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.

1. 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:nH2, where Z is a neutral molecule and n is the number of H2 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].

The adamantane scaffold is widely used due to their steric [23,24], lipophilic [25] and rigid characteristics [26,27,28,29,30]. Derivatives that include heteroatoms have been synthesized, in addition to the well-known aza-(AZADO and hexamethylenetetramine) [31,32,33,34] and oxo-derivatives (tetrodotoxin) [35]. Other derivatives involving C/As/O (arsenicin A) [36], C/N/S (tetramethylenedisulfotetramine) [37], P/S (phosphorus pentasulfide) [38], P/N [39], and C/P/S [40] have also been described.

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 CH2 moieties is substituted by divalent X groups, with X = {CH2, NH, O; SiH2, PH, S} thus leading to B4X6 tetrahedral molecules, as shown in Scheme 1.

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, 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 B4X6 systems and H2 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].

2. Results and Discussion

2.1. Molecular Electrostatic Potential (MESP) and π-Holes in B4X6 Systems

As stated above, we can rationalize the electrostatic nature of the interaction between B4X6 and H2 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 B4X6 systems is an electron (or surplus charge density) attractor, as shown by the positive values of the π-holes.

Figure 1

(a) π-hole on the boron atom (a.u.) and (b) molecular electrostatic potential on the 0.001 au electron density isosurface for the B4O6 molecule. Red and blue colors indicate Molecular Electrostatic Potential (MESP) values < −0.015 and > +0.015 au, respectively. The location of the π-holes is indicated with a black dot.

As shown inpan> 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 π-hole values:

π-hole (n class="Chemical">au): 0.131 (O) >> 0.058 (pan> class="Chemical">NH) > 0.047 (SiH2) > 0.034 (CH2) > 0.025 (PH, S).

2.2. Geometries and Energies of B4X6:nH2 Complexes (n = 1–4)

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-ζ and triple-ζ quality respectively, including diffuse and polarization functions.

Figure 2

MP2/aug-cc-pVDZ optimized geometries of adamantane-like B4X6 systems, (a) X = CH2, (b) X = SiH2, (c) X = NH, (d) X = PH, (e) X = O, (f) X = S. All geometries correspond to energy minima. Cartesian coordinates gathered in 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.

Figure 3

Energy profiles of ΔE = E(B4X6:H2) – E(H2), in kJ/mol, versus d, in Ångström, for different X at MP2/aug-cc-pVDZ computational level. The geometries of B4X6 and H2 are kept frozen along the d coordinate. The inset plot on the upper right corner corresponds to a zoom-in region of ΔE versus d within the range 2.5 ≤ d ≤ 3.3 Å, showing the corresponding energy minima for CH2, NH, PH and S systems.

From Figure 3 we can clearly observe that all energy profiles are attractive for an H2 molecule down to 3 Å, and then three different curve patterns emerge: (i) for X = {CH2, 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 = SiH2 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 {CH2, NH}, and {PH, S} curves show similar energy minima regions: We turn from an attractive to a repulsive system at d ≤ 2.1 Å (CH2), 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 H2 molecule to the B4X6 system where several curves have similar profiles. If we observe closely the curves from the zoom-in inset of Figure 3, the energy minima for CH2, NH, PH, and S are located as follows: dmin(CH2) ~ 2.73 Å, dmin(NH) ~ 2.77 Å, dmin(PH) ~ 3.05 Å, dmin(S) ~ 3.06 Å. For O and SiH2 there are no minima within this region since the curves are always attractive.

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 B4X6:nH2 systems. Due to the different behavior of the B4(SiH2)6 system versus an H2 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 B4(SiH2)6:H2 complex – a geometry optimization shows a bond breaking in the H2 molecule and a rearrangement of the B4(SiH2)6 adamantane structure—this system will be analyzed further in another work. The optimized structures for all B4X6:nH2 complexes (n = 1–4) are depicted in Figure S2, except for B4O6:nH2 (n = 1–4), the latter shown in Figure 4. In Table 1 we gather the average B···H2 and H···H distances in the optimized geometries of the different B4X6:nH2 complexes, all corresponding to energy minima at the MP2/aug-cc-pVDZ level of theory.

Figure 4

Optimized geometries for the B4O6:nH2 complexes (n = 1–4) with MP2/aug-cc-pVDZ computations. All geometries corrrespond to energy minima.

Table 1

Average B···H2 (d) and H···H distances (Å) in the B4X6:nH2 complexes, X = {CH2 ; NH, PH; O, S} with MP2/aug-cc-pVDZ computations. The H-H distance in the isolated H2 molecule is 0.755 Å, computed at the MP2/aug-cc-pVDZ level of theory.

