Initial steps for the thermal decomposition of alkaline-earth metal amidoboranes: a cluster approximation.

A DFT study of thermal decomposition mechanisms of [M(NH2BH3)2]4 clusters with M = Mg, Ca, and Sr is presented. Multi-step reaction pathways leading to elimination of the first H2 molecule are explored at the M06/TZVP level of theory. For all studied M, the clusters adopt similar structures and exhibit similar transformations along the reaction pathways. Their activation energies decrease in the order Mg < Ca ≤ Sr. Four metal atoms in the cluster form a rigid planar construction that is found to be nearly unchanged during all transformations. Cleavage of the B-H bond in the environment of alkaline-earth metal atoms leads to the "capture" of the released H atom by neighboring metal atoms with the formation of a M3H moiety. While the activation energies for the cleavage of Hδ- can be as low as 14.3, 22.6 and 23.3 kcal mol-1 for M = Mg, Ca and Sr, respectively, barriers for the subsequent cleavage of Hδ+via destruction of the M3H moiety are about twice larger.


Introduction
Development of materials with properties appropriate for transportable hydrogen storage is an advanced field in modern chemistry. 1,2 The excellent gravimetric and volumetric hydrogen density of ammonia borane and its derivatives attracts persistent interest in this class of compounds. 3,4 It was found that alkali-metal amidoboranes LiNH 2 BH 3 and NaNH 2 BH 3 release more hydrogen at lower temperatures than pure ammonia borane and also suppress borazine release. 5 However, release of a significant amount of ammonia was observed under thermal decomposition of alkalimetal amidoboranes. [6][7][8][9][10] Alkaline-earth amidoboranes Mg(NH 2 BH 3 ) 2 (MgAB), 11 Ca(NH 2 BH 3 ) 2 (CaAB), 12 and Sr(NH 2 BH 3 ) 2 (SrAB) 13 are known laboratory species which also demonstrate improved dehydrogenation properties compared to ammonia borane. First, CaAB was obtained as a THF adduct, 14 then pure CaAB was synthesized by ball milling of CaH 2 and BH 3 NH 3 . 12 These forms have different dehydrogenation properties. THF containing CaAB releases H 2 mainly in the temperature range from 120 to 245 1C, 14 while the solvent free CaAB eliminates hydrogen at B80 1C with peaks at 100 and 140 1C. 12 H 2 release from SrAB starts at about 60 1C and the decomposition becomes violent as the temperature increases to 93 1C. MgAB exhibits three overlapping dehydrogenation steps with the peak temperatures at 104, 162 and 223 1C. 11 Activation energies for the three dehydrogenation steps are 20.1, 27.7 and 28.4 kcal mol À1 . The third dehydrogenation step of MgAB is found to be mildly endothermic and the thermolysis of MgAB yields no volatile by-products. 11 Dehydrogenation of CaAB also is not accompanied by the release of borazine. 12 The release of B 2 H 6 and NH 3 was noticed during the thermal decomposition of SrAB. 13 Experimental success in the synthesis of alkaline-earth amidoboranes has stimulated related theoretical studies. A number of works based on solid state theory are devoted to the prediction of crystal structure, 15 dehydrogenation mechanisms, 16 possible intermediate products of the dehydrogenation reaction, 17 hydrogen diffusion pathways, 18 and optical 19 and elastic 20 properties of metal amidoboranes (MAB). Advantages of MAB over pure ammonia borane (lower dehydrogenation barriers, a less exothermic overall dehydrogenation reaction and borazine suppression) are attributed to the ionic character of bonds in MAB and the catalytic role of the metal. However, the detailed dehydrogenation mechanism is still unclear. Kim et al. 21 presented a comprehensive ab initio study of the mechanisms and kinetics of H 2 release in monomers and dimers of MAB. They concluded that oligomerization (O-path) and non-oligomerization (D-path) pathways are competitive. The oligomerization pathway is found to be more favorable for alkali-metal amidoboranes. In contrast, the release of H 2 via direct transfer of H À , abstracted by the metal cation from the BH 3 group, to H + of the NH 2 group of the same NH 2 BH 3 unit is more favorable in the case of CaAB and MgAB.
