Ammonia Borane Clusters: Energetics of Dihydrogen Bonding

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Ammonia Borane Clusters: Energetics of Dihydrogen Bonding, Cooperativity and Role of Electrostatics Kunduchi Periya Vijayalakshmi, and Cherumuttathu H Suresh J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b01527 • Publication Date (Web): 20 Mar 2017 Downloaded from http://pubs.acs.org on March 22, 2017

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The Journal of Physical Chemistry

Ammonia Borane Clusters: Energetics of Dihydrogen Bonding, Cooperativity and Role of Electrostatics Kunduchi P. Vijayalakshmi †* and Cherumuttathu H. Suresh‡* †Analytical and Spectroscopy Division, Analytical, Spectroscopy and Ceramics Group, Propellants, Polymers, Chemicals and Materials Entity, Vikram Sarabhai Space Centre, Thiruvananthapuram- 695022, India. ‡Chemical Sciences and Technology Division, CSIR- National Institute for Interdisciplinary Science and Technology, Thiruvananthapuram, 695 019, India. ABSTRACT: Cluster formation of ammonia borane (NH3BH3) driven by non-covalent H...H dihydrogen interaction is investigated at M06L/6-311+G(d,p) level density functional theory. For clusters containing up to six monomers, ladder, cyclic, stacked, crossstacked, end-on, mixed and hexagonal configurations have been screened for their energetic stability. In the dimer, 7.94 kcal/mol stabilization energy per monomer (Em) is observed. Compared to ladder and cyclic configurations, a tetramer consisting of stacked dimer units is more stable by 3.0 kcal/mol whereas a hexamer composed of hexagonally arranged monomers promoting side-on H...H interaction is more stable than a stacked configuration by 2.5 kcal/mol. The hexagonal packing of cluster is repeated to obtain (NH3BH3)12, (NH3BH3)18, (NH3BH3)36, (NH3BH3)48 and (NH3BH3)54 clusters. The Em 17.81 kcal/mol observed for (NH3BH3)54 is 2.24 fold higher than the dimer, suggesting strong cooperativity in cluster growth mechanism. The zwitterionic features of NH3BH3 is characterized in terms of molecular electrostatic potential (MESP) features. During cluster formation, donation of electron density from negatively charged BH3 unit of a monomer to the positively charged NH3 unit of other interacting monomers occurs through H...H dihydrogen bonding. The extent of electron donation is revealed through the value of MESP minium (Vmin) in every monomer. A strong linear correlation between the total value of Vmin for a cluster (ΣVmin) and the total stabilization energy of the cluster (Estb) is established. Further, MESP at the nuclei of N (VN) and B (VB) are found to be very sensitive to the strength of H...H bonding. With respect to free NH3BH3, the total change in VN (Σ∆VN) as well as the total change in VB (Σ∆VB) in a cluster shows nearperfect linear correlation with Estb. Further, the magnitude of the three quantities, viz. Σ∆VN, Σ∆VB and Estb is nearly same and indicates that the cluster formation of NH3BH3 is almost effectively controlled by electrostatics of dihydrogen interactions. The extended network of dihydrogen interactions observed in large clusters and the significant positive cooperativity effect of such interactions support the use of ammonia borane as a potential hydrogen storage material.

