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Article

Non-Covalent Interactions in Hydrogen Storage Materials LiN(CH3)2BH3 and KN(CH3)2BH3

Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, Cracow 30-060, Poland
*
Author to whom correspondence should be addressed.
Crystals 2016, 6(3), 28; https://doi.org/10.3390/cryst6030028
Submission received: 29 January 2016 / Revised: 4 March 2016 / Accepted: 14 March 2016 / Published: 18 March 2016
(This article belongs to the Special Issue Analysis of Hydrogen Bonds in Crystals)

Abstract

:
In the present work, an in-depth, qualitative and quantitative description of non-covalent interactions in the hydrogen storage materials LiN(CH3)2BH3 and KN(CH3)2BH3 was performed by means of the charge and energy decomposition method (ETS-NOCV) as well as the Interacting Quantum Atoms (IQA) approach. It was determined that both crystals are stabilized by electrostatically dominated intra- and intermolecular M∙∙∙H–B interactions (M = Li, K). For LiN(CH3)2BH3 the intramolecular charge transfer appeared (B–H→Li) to be more pronounced compared with the corresponding intermolecular contribution. We clarified for the first time, based on the ETS-NOCV and IQA methods, that homopolar BH∙∙∙HB interactions in LiN(CH3)2BH3 can be considered as destabilizing (due to the dominance of repulsion caused by negatively charged borane units), despite the fact that some charge delocalization within BH∙∙∙HB contacts is enforced (which explains H∙∙∙H bond critical points found from the QTAIM method). Interestingly, quite similar (to BH∙∙∙HB) intermolecular homopolar dihydrogen bonds CH∙∙∙HC appared to significantly stabilize both crystals—the ETS-NOCV scheme allowed us to conclude that CH∙∙∙HC interactions are dispersion dominated, however, the electrostatic and σ/σ*(C–H) charge transfer contributions are also important. These interactions appeared to be more pronounced in KN(CH3)2BH3 compared with LiN(CH3)2BH3.

Graphical Abstract

1. Introduction

An increase in energy consumption as well as the environmental harmfulness of current coal or hydrocarbon based fuels has led to intensive search for alternative energy sources [1,2,3]. Therefore, various hydrogen storage materials, that contain significant amounts of hydrogen, have been recently proposed. Boranes are probably one of the best known group among numerous hydrogen storage materials [4,5,6,7,8,9,10]. For example one can present ammonia borane (NH3BH3) [4,5,6,7,8,9,10]—the attractiveness of this material stems from its high stability, even at higher temperature (the melting point is 104 °C), as well as its large hydrogen storage capacity (19.6 wt% H2). It has been demonstrated that the former feature of ammonia borane crystal originates predominantly from the existence of polar dihydrogen bonds N–Hδ+∙∙∙−δH–B between monomers [11,12,13,14,15,16]. Furthermore, it has been proven that the presence of N–Hδ+∙∙∙−δH–B as well as other non-covalent interactions not only determines the stability, but it can also facilitate various steps of dehydrogenation [5,6,7,8,11,12,13,14,15,16,17,18,19,20,21,22,23].
It has been shown that incorporation of alkali metals into boranes might accelerate thermolitic dehydrogenation as well as reduce formation of volatile byproducts [24,25,26]. Therefore various hybrid type materials have also been proposed and extensively studied—as examples one can present LiBH4/NH3BH3 [27], M[Zn(BH4)3], M = Li, Na, K [28] or Al(BH4)3·NH3BH3 [25].
Quite recently McGrady and coworkers published the cutting-edge article in which they had synthesized and characterized two further hydrogen rich crystals LiN(CH3)2BH3 and KN(CH3)2BH3 [29]. They are depicted in Figure 1. In addition, the authors performed topological electron density based study by means of the QTAIM method of Bader [30]—it was reported that mainly M∙∙∙H–B (M = Li, K) interactions stabilize the crystals. Remarkably, the authors also emphasized that, apart from the mentioned non-covalent interactions, one observes untypical homopolar dihydrogen interactions of the types BH∙∙∙HB and CH∙∙∙HC which are found to determine the chain-like 1D architecture of LiN(CH3)2BH3 and 2D layers in KN(CH3)2BH3 crystal [29], Figure 1 and Figure S1. It is noteworthy that these types of connections are intuitively considered as destabilizing due to the lack of electrostatic attraction between hydrogen atoms—homopolar dihydrogen interactions (especially the intramolecular ones) are still a matter of debate in the literature [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. Very recently more and more evidence has been reported in the literature that highlight the stabilizing nature of homopolar dihydrogen interactions [17,21,29,36,37,38,39,40,41,42,43,44,45,46].
Accordingly, in this work we provide complementary results which shed light on energetic, quantitative and qualitative characteristics of non-covalent interactions that contribute to the stability of LiN(CH3)2BH3 and KN(CH3)2BH3 crystals. It is an important goal as it is known that purely topological QTAIM analysis might provide bond paths between atoms (or fragments) even in situations where the overall interaction energies are positive (destabilizing) [36]. Therefore, we applied the charge and energy decomposition scheme (ETS-NOCV) [47,48,49] which has been proven to provide compact, qualitative and quantitative, descriptions of various types of chemical bonds starting from strong covalent bonds, going through dative connections [47,48,49] and ending up at various non-covalent interactions [7,8,37,50,51]. We applied the ADF program [52,53,54] in which the ETS-NOCV scheme is implemented. In order to achieve our goal we chose two types of cluster models—the first type (containing four monomers), marked by a blue dashed line in Figure 1A, is suitable for extraction of M∙∙∙H–B (M = Li, K), and BH∙∙∙HB interactions, whereas the second one (containing eight monomers), depicted by a red dashed line (Figure 1B), contains the CH∙∙∙HC contacts. For selected models we also plotted the reduced density gradient of the NCI (Non-Covalent Index) method [55] in order to qualitatively characterize non-covalent interactions. In addition, the Interacting Quantum Atoms (IQA) energy decomposition scheme [56] was applied for a quantitative description of selected non-covalent interactions in LiNMe2BH3.