The activation energy of the release of the first H 2 molecule from CaAB and MgAB is equal to 36 kcal mol À1 at the MP2/6-311++G** level of theory. Yuan et al. 22 reported that the release of the first H 2 molecule from the CaAB dimer is kinetically more favorable if it does not involve the Ca atom in the dehydrogenation transition state. No pathways of formation of an oligomeric [BH 3 NH 2 BH 2 NH 2 ] À unit were found at the DFT(PBE/PAW) level of theory. 22 These theoretical studies reveal the importance of intermolecular interactions for the particular development of chemical reactions in MAB. The crystal structure of these compounds features a network based on weak M-N and M-H(BH 3 ) interactions. Cluster approximation is an intermediate approach between molecular and solid state computations. It allows tracking of molecular transformations in the chemical reaction pathways taking into account the local atomic environment. 23

A. Structure of [M(NH 2 BH 3 ) 2 ] 4 tetramers
In the present work, a tetrameric cluster, [Ca(NH 2 BH 3 ) 2 ] 4 (2), was obtained by optimization of a cutout from crystalline CaAB. CaAB adopts a monoclinic structure with the C 2 space group. 12 Each Ca atom is coordinated with two NH 2 and four BH 3 groups (Fig. 1a). The minimal distance between H + and H À of adjacent layers is about 2.4 Å, i.e. no dihydrogen bonds occur. This observation points out that dehydrogenation proceeds within a layer. A chosen piece of crystalline structure is shown in Fig. 1a and the optimized geometry of the resultant C 2h symmetric tetrameric cluster is presented in Fig. 1b (projection onto the XY plane).
The z-axis is chosen to be perpendicular to the layer. NH 2 BH 3 groups in the cluster can be classified according to their positions as shown in Fig. 1b. Expectedly, the Ca-N-B angles are the most affected by optimization, which is reflected in the formation of additional Ca-H(BH 3 ) bonds with x-and y-NH 2 BH 3 groups. The environment of BH 3 groups in z-NH 2 BH 3 is less affected upon the optimization of the cutout from the crystal tetramer. Overall, Ca-H(BH 3 ) distances in the resultant tetramer are in the range 2.30-2.45 Å. In general, optimization leads to bond shortening with respect to the experimental structure. While all experimental B-N bond lengths in the crystal are 1.575 Å, the optimized values in the tetramer are 1.570, 1.543, and 1.527 Å in x-, y-, and z-NH 2 BH 3 , respectively. The respective values of Ca-N distances are 2.352, 2.400, and 2.461 Å, while in the CaAB crystal the Ca-N bond lengths are 2.383 Å.
Several initial experimental attempts of the synthesis of pure MgAB failed, 14,25 which led to the conclusion that the condensed charge on Mg 2+ cations leads to structural instability. However, pure MgAB was finally obtained, 11 but unfortunately, the crystal structure of the compound has not been determined. A computational modelling 15 predicts that MgAB adopts a structure in the same space group as experimentally known CaAB. In the present study, we assumed the structure of [Mg(NH 2 BH 3 ) 2 ] 4 (1) to be similar to that of 2. The optimized structure of 1 ( SrAB adopts a similar structural type in the crystal as CaAB with different atomic coordinates. Positions of hydrogen atoms in the unit cell of SrAB were not determined. 13 To be consistent, we assumed the geometry of the tetrameric cluster [Sr(NH 2 BH 3 ) 2 ] 4 (3) to be similar to that of 2. In the optimized structure of 3, Sr-H(BH 3 ) distances are in the range 2.47-2.60 Å. Sr-N bond lengths are 2.518, 2.586, and 2.632Å, and B-N bond lengths are 1.571, 1.539, and 1.526 Å in x-, y-, and z-NH 2 BH 3 , respectively.
In the following discussion the energy values are reported with respect to the optimized tetrameric clusters 1, 2, and 3.