BH...HN contacts are observed suggesting 3 - 4 kcal/mol enINTRODUCTION ergy for dihydrogen bond. The ab initio MP2 level calculaAmmonia borane (NH3BH3), a solid compound at standard tions report interaction energy 24.4, 41.0, and 52.7 kcal/mol, condition, is regarded as a potential hydrogen storage material 1-7 respectively for trimer, tetramer and pentamer configurations due to 19.6 wt% of H2 in it. The solid state of the system of ammonia borane.27,29 The stability of the cluster configuracharacterized by melting point 104 oC is attributed to a unique tions were attributed to the formation of a network of BH...HN molecular packing supported by dipole–dipole interactions and dihydrogen interactions. Further, DFT studies conducted on a large extended network of non-covalent H...H dihydrogen small clusters of ammonia borane have shown that a major interactions.8,9 The hydrogen attached with the negatively factor for cluster stabilization is electrostatic dipole-dipole charged boron acts as electron donor to the hydrogen attached interactions.28 A plane wave density functional theory study with the positively charged nitrogen. This unique donorshowed that the average strength of a BH...HN interaction in acceptor proton-hydride interaction in NH3BH3 has been the the solid state is around 3.0 kcal/mol.18 10-18 19-30 focus of many experimental and theoretical studies to Our aim is to conduct a systematic study on the cluster explain its hydrogen storage and hydrogen release properties. growth patterns of NH3BH3 up to hexamer and follow one of Crabtree et al. were the first to recognize that the several the most stable cluster configuration patterns to obtain the BH...HN dihydrogen bonds formed between NH3BH3 units 9,17 energetic features of larger clusters. This would enable us to play a vital role in determining the stability of NH3BH3. Usassess the cooperativity effect in cluster growth mechanism by ing quantum theory of atoms-in-molecule (QTAIM) analysis, following one of the leading cluster growth patterns among and a set of criteria developed in the study of conventional several possibilities. However, we do not attempt to reproduce hydrogen bonds, Popelier showed that the proton-hydride the solid state structure of ammonia borane by following a BH...HN close contact indeed qualify as a hydrogen bond in 26 crystal growth pattern as it would require the modeling of a dimeric NH3BH3. Studies using various ab initio and density very large assembly of monomers. Another aim is to quantify functional theory (DFT) methods have proposed different valthe molecular electrostatic potential (MESP) features of the ues for the interaction energy of a NH3BH3 dimer, viz. 12.1 cluster. For a molecular system, MESP at a point r in space, 17 25 (PCI-8O/B3LYP), 15.1 (MP2/cc-pVDZ), 12.8 (B3LYP/6V(r) is defined in eq. 1, wherein the first term defines the bare 28 30 30 311++G**) , 14.5 (BP86/TZ2P), 16.1 (MP2/6-31G) nuclear potential due to all N nuclei with charge31 ZA, posikcal/mol. In the most stable configuration of the dimer, four ACS Paragon Plus Environment


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tioned at32 RA while the second term accounts for the potential due to the electron density ρ(r). The MESP at a nucleus (Vn) is obtained (eq. 2) by dropping out the nuclear contribution due to ZA in eq. 1. The MESP based analysis of molecular interactions and chemical reactivity are widespread in chemistry.33-44 MESP minimum (Vmin) at electron rich sites and Vn have been used for measuring the subtle electronic changes occurring in a molecule due to chemical modifications.45-52 Recently, Vmin and Vn have been utilized for the interpretation of lone pairs in molecules,53,54 hydrogen bonding55 and noncovalent interactions such as halogen, dihydrogen, tetral, pnicogen, and chalcogen bonding.56-59 MESP-guided topographical study of molecular cluster formation was reported by Gadre et al.60 Very recently, MESP analysis has been used to reveal carbon-carbon nonocovalent interactions in dipolar molecules61 and anion-dihydrogen interactions.62 Further, similar analyses have been utilized for understanding the cluster growth patterns of acetonitrile,63 polyyne cluster formation64 and dimer formation of aromatic and antiaromatic carbon rings.65 The present study will show that a fundamental relationship between the critical features of MESP and interaction energy of the cluster exists. N

V (r ) = ∑ A

Vn = ∑ B# A

ZA ρ(r' )d 3r' − r − R A ∫ r − r'

ZB ρ (r ' )d 3r' −∫ RB - RA r - r'

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(ts1) and the activation energy 2.2 kcal/mol mainly accounts for the B-N bond rotation leading to the staggered - eclipsed staggered transformation. The B-N bond is 0.03 Å elongated in the eclipsed structure. In NH3BH3, nitrogen donates the lone pair electrons to boron and BH3 becomes electron rich. The electron donor-acceptor (eDA) interaction in NH3BH3 is clearly seen in the molecular electrostatic potential (MESP) distribution given in Figure 1c. The MESP is distinctly negative at the mid region of H-B-H angles (dark blue-coloured region) while the NH3 end is highly positive (red-coloured region). The MESP isosurface plot given in Figure 1d further authenticates that the electronic charge transferred from the nitrogen lone pair to boron is concentrated at the mid region of the H-B-H angles. The significant charge separation gives a large dipole moment 5.4 D for NH3BH3.

