bond, especially when one of the atoms is highly electronegative, that present positive values for the electrostatic potential [47,48]. On the other hand, when the deficient outer lobe of a p orbital involved in a covalent bond is perpendicular or axially oriented with respect of the molecular frame, the electrostatic nature of the interactions considered between B atoms in B 4 X 6 systems and H 2 molecules can be rationalized in terms of π-holes [49]. We should emphasize the relation between the Lewis acidity of trivalent B centers and the (non)planarity of the structure surrounding the B atom [50].

Results and Discussion
2.1. Molecular Electrostatic Potential (MESP) and π-Holes in B 4 X 6 Systems As stated above, we can rationalize the electrostatic nature of the interaction between B 4 X 6 and H 2 molecules in terms of π-holes, namely regions of positive electrostatic potential perpendicular or axially-oriented (as in the adamantane structure) with respect to a portion of the molecular framework, as shown in Figure 1. The empty/electron-deficient p lobe of Boron pointing outwards in the B 4 X 6 systems is an electron (or surplus charge density) attractor, as shown by the positive values of the π-holes.
As shown in Figure 1b, the MESP of the B 4 O 6 system shows areas of positive (blue) and negative (red) values corresponding to deficient electron density (negative charge attractor) and surplus electron density (positive charge attractor) areas, respectively. Clearly, the electron density deficiency area above the Boron atoms in B 4 X 6 could attract the electron density of the σ bond of the H 2 molecule. As shown in Figure 1b  As shown in Figure 1b, the MESP of the B4O6 system shows areas of positive (blue) and negative (red) values corresponding to deficient electron density (negative charge attractor) and surplus electron density (positive charge attractor) areas, respectively. Clearly, the electron density deficiency area above the Boron atoms in B4X6 could attract the electron density of the σ bond of the H2 molecule. As shown in Figure 1b, the large electronegativity of the three oxygen atoms bound to boron must have a stronger effect on the attachment of H2 molecules as a function of the -hole values: Figure 2 shows the optimized geometries of the isolated B4X6 systems at MP2/aug-cc-pVDZ level, corresponding to energy minima for all cases. The cartesian coordinates for the B4X6 optimized structures are gathered in Table S1, with the MP2 method and basis sets aug-cc-pVDZ and aug-cc-pVTZ, of double- and triple- quality respectively, including diffuse and polarization functions.

Geometries and
Energies of B 4 X 6 :nH 2 Complexes (n = 1-4) Figure 2 shows the optimized geometries of the isolated B 4 X 6 systems at MP2/aug-cc-pVDZ level, corresponding to energy minima for all cases. The cartesian coordinates for the B 4 X 6 optimized structures are gathered in Table S1, with the MP2 method and basis sets aug-cc-pVDZ and aug-cc-pVTZ, of double-ζ and triple-ζ quality respectively, including diffuse and polarization functions.
In the computations, we first obtain the energy profile of a frozen H 2 molecule approaching this B atom (d distance) along the corresponding local C 3 axis, as shown in Figure 3 for the B 4 X 6 :H 2 complexes.
From Figure 3 we can clearly observe that all energy profiles are attractive for an H 2 molecule down to 3 Å, and then three different curve patterns emerge: (i) for X = {CH 2 , NH, PH, S} the energy profile becomes repulsive when d < 3 Å (ii) for X = O, the energy minimum well is flatter and becomes repulsive shifting down to values of d~1.7-2.0 Å; and finally (iii) for X = SiH 2 the energy profile remains attractive down to 1.25 Å. The inset plot of Figure 3-upper right corner-shows an energy profile zoom-in of the region 2.5 Å < d < 3.3 Å in order to see more clearly the positions of the energy minima regions, for a given X. Clearly, the {CH 2 , NH}, and {PH, S} curves show similar energy minima regions: We turn from an attractive to a repulsive system at d ≤ 2.1 Å (CH 2 ), 2.2 Å (NH), 2.48 Å (PH), and 2.55 Å (S). As stated above, a zoom-in of the energy profile for 2.5 Å ≤ d ≤ 3.3 Å is included in order to unveil the effect of approaching a H 2 molecule to the B 4 X 6 system where several curves have similar profiles. If we observe closely the curves from the zoom-in inset of Figure  As shown in Figure 1b, the MESP of the B4O6 system shows areas of positive (blue) and negative (red) values corresponding to deficient electron density (negative charge attractor) and surplus electron density (positive charge attractor) areas, respectively. Clearly, the electron density deficiency area above the Boron atoms in B4X6 could attract the electron density of the σ bond of the H2 molecule. As shown in Figure 1b Figure 2 shows the optimized geometries of the isolated B4X6 systems at MP2/aug-cc-pVDZ level, corresponding to energy minima for all cases. The cartesian coordinates for the B4X6 optimized structures are gathered in Table S1, with the MP2 method and basis sets aug-cc-pVDZ and aug-cc-pVTZ, of double- and triple- quality respectively, including diffuse and polarization functions.   Table S1.

