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

Abstract

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.

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.

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 π-hole values:

π-hole (au): 0.131 (O) >> 0.058 (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.

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.

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: d_min(CH₂) ~ 2.73 Å, d_min(NH) ~ 2.77 Å, d_min(PH) ~ 3.05 Å, d_min(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. 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

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.

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 in 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. 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

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 (ΔE_CBS ~ 22 kJ/mol). For comparative purposes, the electronic binding energy of the water dimer is ΔE[(H₂O)₂] ~ 21 kJ/mol [51].

The maximum binding energy 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 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.

$$E_{HF,k}=E_{HF,lim}+A{e}^{-Bk}$$

(1)

with k = 2, 3 and 4 for aug-cc-pVDZ, aug-cc-VTZ and aug-cc-pVQZ basis sets, respectively [57,58].

$$E_{coor,k}=E_{corr,lim}+A{k}^{-3}$$

(2)

with k = 3 and 4 for aug-cc-VTZ and aug-cc-pVQZ basis sets, respectively [59]. Finally, we have

$$E_{MP2}\left(CBS\right)=E_{HF,lim}+E_{corr,lim}$$

(3)

4. Conclusions

From the results obtained in this work we can conclude with the following points:

1) The MESP in the adamantane-like structures 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_3v 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 binding energies 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.