(1) (2)

COMPUTATIONAL METHODS Geometries of all (NH3BH3)n clusters were optimized using M06L/6-311+g(d,p) density functional theory (DFT).66 A previous benchmark study had shown that this level of theory is the best among a very large set of DFT functionals to reproduce the geometry and interaction energy of a variety of weakly interacting small molecular dimers at CCSD(T)/CCSD level.56 The fully optimized clusters up to dodecamer were characterized by vibrational frequencies calculation to verify that the stationary points show no imaginary frequency. For 18mer to 54mer, the number of basis functions used in the calculation is in the range 1440 to 4320 and a frequency calculation on them were computationally expensive. However, a linear extrapolation scheme based on the energy parameters of clusters up to dodecamer is found to be adequate to obtain the thermal correction to Gibbs free energy and used this approach to calculate the free energy of larger clusters (ESI). For the head-totail antiparallel orientation of ammonia borane dimer, CCSD(T)/6-311G**//CCSD/6-311G** calculation67 is also performed to verify the accuracy of the DFT method. Binding energy (stabilization energy) and Gibbs free energy change for all the clusters were calculated using the super molecule approach and corrected for basis set superposition error (BSSE) using the counterpoise (CP) procedure by Boys and Bernardi.68 For 18mer, 36mer, 48mer and 54mer clusters, BSSE was estimated by extrapolating the BSSE values of clusters up to dodecamer using a linear equation (ESI). The MESP features of the molecules were studied at M06L/6311+g(d,p) level. All the computations were performed using the Gaussian 09 package.69 RESULTS AND DISCUSSION The minimum energy structure of ammonia borane (NH3BH3) is C3v symmetric and it shows staggered arrangement of B-H and N-H bonds. The eclipsed structure is a transition state

(a)

(b)

(c)

(d)

Figure 1. Optimized geometry of (a) NH3BH3, (b) eclipsed configuration, (c) molecular electrostatic potential plotted on to the vdW surface and (d) molecular electrostatic potential isosurface of value -0.06 au. Distances in Å.

(NH3BH3)2-1

(NH3BH3)2-2 Figure 2. Optimized dimer geometries of ammonia borane. Distances in Å.

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NH3BH3 dimer, abbreviated as (NH3BH3)2-1 has C2h symmetry and possesses an antiparallel arrangement of monomer dipoles (Figure 2). It shows four equivalent dihydrogen BH...HN interactions with distance 1.98 Å. Energy released during dimer formation (dimerization) of NH3BH3, considered as the stabilization energy (Estb) is 16.4 kcal/mol meaning that stabilization energy per monomer (Em) is 8.2 kcal/mol. Since there are four BH...HN contacts in the dimer, the stabilization due to one BH...HN interaction becomes 4.1 kcal/mol which is in agreement with the 3 - 4 kcal/mol range reported previously in other DFT and ab initio studies. We also computed the monomer and dimer geometries of NH3BH3 at CCSD/6311G** level and found that they agree closely to the M06L/6-311+G** level results. Further, the BH...HN interaction energy at CCSD(T)/6-311G**//CCSD/6-311G** level is 3.6 kcal/mol which is 0.5 kcal/mol less than the DFT result. Gibbs free energy change (∆G) for the dimerization at DFT level is -5.1 kcal/mol indicating that NH3BH3 dimerizes spontaneously. In (NH3BH3)2-1 (Figure 2), the BN bond is strengthened compared to NH3BH3 due to the weakening of the B-H and N-H bonds involved in H...H interactions which in turn enhances the electron sharing at the B-N bond. Dimer of NH3BH3 in a head-to-tail end-on fashion, (NH3BH3)2-2 is also located as an energy minimum (Figure 2). In (NH3BH3)2-2, the negatively charged BH3 of one monomer interacts with the positively charged NH3 of the other monomer. The Estb of this structure is 9.6 kcal/mol smaller than (NH3BH3)2-1 and also the ∆G for dimerization is positive, 2.1 kcal/mol. Hence, it can be concluded that (NH3BH3)2-1 is the global minimum of the dimer and the higher energy end-on configuration can be neglected for building larger clusters. Extending the (NH3BH3)2-1 structure to trimer gives a ladder type configuration, (NH3BH3)3-1 (Figure 3). A cyclic structure, (NH3BH3)3-2 is also considered which shows the three monomers in a head-to-tail triangular arrangement (Figure 3). Yet another configuration is (NH3BH3)3-3 wherein the third monomer interacts simultaneously with the other two antiparallelly arranged monomers (Figure 3). Compared to (NH3BH3)2-1, B-N bond of the central monomer in (NH3BH3)3-1 is shortened by 0.02 Å whereas B-N bond of the other two monomers are elongated by 0.01 Å. The central monomer of (NH3BH3)3-1 has eight H...H interactions compared to four in (NH3BH3)2-1. Further, the H..H interactions of distance 1.94 Å is expected to be stronger in (NH3BH3)3-1 than the H...H interactions of distance 1.98 Å in (NH3BH3)2-1. These observations suggest that increase in the number of H...H interactions is responsible for the B-N bond shortening as it demands more electron sharing between B and N atoms. These observations are also valid for (NH3BH3)3-2 and (NH3BH3)3-3 configurations. In the cyclic structure, the B-N bonds are shortened compared to the dimer by 0.01 Å which can be attributed to increase in the H...H interactions with distances 1.81, 1.84 and 1.90 Å. Similarly the H...H interactions showing distances 1.80 and 1.90 Å in (NH3BH3)3-3 are relatively stronger than the H...H interactions in (NH3BH3)2-1. The Estb of (NH3BH3)3-1, (NH3BH3)3-2 and (NH3BH3)3-3 are 29.8, 28.3 and 28.7 kcal/mol, respectively suggesting Em 9.9, 9.4 and 9.6 kcal/mol. In all the three configurations of trimer, Em is higher than that observed for the dimer (NH3BH3)2-1 indicating enhancement in H...H interactions in the trimer. Trimer formation leads to significant decrease in free energy by 6.7, 6.4 and 6.2 kcal/mol, respec-