2. Materials and Methods

Our calculations were performed by means of the Amsterdam Density Functional (ADF) program [52,53,54]. We used DFT/BLYP-D3/TZP because it has been proven many times in the past that they provide satisfactory results for non-covalent interactions [57,58,59]. The empirical Grimme correction (D3) [60] was used as implemented in the ADF program. We did not calculate basis set superposition errors (BSSE) because these effects are captured in the empirical correction D3 [60]. It is important to emphasize that we also performed additional test calculations for the tetrameric cluster of LiN(CH3)2BH3 using the following methods: PBE-D3/TZP, BP86-D3/TZP (ADF program) as well as MP2/6-311 + G**, PBE-D3/6-311 + G**, BP86-D3/6-311 + G**, MO6-2X/6-311 + G**, wB97XD/6-311 + G** (based on the Gaussian package) [61]—the results of total bonding energies appeared to be very similar among all these methods, Tables S1,S2 in ESI file. Accordingly, in the main text we have only discussed the results from ADF/DFT/BLYP-D3/TZP.
In the next paragraph the main formulas of charge and energy decomposition scheme ETS-NOCV are outlined.

2.1. ETS-NOCV

ETS-NOCV method [49] is a merger of the energy decomposition scheme by Ziegler-Rauk [53,62] with the Natural Orbitals for Chemical Valence (NOCV) [47,48].
The natural orbitals for chemical valence (NOCV) are eigenvectors that diagonalize the deformation density matrix:
Δ P C i = v i C i , Ψ i = j N C i , j λ j
where Ci is a vector of coefficients, expanding Ψi in the basis of fragment orbitals λj; N is a total number of fragment λj orbitals. It was shown that the natural orbitals for chemical valence pairs (ψ–kk) decompose the differential density Δρ into NOCV-contributions (Δρk):
Δ ρ ( r ) = k = 1 M / 2 v k [ ψ k 2 ( r ) + ψ k 2 ( r ) ] = k = 1 M / 2 Δ ρ k ( r )
where vk and M stand for the NOCV eigenvalues and the number of basis functions, respectively. Visual inspection of deformation density plots (Δρk) helps to attribute symmetry and the direction of the charge flow. In addition, these pictures are enriched by providing the energetic estimations, ΔEorb(k), for each Δρk within the ETS-NOCV scheme.
The exact formula, which links the ETS and NOCV methods, is given in the next paragraph, after we briefly present the basic concept of the ETS scheme. In this method the total bonding energy, ΔEtotal, between interacting fragments is divided into four components:
ΔEtotal = ΔEdist + ΔEelstat + ΔEPauli + ΔEorb = ΔEdist + ΔEint
One could add that the negative value –ΔEtotal is a bond dissociation energy. The first contribution of Equation (3), ΔEdist, describes the amount of energy required to promote fragments from their equilibrium geometry to the conformations they adopt in the final optimized molecule. The second term, ΔEelstat, corresponds to the classical electrostatic interaction between the promoted fragments as they are brought to their positions in the final complex. The third term, ΔEPauli, accounts for the repulsive Pauli interaction between occupied orbitals on the two fragments in the combined molecule. Finally, the last stabilizing term, ΔEorb, represents interactions between the occupied molecular orbitals of one fragment with the unoccupied molecular orbitals of the other fragment as well as mixing of occupied and virtual orbitals within the same fragment (inner-fragment polarization). This energy term is linked to the electronic bonding effect coming from the formation of a chemical bond. In the combined ETS-NOCV scheme [49] the orbital interaction term (ΔEorb) is expressed in terms of NOCV’s eigenvalues (vk) as:
Δ E o r b = k Δ E o r b ( k ) = k = 1 M / 2 v k [ F k , k T S + F k , k T S ]
where F i , i T S are diagonal Kohn-Sham matrix elements defined over NOCV with respect to the transition state (TS) density at the midpoint between the density of the molecule and the sum of fragment densities. The above components ΔEorb(k) provide the energetic estimation of Δρk that may be related to the importance of a particular electron flow channel for the bonding between the considered molecular fragments. Finally, in this work we applied a dispersion corrected functional, so this term (ΔEdisp) enters additionally into Equation (3). The ETS-NOCV analysis was done based on the Amsterdam Density Functional (ADF) package in which this scheme was implemented.
For ETS-NOCV analyses the crystal coordinates (not reoptimized) have been predominantly used in order to reflect the real structures of LiN(CH3)2BH3 and KN(CH3)2BH3. Accordingly, the distortion energy term, ΔEdist (Equation (3)), was not calculated. Hence, an interaction energy ΔEint was mostly analyzed in this work. We found for the tetrameric lithium model that the reoptimized geometry as well as bonding properties corresponds well to the crystal structure—accordingly, for this system we also considered the ΔEdist term (Figure 2A) and discussed the corresponding total bonding ΔEtotal and interaction ΔEint energies. It needs to be added that our efforts to reoptimize the remaining models provided geometries which do not correspond to the crystal structures of LiN(CH3)2BH3 and KN(CH3)2BH3. For monomers the optimized structures are considered for ETS-NOCV analysis as they are similar to crystal geometries—in addition, it allows for discussion of the overall stability of monomers (ΔEtotal values).