B. Cleavage of B-H bonds and M 3 H moiety formation
B-H dissociation energies in MAB are lower than N-H dissociation energies, 18 thus, the first obvious step in the dehydrogenation mechanism is the cleavage of the B-H bonds. Metal atoms in the considered tetramers form a diamond-shaped arrangement in the XY plane (Fig. 1b). Atomic charges of Mg from the natural population analysis are 1.398 for atoms arranged parallel to the X-axis and 1.500 À e for atoms arranged parallel to the Y-axis. The respective charges of Sr are 1.157 and 1.260 À e. The NBO analysis provides the respective charges for Ca in 2, 0.857 and 0.930 À e, to be somewhat smaller than those for Sr in 3 because of the higher natural population of valence orbitals. B-H bonds of z-NH 2 BH 3 directed toward the XY plane are the longest (for example, 1.259 Å compared to 1.229 Å for other B-H bonds in this BH 3 group in 2) with the largest negative charge at H atoms (NBO charges are À0.100 À e; À0.070 À e; and À0.114 À e for 1, 2, and 3, respectively). Cleavage of these B-H bonds leads to the hydrogen atom takeover by three neighboring metal cations in E1z(M) local minima (see the energy diagram in Fig. 2). It was shown earlier that the formation of a Li 3 H moiety is a key feature of dehydrogenation pathways in LiAB. 23,24 The analogous pyramidal M 3 H moiety is also formed upon activation of alkaline-earth amidoboranes. The highest bonding orbital of E1z(Ca) is delocalized over the Ca 3 H moiety (Fig. 3). Geometrical parameters of the M 3 H moieties in E1z(M) are provided in the ESI † (Table S1). The removed hydrogen atom gains significant charge in the environment of the three metal cations. It has a natural charge of À0.580, À0.358 and À0.484  Fig. 4. In the case of Ca and Sr, the highest bonding orbitals are delocalized over the removed H atom and two neighboring metal atoms, and the NH 2 BH 2 intermediate is released (Fig. 4a). As in the case of the z-pathway, E1y(Ca) and E1y(Sr) are only slightly lower in energy than the respective transition states T1y(M). In the case of Mg, the release of the NH 2 BH 2 intermediate is not observed. Instead, [BH 3 NH 2 CaNH 2 BH 2 ] + is formed, where one H bridges two BH 2 groups (Fig. 4b). This significantly stabilizes the E1y(Mg) state DE  (Fig. 2). Transition states leading to the formation of H 2 are the key states for the z-and y-pathways with activation energies ranging from 40.9 to 44.4 kcal mol À1 (Fig. 2). The M 3 H pyramidal moiety in T2z(M) and the M 3 H kite-shaped arrangement in T2y(M) are destroyed (Fig. 5a). The hydrogen atoms in the transition states are located between two M atoms. The destruction of the M 3 H pyramidal moiety requires somewhat higher energy barriers. The While E2z(Ca) and E2z(Sr) are lower in energy with respect to E2z*(M) and free H 2 molecules, E2z(Mg) is higher in energy (Fig. 2).   For the sake of comparison, we also explored a direct dehydrogenation pathway which proceeds through hydrogen evolution via N-H d+ Á Á ÁH dÀ -B interaction in the same NH 2 BH 3 group. This pathway was found to be the most favorable for the CaAB dimer in the theoretical study of Yuan et al. 22 (TS could be as low as 21.7 kcal mol À1 computed within an extended unit cell PBE/PAW method). The direct intramolecular dehydrogenation pathway was also assumed for CaAB and MgAB thermal decomposition in the theoretical study of Wang et al. 16 The release of the first H 2 molecule requires to overcome a barrier of 69.0 kcal mol À1 for MgAB and 73.5 kcal mol À1 for CaAB at the CCSD(T)/ 6-311++G(3d,2p) level of theory. 16 In the present study on the example of 2 we found this pathway to be the most energetically demanding. The energy of the N-HÁ Á ÁH-B transition state (Fig. S3 in the ESI †) leading to the release of the first H 2 molecule from x-NH 2 BH 3 is 59.7 kcal mol À1 . Optimization of the corresponding transition states for y-and z-NH 2 BH 3 converged to the alternative transition states T2z(M)/T2y(M) considered above.