Geometries and Energies of B4X6:nH2 Complexes (n = 1-4)
In the computations, we first obtain the energy profile of a frozen H2 molecule approaching this B atom (d distance) along the corresponding local C3 axis, as shown in Figure 3 for the B4X6:H2 complexes.   Table S1.  Table S1.
In the computations, we first obtain the energy profile of a frozen H2 molecule approaching this B atom (d distance) along the corresponding local C3 axis, as shown in Figure 3 for the B4X6:H2 complexes.  Once we choose the d which corresponds to the energy minimum in Figure 3, we relax the nuclear coordinates in the whole complexes hence determining the energy minimum structure for the B 4 X 6 :nH 2 systems. Due to the different behavior of the B 4 (SiH 2 ) 6 system versus an H 2 molecule-permanent attractive profile for d down to 1.25 Å-as compared to the other complexes- Figure 3-and the lack of an energy minimum geometry for the B 4 (SiH 2 ) 6 :H 2 complex -a geometry optimization shows a bond breaking in the H 2 molecule and a rearrangement of the B 4 (SiH 2 ) 6 adamantane structure-this system will be analyzed further in another work. The optimized structures for all B 4 X 6 :nH 2 complexes (n = 1-4) are depicted in Figure S2, except for B 4 O 6 :nH 2 (n = 1-4), the latter shown in Figure 4. In Table 1 we gather the average B···H 2 and H···H distances in the optimized geometries of the different B 4 X 6 :nH 2 complexes, all corresponding to energy minima at the MP2/aug-cc-pVDZ level of theory.  Finally, we show the computed binding energies of the H2 molecules for the different complexes B4X6:nH2 (n = 1-4), as seen in Table 2 and displayed in Figure 5, where we also include the CBS extrapolated values. As expected from the computed MESP and energy profiles in B4X6:H2 complexes, the larger binding energy for one H2 molecule corresponds to the B4O6 system, with ΔE  29 kJ/mol (ΔECBS  22 kJ/mol). For comparative purposes, the electronic binding energy of the water dimer is ΔE[(H2O)2]  21 kJ/mol [51]. Table 2. Binding energies (kJ/mol) in optimized (B4X6:nH2) complexes, X = {CH2, NH, PH, O, S} with MP2/aug-cc-pVDZ computations and the MP2 complete basis set (CBS) limit obtained by extrapolation of the HF energies calculated at aug-cc-pVkZ, with k = D, T and Q, following Equations (1)-(3). E(1:n) for a given X corresponds to the binding energy of the complex B4X6:nH2.   Finally, we show the computed binding energies of the H 2 molecules for the different complexes B 4 X 6 :nH 2 (n = 1-4), as seen in Table 2 and displayed in Figure 5, where we also include the CBS extrapolated values. As expected from the computed MESP and energy profiles in B 4 X 6 :H 2 complexes, the larger binding energy for one H 2 molecule corresponds to the B 4 O 6 system, with ∆E~29 kJ/mol (∆E CBS~2 2 kJ/mol). For comparative purposes, the electronic binding energy of the water dimer is ∆E[(H 2 O) 2 ]~21 kJ/mol [51]. Table 2. Binding energies (kJ/mol) in optimized (B 4 X 6 :nH 2 ) complexes, X = {CH 2 , NH, PH, O, S} with MP2/aug-cc-pVDZ computations and the MP2 complete basis set (CBS) limit obtained by extrapolation of the HF energies calculated at aug-cc-pVkZ, with k = D, T and Q, following Equations (1)-(3). ∆E(1:n) for a given X corresponds to the binding energy of the complex B 4 X 6 :nH 2 .  Finally, we show the computed binding energies of the H2 molecules for the different complexes B4X6:nH2 (n = 1-4), as seen in Table 2 and displayed in Figure 5, where we also include the CBS extrapolated values. As expected from the computed MESP and energy profiles in B4X6:H2 complexes, the larger binding energy for one H2 molecule corresponds to the B4O6 system, with ΔE  29 kJ/mol (ΔECBS  22 kJ/mol). For comparative purposes, the electronic binding energy of the water dimer is ΔE[(H2O)2]  21 kJ/mol [51]. Table 2. Binding energies (kJ/mol) in optimized (B4X6:nH2) complexes, X = {CH2, NH, PH, O, S} with MP2/aug-cc-pVDZ computations and the MP2 complete basis set (CBS) limit obtained by extrapolation of the HF energies calculated at aug-cc-pVkZ, with k = D, T and Q, following Equations (1)-(3). E(1:n) for a given X corresponds to the binding energy of the complex B4X6:nH2.  The maximum binding energy for the complexes corresponds to B 4 O 6 :4H 2 with a value of 79 kJ/mol (CBS extrapolation 60 kJ/mol). However, the binding energy of one H 2 molecule attached to the other B 4 X 6 systems is remarkably smaller in comparison, especially when the CBS extrapolation is added. The addition of more H 2 molecules to the complexes shows practically additive relations for all X. As displayed in Figure 5, when extrapolated to the CBS limit, we can see several features regarding the binding energies in B 4 X 6 :nH 2 (n = 1-4) complexes as compared to the MP2/aug-cc-pVDZ energies: (1) the CBS extrapolated binding energies are smaller for a given X and n (2) the (absolute value of the) slope of ∆E versus n (number of H 2 ) molecules decreases for CBS extrapolated values (3) both CBS extrapolated and non-extrapolated binding energies follow a similar linear trend, except for X = O, the latter with clearly larger (CBS) binding energies, from 20 kJ/mol (n = 1) to 60 kJ/mol (n = 4).
We should notice that for X = O, though the CBS extrapolated slope is smaller than the non-extrapolated one, yet this slope is larger (in absolute value) as compared to the other Xs hence the peculiar behavior of B 4 O 6 :nH 2 as compared to complexes with different Xs. We should also emphasize the small differences (less than~5 kJ/mol ) between binding energies for different Xs for a given number n of attached H 2 molecules, with the exception of X = O with larger binding energies.