2.2. NCI Technique

It has been shown that the reduced density gradient:
s = 1 2 ( 3 π 2 ) 1 / 3 | ρ | ρ 4 / 3
appeared to be a useful quantity for a description of non-covalent interactions. In order to obtain information about the type of bonding, plot of reduced density gradient s against molecular density ρ is very often examined. When a weak inter- or intramolecular interaction is present, there exists a characteristic spike lying at low values of both density ρ and reduced density gradient s. To distinguish between attractive and repulsive interactions the eigenvalues (λi) of the second derivative of density (Hessian, ∇2ρ) are used, ∇2ρ = λ1 + λ2 + λ3. Namely, bonding interactions are characterized by λ2 < 0, whereas λ2 > 0 indicates that the atoms are in non-bonded contact. Therefore, within the NCI technique, one can draw information about non-covalent interactions from the plots of sign(λ2)ρ vs. s. In such plots the low gradient spike, an indicator of stabilizing interaction, is located within the region of negative values of the density. On the contrary, the repulsive interactions are characterized by positive values of sign(λ2)ρ. One can also plot the contour of s colored by the value of sign(λ2)ρ providing a pictorial representation of non-covalent interactions.

2.3. IQA (Interacting Quantum Atoms) Energy Decomposition Scheme

The Interacting Quantum Atoms (IQA) approach of Blanco and coworkers [56] allows to partition an electronic energy E into atomic ( E self A ) and diatomic contributions ( E int AB ):
E = A E self A + 1 2 A B A E int AB
The interatomic interaction energy E int AB covers all inter-particle interactions: nucleus-nucleus, V nn AB , nucleus-electron, V ne AB , electron-nucleus, V en AB , and electron-electron, V ee AB , coming from interatomic interaction energies of particles ascribed to atom A with particles ascribed to atom B:
E int AB = V nn AB + V en AB + V ne AB + V ee AB = V nn AB + V en AB + V ne AB + V eeC AB + V eeX AB
The V ee AB term can be further divided into exchange ( V eeX AB ) and Coulomb ( V eeC AB ) contributions. The AIMALL program was used for the IQA calculations [63]. Due to the fact that we are interested in interaction energies in crystals we focused our attention on E int AB . More details and numerous applications of the IQA technique can be found in Reference [56].

2.4. Molecular Electrostatic Potential (MEP)

The electrostatic potential V(r) of a molecule at point “r”, due to nuclei and electrons, is defined as:
V ( r ) = A Z A | R A r | ρ ( r ) d r | r r |
where ZA is the charge of nucleus at position RA and ρ (r) is the total electronic density. The sign of V(r) depends upon whether the positive contribution of the nuclei or negative from the electrons is dominant. Negative values of V(r) correspond to nucleophilic areas of the molecule, whereas the positive to electrophilic regions. It has been demonstrated in numerous works that MEP is a very useful quantity for in depth description of electron density distribution [64,65,66,67].