tively for (NH3BH3)3-1, (NH3BH3)3-2 and (NH3BH3)3-3. Hence, we can conclude that from dimer, formation of the ladder type trimer could yield the most effective pathway for the cluster and it may occur spontaneously by further decreasing the free energy by 1.6 kcal/mol compared to dimer.

(NH3BH3)3-1

(NH3BH3)3-2

(NH3BH3)3-3 Figure 3. Optimized trimer geometries of ammonia borane. Distances in Å.

Since (NH3BH3)3-1 is the most stable trimer, extension of the ladder configuration to the forth monomer is considered to generate the tetramer cluster (NH3BH3)4-1 (Figure 4). Similarly, by adding one more monomer, the cyclic (NH3BH3)3-2 can be extended to a cyclic square shaped tetramer. However, a starting structure in this configuration has drastically changed during optimization and the final structure was turned out to be a non-cyclic (NH3BH3)4-2 (Figure 4). The (NH3BH3)4-2 can be considered as the dimer of the dimer (NH3BH3)2-1 wherein the dimer units interact in an end-on fashion with an end-on BN distances 3.10 Å or it can be considered as dimer of the dimer (NH3BH3)2-2 wherein the dimer units interact side-wise with interactions distances 1.93 and 2.10 Å. Two dimer units arranged in a stacking configuration will generate the structure (NH3BH3)4-3 and this structure is same as the heavy-atom box model located by Guerra et al.27 Yet another box model is (NH3BH3)4-4 wherein dimer units are cross-stacked (Figure 4). Extension of the trimer (NH3BH3)3-3 to the tetramer configuration led to the formation of (NH3BH3)4-5 (Figure 4). The Estb values of (NH3BH3)4-1, (NH3BH3)4-2, (NH3BH3)4-3, (NH3BH3)4-4 and (NH3BH3)4-5 are 43.8, 44.4, 50.8, 47.7 and 43.0 kcal/mol, respectively which suggest that the corresponding Em values



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(NH3BH3)6-1

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(NH3BH3)6-2

(NH3BH3)4-1

(NH3BH3)4-2 (NH3BH3)6-3

(NH3BH3)4-3

(NH3BH3)6-4

(NH3BH3)4-4

(NH3BH3)6-5 Figure 5. Optimized structures for the ammonia borane hexamers. Distances in Å.