Computational Method
All geometries of the B 4 X 6 systems and the corresponding B 4 X 6 :nH 2 (n = 1-4) complexes were optimized with second-order Møller-Plesset perturbation theory (MP2) [52] and a double-ζ basis set including polarization and diffuse functions [53], such as aug-cc-pVDZ. The interactions between B 4 X 6 systems and H 2 molecules are clearly of noncovalent nature, weaker than conventional chemical bonds, given the closed-shell nature of the species involved and the lack of any further singlet coupling between unpaired electrons. We search for stable complexes B 4 X 6 :nH 2 and dispersive corrections are important given the neutral and spin-zero nature of the involved systems, hence the use of MP2 theory in computations. This theory improves on the Hartree-Fock (a mean-field-molecular-orbital-theory of electronic structure) method by adding electron correlation effects by means of Rayleigh-Schrödinger perturbation theory (RS-PT).
The quantum-chemical computations in this work were carried out at the MP2 level of theory with the scientific software Gaussian09 (Gaussian Inc, Wallingford, CT, USA) [54], and the molecular electrostatic potential (MESP) for the B 4 X 6 systems was computed with the DAMQT program [55,56], also at the MP2 level of theory. Frequency computations were performed in order to check the energy minimum nature in all B 4 X 6 systems and B 4 X 6 :nH 2 complexes (n = 1-4). The binding energies for the B 4 X 6 :nH 2 complexes are computed as ∆E = E(B 4 X 6 :nH 2 ) -E(B 4 X 6 ) -n·E(H 2 ), and reported in kJ/mol. Further geometry optimizations of all B 4 X 6 complexes were carried out with the MP2/aug-cc-pVTZ computational model-with a triple-ζ basis set-in order to check the validity of the optimized geometries (see Supplementary Information). A single-point energy profile (MP2) versus B···H 2 distance in the complex B 4 (CH 2 ) 6 :H 2 was computed using both basis sets: aug-cc-pVDZ and aug-cc-pVTZ (see Supplementary Information), double-ζ and triple-ζ respectively. As shown in Figure S1, the results show similar profiles along the localĈ 3 axis of rotation on the B atom and therefore we can confirm the validity of the MP2/aug-cc-pVDZ computational model for geometries and binding energies.
In order to assess the dependency of the binding energies on basis set incompleteness, we also computed the binding energies of all complexes in the extrapolated complete basis set (CBS) limit. The CBS energy has been calculated by extrapolation of the HF energies calculated at aug-cc-pVkZ, with k = D, T and Q, and Equation (1) and the correlation part with Equation (2). The sum of the two components (HF and correlation) (Equation (3)) provides the MP2(CBS) energy.

Conclusions
From the results obtained in this work we can conclude with the following points: 1) The MESP in the adamantane-like structures B 4 X 6 , with X ={CH 2 , NH, O ; SiH 2 , PH, S}, show π-holes above the B atom with electron (density) attraction forces largest for B 4 O 6 and lowest for B 4 (PH) 6 and B 4 S 6 .
2) The energy profiles of one H 2 molecule approaching along a C 3v axes the B atom of B 4 X 6 systems show attractive patterns up to certain values for all systems where it turns to repulsive below 2.1 Å for B 4 (CH 2 ) 6 and B 4 (NH) 6 and below~2.5 Å for B 4 (PH) 6 and B 4 S 6 , except for B 4 (SiH 2 ) 6 where the profile is always attractive with H 2 bond breaking and cage rearrangement. For B 4 O 6 , there is a flat energy minimum region within 1.7-2.0 Å.
3) The attraction strength for electron density towards boron atoms in B 4 X 6 is also shown in the energy profiles of the B 4 X 6 :H 2 complexes as a function of the B···H 2 distance d. The d distances in the energy minima structures coincide with the predicted distances from the energy profiles.
4) The binding energies of the B 4 X 6 :nH 2 complexes-n = 1-4, follow a similar linear additive pattern (in magnitude and direction) for all X, except X = O, with larger binding energies. CBS extrapolation shows a significant decrease in the binding energies.