3. Results and Discussion

Let us start by discussing factors determining the stability of LiN(CH3)2BH3. It can be seen from Figure 2A that the overall interaction energy between fragments, each consisting of the two LiN(CH3)2BH3 monomers, is ΔEint = −35.63 kcal/mol (−17.81 kcal/mol permonomer-monomer interaction). This is in very good agreement with ΔEint obtained for the crystal (non-optimized) geometry, Figure S2. An inclusion of the geometry distortion term leads to an overall bonding energy, ΔEtotal = −29.57 kcal/mol. It is noteworthy that other computational protocols provide very similar ΔEtotal values, Table S1 and Table S2.
The dominating contribution (55%) to ΔEtotal stems from the electrostatic stabilization ΔEelstat = −35.56 kcal/mol, followed by the orbital interaction ΔEorb = −18.17 kcal/mol (28%) and the dispersion components ΔEdisp = −11.38 kcal/mol (17%), Figure 2A. The molecular electrostatic potential (MEP) of the monomer demonstrates (Figure 3A) that the borane group is negatively charged, whereas the electrophilic region (positive MEP values) is seen around Li which explains the dominance of the electrostatic term in the intermolecular stabilization of LiN(CH3)2BH3.
Further decomposition of ΔEorb into deformation density contributions according to the ETS-NOCV scheme is shown in Figure 2B. It can be seen that the leading deformation densities, Δρ1 and Δ2, depict the formation of Li∙∙∙H–B bonds. They originate from an outflow of electron density from σ (B–H) bonds to Li+ ions, Figure 2B, and correspond to the following stabilization, ΔEorb(1) = −11.91 kcal/mol, ΔEorb(2) = −3.47 kcal/mol, respectively. Such outflow leads to the elongation of B-H bonds by ~0.1 Å (as compared with non-bonding monomers). It is important to emphasize that Li∙∙∙H–B interactions also lead to some charge delocalization within the “bay” containing two Li ions and two borane units, see Δρ2 in Figure 2B. This is fully consistent with the presence of QTAIM bond critical points between hydrogen atoms in homopolar bridges BH∙∙∙HB as found by McGrady and coworkers [29]. However, an interesting question emerges at this point: is the LiN(CH3)2BH3 dimer consisting of two monomers exposed to each other via pure BH∙∙∙HB interaction stable? Such a situation, i.e., the dimer in the geometry of the optimized tetrameric cluster model, is depicted in Figure 4B. Our results clearly indicate that in such a case the overall monomer-monomer interaction energy is positive due to significant Pauli and electrostatic repulsions (with total of +9.06 kcal/mol) that overcome subtle stabilization from charge transfer ΔEorb and dispersion ΔEdisp (summing up to −4.16 kcal/mol)—accordingly, pure BH∙∙∙HB interactions would destabilize the LiN(CH3)2BH3 crystal. The same conclusions are valid when considering the dimer in crystal geometry, Figure S3.
Furthermore, we have not found any local minimum energy structure on the potential energy surface for a dimer that would contain solely BH∙∙∙HB interaction (a dimer where BH3 units are exposed to each other). Summarizing, the major stabilization in the LiN(CH3)2BH3 crystal arises from electrostatically dominated intermolecular Li∙∙∙H–B interactions, as previously reported by McGrady et al. [29]. The formation of such bonds additionally enforce some charge delocalization within BH∙∙∙HB contacts (Δρ2 in Figure 2B), however, the overall BH∙∙∙HB interaction is destabilizing. Our conclusions are fully in line with the other, mostly experimental studies, in which the destabilizing role of BH∙∙∙HB interactions were also suggested [68,69,70,71,72]. McGrady and coworkers reported the opposite in their series of recent articles [17,20,21,29]. Due to the fact that such interactions are clearly a matter of debate, in addition, we performed the Interacting Quatum Atoms (IQA) based study for the tetrameric models of LiNMe2BH3. The results are gathered in Table 1.