D. Oligomerization pathways
An oligomerization pathway going through B-N bond formation between NH 2 BH 3 and NH 2 BH 2 units was found to be the most favorable in the case of LiAB tetramers. 23 Compared with the D-path, the O-path was found to be more favorable for LiAB, KAB, and NaAB dimers and less favorable for CaAB and MgAB monomers in Kim's study. 21 For tetramers, considered in the present work, B-N bond formation between NH 2 BH 3 and NH 2 BH 2 units can proceed along both z-and y-pathways. Oligomerization pathways are structurally similar for M = Mg, Ca and Sr. As an example, structural transformation leading to the B-N bond formation along the z-pathway is shown in Fig. 6 for M = Ca. The Ca 3 H moiety is retained along the oligomerization pathway. Structural transformations along the y-pathway are analogous (ESI, † Fig. S4). The energy diagram is presented in Fig. 7. T3y(M) energies in the oligomerization step (30.5 and 33.2 kcal mol À1 for M = Ca and Sr, respectively) are similar to those leading to the cleavage of the B-H bonds. For the z-pathway the oligomerization step is more energetically demanding than the first T1z(M) step by 3-5 kcal mol À1 , but somewhat lower in energy than the oligomerization step for the y-pathway. Energies of T3z(M) are 17.3, 26.4, and 28.0 kcal mol À1 for M = Mg, Ca and Sr, respectively. Formation of the B-N bond significantly stabilizes E3z(M) though it is still notably endothermic for M = Ca and Sr. In contrast, formation of E3z(Mg) is slightly exothermic (À0.2 kcal mol À1 ), and after an isomerization step via T3 0 z(Mg), formation of the E3 0 z(Mg) product is exothermic by À8.1 kcal mol À1 (see Fig. 7).
The dehydrogenation step implies further cleavage of N-H bonds. Possible sites of involved NH 2 groups are shown in Fig. 6 for the product E3z(M). Five transition states found for the dehydrogenation of E3z(Ca) are given in Fig. S5, ESI. † Energies of T4z(Ca) vary from 43 to 53 kcal mol À1 . The dehydrogenation transition states T4z(M) in the oligomerization pathway are higher in energy than T2z(M) in the pathway avoiding the oligomerization step, similar to previous findings for the alkaline-earth amidoborane monomers. 21 The lowest energy barrier corresponds to the transition state leading to the hydrogen release from site number 3 where the NH 2 group is associated with two B atoms. The transition state,   It should be noted that the energy of the lowest dehydrogenation transition state from the [LiNH 2 BH 3 ] 4 cluster is 31.2 kcal mol À1 at the M06/6-311(d,p) computational level. The energy of the lowest transition state leading to the oligomerization is 25.5 kcal mol À1 . 23 Analogous values for tetramer 2 at the same level of theory are 42.6 T4z(Ca) and 26.0 T3z(Ca) kcal mol À1 . While oligomerization in the case of [Ca(NH 2 BH 3 ) 2 ] 4 needs to overcome nearly the same energy barrier as that in the case of [LiNH 2 BH 3 ] 4 , the dehydrogenation step is significantly more energy consuming. Presumably the reason is the better mobility of the closed shell LiH unit formed after the cleavage of the B-H bond. In contrast to LiAB tetramers, the diamond-shaped arrangement of metal atoms in 2 is maintained in the cluster during all transformations in the reaction direction.
While H 2 elimination is a major result of thermal decomposition of MAB, some amount of ammonia release is observed experimentally. 6,7,13 According to the mechanisms of the thermal decomposition of the alkali-metal amidoboranes suggested by Fijalkowski et al., 8  To estimate whether the cleavage of B-N bonds in alkaline-earth metal amidoboranes is a competitive process with the H 2 elimination mechanisms suggested above, we considered several B-N bond breaking pathways in 2. Three different transition states leading to the cleavage of B-N bonds of z-NH 2 BH 3 are provided in the ESI † (Fig. S6). One of the possibilities, T5z(Ca), leads to the formation of [CaNH 3 ] + cations in E5z(Ca). However, the activation energy is 81.1 kcal mol À1 , i.e. 3.5 times larger than the activation energy of B-H bond cleavage via T1z(Ca), and about twice as large as that of the key state for H 2 release via the oligomerization pathway, T4z(Ca). Transfer of BH 3 to one of the y-NH 2 BH 3 units is accompanied by the occupation of the [NH 2 ] À residue at the position between three Ca atoms forming a pyramidal Ca 3 NH 2 moiety analogously to the Ca 3 H moiety discussed above. One of the transition states, T6z(Ca) with an energy of 50.8 kcal mol À1 , leads to bridging of the released BH 3 with the BH 3 group of y-NH 2 BH 3 by the H atom. The other transition state, T7z(Ca) with an energy of 51.3 kcal mol À1 , leads to head-to-tale dimerization with the formation of a [BH 3 NH 2 BH 3 ] À unit. Thus, it follows that B-N bond breaking pathways have larger activation energies than H 2 elimination pathways. This is consistent with the minor role of mechanisms leading to the release of ammonia.