	B···H2				H-H
X	1:1	1:2	1:3	1:4	1:1	1:2	1:3	1:4
CH2	2.737	2.740	2.745	2.750	0.755	0.755	0.754	0.754
NH	2.777	2.727	2.705	2.727	0.755	0.755	0.755	0.755
PH	3.080	3.045	3.046	3.049	0.755	0.755	0.755	0.755
O	1.624	1.687	1.766	1.850	0.774	0.770	0.766	0.763
S	3.071	3.070	3.068	3.068	0.755	0.755	0.755	0.755

As regards to the B···H2 distances (d) in the B4X6:nH2 complexes, as gathered in Table 1, three groups can be clearly distinguished: (i) X = {CH2, NH} with d distances of ~ 2.7 Å (ii) X = {PH, S} with d distances of ~ 3.0 Å and (iii) X = O, with shorter d distances down to ~ 1.6 Å. The case for B4O6 is quite remarkable. As more H2 molecules are attached to B4O6, the d(B···H2) distances are elongated steadily up to d ~ 1.85 Å, and the H···H molecules remain slightly stretched down to Δ ~ 0.016 Å. This behavior for the B4O6 systems is unique as compared to the other systems since in the latter the attachment of the H2 molecules is quite farther to the B atom and the H2 molecules remain practically unaltered. There is no clear tendency—as compared to B4O6—for the d distances as more H2 molecules are added for X = {CH2, NH, PH, S}, with tiny differences for the series 1 ≤ n ≤ 4.

Turning now to the H-H distances inpan> the complexes, as shown in Table 1, in the energy minimum structures of the complexes, the H-H distances are very similar as compared to the isolated H2 molecule, 0.755 Å. However, there is an exception for the oxygen complexes: when one H2 molecule is attached to the B4O6 system, the H···H bond is elongated by Δ ~ 0.02 Å. As further H2 molecules are attached to the B4O6 system, this elongated H-H bond is shortened consecutively by ~ 0.004 Å, down to 0.763 Å in each H-H molecule of the B4O6:4H2 complex, though still 0.008 Å longer than in the isolated H-H molecule.

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). ΔE(1:n) for a given X corresponds to the binding energy of the complex B4X6:nH2.

X	ΔE(1:1)	ΔE(1:2)	ΔE(1:3)	ΔE(1:4)
	MP2 CBS	MP2 CBS	MP2 CBS	MP2 CBS
CH2	−6.6 −2.8	−13.3 −5.4	−20.1 −8.0	−26.8 −10.7
NH	−5.8 −2.5	−12.9 −6.1	−20.0 −9.7	−25.8 −12.2
PH	−6.2 −1.6	−13.3 −3.9	−19.9 −6.1	−26.4 −7.7
O	−28.6 −22.1	−49.5 −37.6	−65.5 −49.1	−79.2 −58.9
S	−7.9 −3.3	−15.8 −6.7	−23.4 −10.1	−31.6 −13.5

Figure 5

Binding energies of the B4X6:nH2 complexes (n = 1–4) as function of attached H2 molecules. MP2/aug-cc-pVDZ computations (solid lines) and extrapolated MP2/CBS limit (dashed lines).

The maximum binpan>dinpan>g enpan>ergy for the complexes corresponds to B4O6:4H2 with a value of 79 kJ/mol (CBS extrapolation 60 kJ/mol). However, the binding energy of one H2 molecule attached to the other B4X6 systems is remarkably smaller in comparison, especially when the CBS extrapolation is added. The addition of more H2 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 B4X6:nH2 (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 ΔE versus n (number of H2) 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 B4O6:nH2 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 H2 molecules, with the exception of X = O with larger binding energies.

3. Computational Method

All geometries of the B4X6 systems and the corresponding B4X6:nH2 (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 B4X6 systems and H2 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 B4X6:nH2 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 B4X6 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 B4X6 systems and B4X6:nH2 complexes (n = 1–4). The binding energies for the B4X6:nH2 complexes are computed as ΔE = E(B4X6:nH2) – E(B4X6) – n·E(H2), and reported in kJ/mol. Further geometry optimizations of all B4X6 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···H2 distance in the complex B4(CH2)6:H2 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 local Ĉ3 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 depenpan>denpan>cy 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. with k = 2, 3 and 4 for aug-cc-pVDZ, aug-cc-VTZ and aug-cc-pVQZ basis sets, respectively [57,58]. with k = 3 and 4 for aug-cc-VTZ and aug-cc-pVQZ basis sets, respectively [59]. Finally, we have

4. Conclusions

From the results on class="Chemical">btainpan>ed inpan> this work we pan> class="Chemical">can conclude with the following points:

1) The MESP in the n class="Chemical">adamantane-like strupan> class="Chemical">ctures B4X6, with X ={CH2, NH, O ; SiH2, PH, S}, show π-holes above the B atom with electron (density) attraction forces largest for B4O6 and lowest for B4(PH)6 and B4S6.

2) The energy profiles of one H2 molecule approaching along a C axes the B atom of B4X6 systems show attractive patterns up to certain values for all systems where it turns to repulsive below ~ 2.1 Å for B4(CH2)6 and B4(NH)6 and below ~ 2.5 Å for B4(PH)6 and B4S6, except for B4(SiH2)6 where the profile is always attractive with H2 bond breaking and cage rearrangement. For B4O6, there is a flat energy minimum region within 1.7–2.0 Å.

3) The attraction strength for electron density towards boron atoms in B4X6 is also shown in the energy profiles of the B4X6:H2 complexes as a function of the B···H2 distance d. The d distances in the energy minima structures coincide with the predicted distances from the energy profiles.

4) The binpan>dinpan>g enpan>ergies of the B4X6:nH2 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.