It is visible from Table 1 that the overall diatomic interaction energies, E int AB , for Li∙∙∙H(B) and (C)H∙∙∙H(C) are negative, E int Li H(B) = 98.8  kcal / mol , E int (C)H H(C) = 0.80  kcal / mol , which indicates the stabilizing interactions as opposed to the homopolar (B)H∙∙∙H(B) contacts which appeared to be significantly destabilizing, E int (B)H H(B) = + 49.4  kcal / mol . This is due to the significantly positive electron-electron repulsion term, V ee AB = 327.2  kcal / mol , caused in turn by the Coulomb contribution V eeC AB = 330.0  kcal / mol , Table 1. We also looked at the partial charges in the monomer and tetramer of LiN(CH3)2BH3 and found that in both cases the borane units are negatively charged, which conforms to the significant value of the Coulomb repulsion V eeC AB found from the IQA analysis, Figure S4 and Table 1. We further calculated the electrostatic interaction between the monomers bonded via BH∙∙∙HB contacts in the presence of the two other monomers (Figure S5). Interestingly, we found the electrostatic repulsion, ca. 15.6 kcal/mol, which is even more pronounced than the repulsion noted for the dimer without the neighboring monomers, 7.08 kcal/mol, Figures S3,S5—we determined that it is due to the closely located Li ions which act as electron density attractors making BH3 units more nucleophilic compared with the monomer, Figure S6. All these results based on the ETS-NOCV, IQA methods, atomic charges and molecular electrostatic potentials allow to conclude on the destabilizing nature of BH∙∙∙HB contacts in LiN(CH3)2BH3—it is important to admit that our results are based on cluster models which might lead to omission of some bonding features in real crystals especially as far as weak non-covalent interactions are taken into account—accordingly, further studies based on other methods within the periodic calculations are necessary in order to fully delineate the nature of homopolar BH∙∙∙HB interactions. Unfortunately, the ETS-NOCV and IQA schemes are not yet available for public use in periodic calculations codes. On the other hand, it seems rational to comment, based on the very huge positive value of the (B)H∙∙∙H(B) interaction energy E int (B)H H(B) = + 49.4  kcal / mol in the tetrameric Li-model, that it is to be expected that in the real Li-crystal the BH∙∙∙HB interactions are likely to be destabilizing.
It is probably important to add that the electron density accumulation in the inter-hydrogen region of BH∙∙∙HB is indeed sufficient to observe a bond path (as it has been noted by McGrady et al. [29])—however, it does not necessarily imply the overall stabilizing interactions: for example, as nicely demonstrated by Cukrowski et al. [36], two water molecules enforced to approach each other via oxygen atoms leads to formation of the oxygen-oxygen bond critical point, however, the overall binding energy is as expected positive (destabilizing) due to the fact that some subtle stabilization arising from the electron-exchange channel (resulting also in the negative ΔEorb values) is diminished by the Pauli and electrostatic repulsion. A similar situation is observed in dimers of M2X2 (for M = Li, K, X = H, Cl) where M-X stabilization outweighs the repulsion stemming from M-M and X-X interactions [73].
In Figure 3A the structure of the LiN(CH3)2BH3 monomer is presented. It can be seen that lithium ion forms a chemical bond not only with the nitrogen atom, but also with the BH3 unit through intramolecular Li∙∙∙H–B interactions. The binding energy of BH3 to NMe2Li appears to be significant, ΔEtotal = −63.99 kcal/mol, Figure 3B. Just for comparison, the binding energy of BH3 to ammonia in NH3BH3 is only −30.3 kcal/mol [13]. Such a difference is related to the existence of strong intramolecular Li∙∙∙H–B interactions. ETS-NOCV allowed us to conclude that, apart from strong dative bonds, described by Δρ(N-B) and the corresponding ΔEorb(B–N) = −105.63 kcal/mol, additional intramolecular Li∙∙∙H–B interactions are formed, Δρ(Li∙∙∙H–B). The latter component corresponds to significant charge transfer stabilization, ΔEorb(Li∙∙∙H–B) = −20.94 kcal/mol, Figure 3B. It is noteworthy that the intramolecular Li∙∙∙H–B charge transfer component (Figure 3B) appears to be stronger than the intermolecular one, ΔEorb(Li∙∙∙H–B) = −15.38 kcal/mol (Figure 2B)—this is related to the fact that in the latter case B–H bonds interact with the single Li ion, whereas in the former one with multiple Li ions.