Computational details
The conventional transition state theory was used to predict the optimized structures and transition states of [M(NH 2 BH 3 ) 2 ] 4 tetramers, where M = Mg, Ca, and Sr. The intrinsic reaction coordinate (IRC) scans confirmed the connectivity of all the transition states to reactants and products of a given step. It was noted in previous theoretical investigations that taking into account van der Waals interactions is important to reproduce experimental parameters of SrAB. 20 All computations were performed within DFT using the M06 27 functional, which takes dispersion interaction into account. The TZVP 28 basis set was used throughout. The same computation level was used for the Natural Bond Orbital (NBO) analysis. 29 The Gaussian 09 code 30 was utilized in all computations.

Conclusion
A cluster approximation was used to explore the release of the first H 2 molecule from alkaline-earth metal amidoboranes. To form the cluster, geometries of four neighboring molecules were extracted from a layer of experimental crystal structure of CaAB. The cleavage of B-H bonds in the NH 2 BH 3 unit in the environment of alkaline-earth metal atoms leads to the ''capture'' of the released H atom by neighboring metal atoms with the formation of a M 3 H moiety. Such a moiety was found to be a key feature of the dehydrogenation process in small (trimeric and tetrameric) LiAB clusters. 23,24 The formation of this Li 3 H moiety was ascribed to the existence of stable Li 3 H clusters. 31,32 Despite the fact that similar free M 3 H clusters are not found in alkaline-earth metal hydrides (unlike Li 3  While the cleavage of the B-H bonds and further oligomerization of amidoboranes require moderate energy, the cleavage of N-H bonds accompanied by destruction of the M 3 H moiety in favor of H 2 formation is much more energy consuming. This step requires significant energy uptake both for oligomerization and non-oligomerization pathways.
Kinetically, after the cleavage of the first B-H bond, the cleavage of other B-H bonds or/and oligomerization with B-N bond formation require much less energy uptake than a direct H 2 release. This indicates that compounds featuring MNH 2 BH 2 NH 2 BH 3 units are potential intermediates in the dehydrogenation process. The large number of possible isomers of such compounds makes the use of a convenient transition state method ineffective for the exploration of pathways for the release of second and subsequent hydrogen molecules. In such a situation, use of the GRRM 26 method is recommended for further studies.
The cleavage of B-N bonds is found to be significantly less favorable than the cleavage of B-H bonds. If local overheating leads to the B-N bond cleavage, then the formation of the M 3 NH 2 moiety is more favorable than the formation of the MNH 3 complex. This may be accompanied by the formation of an intermediate [BH 3 NH 2 BH 3 ] À or the release of diborane. The following NH 3 release is likely to be a multistep side process which requires additional studies which are outside the scope of the present research.
Tetramers of alkaline-earth metal (Mg, Ca and Sr) amidoboranes show similar tendencies along the reaction pathways with energy barriers increasing in the order Mg o Ca r Sr. However, according to experiments, 11 a higher temperature is required for the start of the dehydrogenation in the case of MgAB, which suggests a larger barrier for H 2 release from MgAB compared to CaAB and SrAB. One of the reasons for this disagreement could be our assumption of a similar crystal structure for MaAB and CaAB, and, consequently, a similar local environment of the atoms in tetramer clusters 1 and 2.
Note that previous computational studies based on such an assumption also resulted in lower energy barriers for the thermal decomposition of MgAB compared to CaAB. 18 In the present study, we demonstrate that unlike Ca and Sr, in the case of Mg, oligomerization of NH 2 BH 3 and NH 2 BH 2 units in 1 makes the formation of the E3 0 z (Mg) intermediate exothermic and significantly increases the activation energy for the subsequent dehydrogenation steps. We suppose that similar transformations occur in the crystal structure of MgAB prior to the dehydrogenation which increases the overall activation energy for MgAB dehydrogenation compared to CaAB and SrAB.