We further performed similar calculations for the tetrameric model of KN(CH3)2BH3 as well as for the monomer—the results of ETS-NOCV calculations are shown in Figure 5 and Figure 6 . Similarly to LiN(CH3)2BH3, intermolecular interactions in the tetramer of KN(CH3)2BH3 are dominated by electrostatic forces (60% of total stabilizing contributions), followed by dispersion (22%) and orbital interaction components (18%), Figure 5. The overall intermolecular K∙∙∙H–B interaction energy is slightly less pronounced compared to the corresponding Li∙∙∙H–B due to the larger size of potassium compared to lithium. One should point out the lack of BH∙∙∙HB electron delocalization within the “bay” between the two potassium atoms and BH3 groups, which is present in LiN(CH3)2BH3 (Δρ2 in Figure 2b). It has been already noted by McGrady and coworkers [29]. The B–N dative bond in KN(CH3)2BH3 monomer is of similar strength ΔEorb(B–N) = −104.30 kcal/mol with respect to LiN(CH3)2BH3. The intramolecular K∙∙∙H–B charge delocalization is of similar magnitude to the intermolecular-one, Figure 5B and Figure 6B. Finally, the overall bonding energy of BH3 to KN(CH3)2 in the monomer, ΔEtotal = −67.34 kcal/mol, appeared to be more negative compared to the corresponding ΔEtotal = −63.99 kcal/mol for LiN(CH3)2BH3 predominantly due to a lower Pauli repulsion contribution, Figure 3 and Figure 6.
Finally, we consider the two remaining cluster models of LiN(CH3)2BH3 and KN(CH3)2BH3 where homopolar CH∙∙∙HC interactions are involved, Figure 1B, Figure 7A and Figure 8A.
The results of energy decomposition analyses demonstrate the stabilizing nature of CH∙∙∙HC interactions in both crystals—the overall interaction energy is ΔEint = −17.45 kcal/mol for KN(CH3)2BH3, whereas it is only ΔEint = −4.34 kcal/mol for LiN(CH3)2BH3, Figure 7A and Figure 8A. Significantly more pronounced stabilization in potassium crystal originates from larger number of CH∙∙∙HC contacts as compared to the lithium analog. It constitutes the 2D layers architecture of the potassium crystal as compared to rather 1D chain-like structure in LiN(CH3)2BH3. In both cases the main contribution (64%–68%) to overall stabilization is dispersion, ΔEdisp = −4.63 kcal/mol for LiN(CH3)2BH3 and ΔEdisp = −18.78 kcal/mol for KN(CH3)2BH3, Figure 7A and Figure 8A. The same has been already suggested by McGrady and coworkers [29]. We found in addition that the electrostatic ΔEelstat and orbital interaction ΔEorb terms are also important, Figure 7A and Figure 8A. Figure 7B and Figure 8B shows that the formation of the CH∙∙∙HC interactions is accompanied by a charge outflow from the occupied σ(C–H) bonds and the electron density accumulation is visible in the inter-hydrogen region of CH∙∙∙HC units. Considering the classical language of a molecular orbital theory one can summarize that the “electronic” part of the CH∙∙∙HC bonding is based on both donation from the occupied σ (C–H) bonds into the empty σ*(C–H) of methyl groups as well as polarization of the C–H bonds (mixing of σ/σ*(C–H)). These stabilizing contributions (the polarization and charge transfer) are clearly mixed—at this point one can reference other important and interesting works in which the meaning of both contributions is debated in terms of non-covalent interactions [67,68,74,75,76].
It is important to reference other works where dispersion dominated CH∙∙∙HC interactions have been found—Echeverría and coworkers found, based on MP2 studies, the “subtle but not faint” stabilizing CH∙∙∙HC interactions between alkanes [77]. Further Valence Bond studies have revealed [78], in line with our conclusions, that, apart from the crucial dispersion term, also the σ/σ*(C–H) polarization/charge transfer and electrostatic contributions are important. Recently, numerous reports are present in the literature on the stabilizing nature of CH∙∙∙HC interactions in various types of hydrocarbons [37,38,79,80,81,82,83,84,85], as well as their importance in catalysis [42,43,86].
In order to complement and confirm the conclusions obtained by the ETS-NOCV method we additionally plotted the contour of the reduced density gradient of the NCI (Non-Covalent Index) method [55] for KN(CH3)2BH3, Figure 9. It was demonstrated that this method is well suited for visualization of non-covalent interactions [55]. It is clearly seen, in line with ETS-NOCV based study, that the crystal of KN(CH3)2BH3 is stabilized by numerous inter and intramolecular K∙∙∙H–B as well as additionally by CH∙∙∙HC interactions. The same is valid for LiN(CH3)2BH3. It is to be anticipated that the existence of strong M∙∙∙H–B interactions in both crystals might affect the mechanism of dehydrogenation similarly as has been already shown for the parent compound LiNH2BH3 for which dehydrogenation is initiated by Li∙∙∙H–B interactions and proceeds further through formation of LiH hydride and NH2BH2 as intermediates [87,88,89].

4. Conclusions

In the present study non-covalent interactions in the hydrogen storage materials LiN(CH3)2BH3 and KN(CH3)2BH3 are for the first time quantitatively (and qualitatively) described by means of the charge and energy decomposition method ETS-NOCV as well as the Interacting Quantum Atoms (IQA) approach.
It was found, in line with the pioneering work of McGrady et al. [29], that both crystals are stabilized by numerous intra- and intermolecular M∙∙∙H–B interactions (M = Li, K). The ETS-NOCV calculations indicated that these bonds are electrostatically dominated, followed by charge transfer and dispersion contributions. Interestingly, the intramolecular charge transfer contributing to Li∙∙∙H–B interaction appeared to be more pronounced than the corresponding intermolecular delocalization. We further noticed in LiN(CH3)2BH3 that formation of intermolecular Li∙∙∙H–B interactions enforces charge delocalization within the homopolar BH∙∙∙HB contacts which explains the presence of the QTAIM bond critical points between clashing hydrogen atoms as was found by McGrady et al. [29]. In contrast, our investigations allowed us to conclude that monomers of LiN(CH3)2BH3 are not likely to spontaneously form any stable aggregates via “pure” stabilizing BH∙∙∙HB interactions (BH3 to BH3 orientation) due to the presence of negatively charged borane units—from a fundamental point of view it demonstrates that BH∙∙∙HB interactions can be rather considered as destabilizing in this type of compounds. We further confirmed this conclusion by the Interacting Quantum Atoms (IQA) energy decomposition calculations—namely, the dihydrogen interaction energy in BH∙∙∙HB appared to be significantly positive (destabilizing), E int B ( H ) H ( B ) = + 49.4  kcal / mol as opposed to Li∙∙∙H–B interactions, E int Li H ( B ) = 98.8  kcal / mol .
Contrary to homopolar BH∙∙∙HB interactions, the ETS-NOCV and IQA methods allowed us to identify stabilizing homopolar dihydrogen interactions CH∙∙∙HC in both LiN(CH3)2BH3 and KN(CH3)2BH3—the presence of such stabilization has already been suggested by McGrady and coworkers based on a topological QTAIM study [29]. We found herein quantitatively that these interactions are dispersion dominated (64% for LiN(CH3)2BH3 and 69% for KN(CH3)2BH3), followed by charge transfer (13% for both LiN(CH3)2BH3 and KN(CH3)2BH3) and electrostatic (23% for LiN(CH3)2BH3 and 17% for KN(CH3)2BH3) terms. It was confirmed that these interactions are far stronger in the potassium crystal due to the larger number of CH∙∙∙HC contacts compared to the lithium analogue. Moreover, the NOCV-based deformation density contributions allowed to state that the “electronic” part of the CH∙∙∙HC interaction is based on both donation from the occupied σ(C–H) bonds into the empty σ*(C–H) of methyl groups as well as polarization of the C–H bonds (mixing of σ/σ*(C–H)).
Briefly summarizing, our in-depth theoretical investigations performed by means of the ETS-NOCV and IQA energy decomposition methods, electrostatic potentials and charges, allowed us to confirm most of the findings that have been already reported in the pioneering work of McGrady et al. [29]. Furthermore, we provided for the first time the energetic description of non-covalent interactions contributing to the stability of LiNMe2BH3 and KNMe2BH3 as well demonstrating, contrary to McGrady et al. [29], the repulsive nature of the homopolar interactions BH∙∙∙HB. The latter is in line with numerous experimental papers [68,69,70,71,72]. Due to the fact that our calculations are based on the cluster approach as well as the fact that all theoretical methods are not free from approximations and very often not from arbitrariness, we believe that further works are needed from both theoretical and experimental laboratories in order to fully uncover the nature of homopolar BH∙∙∙HB interactions.

Supplementary Materials

The supplementary materials are available at https://www.mdpi.com/2073-4352/6/3/28/s1.

Acknowledgments

Results presented in this work were partially obtained using PL-Grid Infrastructure and resources provided by ACC Cyfronet AGH.

Author Contributions

Filip Sagan performed the majority of the calculations presented in this work. In addition, Filip Sagan contributed to the interpretation of the results and the final manuscript form. Radosław Filas initiated the work on bonding in LiN(CH3)2BH3 and KN(CH3)2BH3. Mariusz P. Mitoraj interpreted the results as well as writing the manuscript text.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The crystal structures of LiN(CH3)2BH3 and KN(CH3)2BH3. In addition the cluster models used in the charge and energy decomposition method (ETS-NOCV) analysis are marked by blue (part A) and red dotted lines (part B). The unit cell is also highlighted in the part A.
Figure 1. The crystal structures of LiN(CH3)2BH3 and KN(CH3)2BH3. In addition the cluster models used in the charge and energy decomposition method (ETS-NOCV) analysis are marked by blue (part A) and red dotted lines (part B). The unit cell is also highlighted in the part A.
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Figure 2. The optimized tetrameric cluster model of LiN(CH3)2BH3 along with energy decomposition results describing the interaction between two dimeric fragments in LiN(CH3)2BH3 (A). The fragmentation pattern used in ETS-NOCV analysis is indicated by black dashed line. (B) displays the most relevant deformation density contributions describing Li∙∙∙H–B interactions. The red color of deformation densities shows charge depletion, whereas the blue an electron accumulation due to Li∙∙∙H–B interaction.
Figure 2. The optimized tetrameric cluster model of LiN(CH3)2BH3 along with energy decomposition results describing the interaction between two dimeric fragments in LiN(CH3)2BH3 (A). The fragmentation pattern used in ETS-NOCV analysis is indicated by black dashed line. (B) displays the most relevant deformation density contributions describing Li∙∙∙H–B interactions. The red color of deformation densities shows charge depletion, whereas the blue an electron accumulation due to Li∙∙∙H–B interaction.
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Figure 3. Monomer of LiN(CH3)2BH3 along with the corresponding molecular electrostatic potential (A). In (B) the results of ETS-NOCV analysis are presented that describe bonding between the BH3 unit and the LiN(CH3)2 fragment.
Figure 3. Monomer of LiN(CH3)2BH3 along with the corresponding molecular electrostatic potential (A). In (B) the results of ETS-NOCV analysis are presented that describe bonding between the BH3 unit and the LiN(CH3)2 fragment.
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Figure 4. Dimer of LiN(CH3)2BH3 consisting of BH∙∙∙HB interactions together with results of ETS-NOCV analysis (B). The dimer was cut from the optimized tetramer model and it is marked with black dotted lines (A).
Figure 4. Dimer of LiN(CH3)2BH3 consisting of BH∙∙∙HB interactions together with results of ETS-NOCV analysis (B). The dimer was cut from the optimized tetramer model and it is marked with black dotted lines (A).
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Figure 5. The tetrameric cluster model of KN(CH3)2BH3 along with energy decomposition results describing the interaction between two dimeric fragments in KN(CH3)2BH3 (A). The fragmentation pattern used in ETS-NOCV analysis is indicated by a black line. Part (B) displays the most relevant deformation density contributions describing K∙∙∙H–B interactions. The red color of the deformation densities shows charge depletion, whereas the blue an electron accumulation due toK∙∙∙H–B interaction.
Figure 5. The tetrameric cluster model of KN(CH3)2BH3 along with energy decomposition results describing the interaction between two dimeric fragments in KN(CH3)2BH3 (A). The fragmentation pattern used in ETS-NOCV analysis is indicated by a black line. Part (B) displays the most relevant deformation density contributions describing K∙∙∙H–B interactions. The red color of the deformation densities shows charge depletion, whereas the blue an electron accumulation due toK∙∙∙H–B interaction.
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Figure 6. Monomer of KN(CH3)2BH3 along with the corresponding molecular electrostatic potential (part (A)). In part (B) the results of ETS-NOCV analysis are presented that describe bonding between the BH3 unit and the NKMe2 fragment.
Figure 6. Monomer of KN(CH3)2BH3 along with the corresponding molecular electrostatic potential (part (A)). In part (B) the results of ETS-NOCV analysis are presented that describe bonding between the BH3 unit and the NKMe2 fragment.
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Figure 7. Cluster model containing eight monomers of LiN(CH3)2BH3 along with energy decomposition results describing CH∙∙∙HC interactions between the two selected fragments (marked by the black line), part (A). In part (B) the overall deformation density Δρorb is depicted together with the corresponding stabilization ΔEorb.
Figure 7. Cluster model containing eight monomers of LiN(CH3)2BH3 along with energy decomposition results describing CH∙∙∙HC interactions between the two selected fragments (marked by the black line), part (A). In part (B) the overall deformation density Δρorb is depicted together with the corresponding stabilization ΔEorb.
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Figure 8. Cluster model containing eight monomers of KN(CH3)2BH3 along with energy decomposition results describing CH∙∙∙HC interactions between the two selected fragments (marked by the black line), part (A). In part (B) the overall deformation density Δρorb is depicted together with the corresponding stabilization ΔEorb.
Figure 8. Cluster model containing eight monomers of KN(CH3)2BH3 along with energy decomposition results describing CH∙∙∙HC interactions between the two selected fragments (marked by the black line), part (A). In part (B) the overall deformation density Δρorb is depicted together with the corresponding stabilization ΔEorb.
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Figure 9. The surfaces describing the reduced density gradient at an isovalue of 0.5 a.u. for the octamer of KN(CH3)2BH3. The surfaces are coloured on a blue-green-red scale according to the values of sign(λ2)ρ, ranging from –0.05 to 0.02 au.
Figure 9. The surfaces describing the reduced density gradient at an isovalue of 0.5 a.u. for the octamer of KN(CH3)2BH3. The surfaces are coloured on a blue-green-red scale according to the values of sign(λ2)ρ, ranging from –0.05 to 0.02 au.
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Table 1. The interacting quatum atoms (IQA) energy decomposition results (in kcal/mol) describing the two atomic interactions X∙∙∙Y (X=Li, H; Y=H) in LiNMe2BH3.
Table 1. The interacting quatum atoms (IQA) energy decomposition results (in kcal/mol) describing the two atomic interactions X∙∙∙Y (X=Li, H; Y=H) in LiNMe2BH3.
IQA(X∙∙∙Y) V ne AB V en AB V nn AB V ee AB V eeC AB V eeX AB E int AB *
Li∙∙∙H(B)–805.9–338.4480.1565.4568.2–2.8–98.8
(C)H∙∙∙H(C)–140.6–138.2130.8147.2148.6–1.4–0.80
(B)H∙∙∙H(B)–198.9–198.6119.7327.2330.0–2.7+49.4
* E int AB = V nn AB + V en AB + V ne AB + V ee AB = V nn AB + V en AB + V ne AB + V eeC AB + V eeX AB .

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Sagan, F.; Filas, R.; Mitoraj, M.P. Non-Covalent Interactions in Hydrogen Storage Materials LiN(CH3)2BH3 and KN(CH3)2BH3. Crystals 2016, 6, 28. https://doi.org/10.3390/cryst6030028

AMA Style

Sagan F, Filas R, Mitoraj MP. Non-Covalent Interactions in Hydrogen Storage Materials LiN(CH3)2BH3 and KN(CH3)2BH3. Crystals. 2016; 6(3):28. https://doi.org/10.3390/cryst6030028

Chicago/Turabian Style

Sagan, Filip, Radosław Filas, and Mariusz P. Mitoraj. 2016. "Non-Covalent Interactions in Hydrogen Storage Materials LiN(CH3)2BH3 and KN(CH3)2BH3" Crystals 6, no. 3: 28. https://doi.org/10.3390/cryst6030028

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