(NH3BH3)4-5 Figure 4. Optimized tetramer geometries of ammonia borane. Distances in Å.

are 11.0, 11.1, 12.7, 11.9 and 10.7 kcal/mol. The most stable structures (NH3BH3)4-3 and (NH3BH3)4-4 show 'box configuration' reported earlier by Restrepo et al.29 All the tetramer clusters are more stable than the most stable trimer. Tetramer cluster formation leads to significant lowering of the free energy. The ∆G for the ladder type tetramer is -9.3 kcal/mol which is 2.6 kcal/mol lower than the ladder type trimer. The most stable (NH3BH3)4-3 shows a ∆G -12.9 kcal/mol while the crossstacked (NH3BH3)4-4 has the next lowest ∆G -11.1 kcal/mol. The lowering of free energy is the lowest for (NH3BH3)4-5 (-7.6 kcal/mol) followed by (NH3BH3)4-2 (-9.6 kcal/mol). The ener-


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getics of the tetramer clusters suggest that stacking of dimer units improves the overall stability of the cluster. For developing configurations of higher clusters, dimer unit (NH3BH3)-1 can be considered as a basic building block. From the energetics of tetramer clusters, it is very clear that stacked and cross-stacked dimer units have more stabilization energy than other configurations. Hence, further one dimensional extension of (NH3BH3)4-1, (NH3BH3)4-2, and (NH3BH3)4-5 is not considered. Extension of the stacked tetramer (NH3BH3)4-3 to one more layer will give rise to the stacked hexamer (NH3BH3)6-1 whereas a similar extension of the crossstacked tetramer (NH3BH3)4-4 will give rise to the crossstacked hexamer (NH3BH3)6-2 (Figure 5). Extension of the stacked dimers significantly strengthen some of the H...H interactions in both (NH3BH3)6-1 and (NH3BH3)6-2. For instance, the shortest H...H interaction distance is 1.70 Å in (NH3BH3)6-1 and 1.67 Å in (NH3BH3)6-2 which are significantly shorter than the shortest distance of 1.80 Å in (NH3BH3)4-3 and 1.84 Å in (NH3BH3)4-4, respectively. Two more hexamer structures can be obtained by stacking a pair of cyclic trimer (NH3BH3)3-2 and another pair of (NH3BH3)3-3 which would yield (NH3BH3)6-3 and (NH3BH3)6-4, respectively (Figure 5). A highly symmetric hexagonal arrangement of the monomers (NH3BH3)6-5 is also located for the hexamer (Figure 5). The Estb values of (NH3BH3)6-1, (NH3BH3)6-2, (NH3BH3)6-3, (NH3BH3)6-4 and (NH3BH3)6-5 are 82.5, 79.5, 81.4, 83.0 and 85.1 kcal/mol, respectively and the corresponding Em values are 13.8, 13.2, 13.6, 13.8 and 14.2 kcal/mol. This result further ascertain that increase in the number of H...H interactions through stacking improves the stability of the clusters (NH3BH3)6-1 to (NH3BH3)6-4. In (NH3BH3)6-5, stacking H...H interaction is absent and the highest Estb observed for this cluster can be explained by the combined strength of the highest number 24 BH...HN interactions. Though these BH...HN interactions in (NH3BH3)6-5 showing average interaction distance 2.03 Å are weaker than the shorter BH...HN interactions found in the dimer (NH3BH3)-1 and other structures, the accumulated strength of 24 BH...HN interactions become highly significant for the stability of (NH3BH3)6-5. The interacting NH bond is directed towards the middle of the electron rich H-B-H bond angle region which can be visualised with the aid of the MESP picture depicted in Figure 1d. According to the parlance by Politzer et al., BH...HN proton-hydride interaction can be envisaged as a hole-σ interaction.34 Thus in (NH3BH3)6-5, out of the 18 NH bonds, 12 are optimally oriented towards the electron rich site of the BH3 unit leading to 24 BH...HN interactions. Such interactions found in the dimer (NH3BH3)2-1 is 4.1 kcal/mol whereas the slightly weaker BH...HN interaction in (NH3BH3)6-5 has an average value 3.5 kcal/mol. Thus we may conclude that the collective strength of 24 such interactions can exceed the fewer, but stronger stacking BH...HN interactions observed in other hexamer structures. Among the clusters up to hexamer, (NH3BH3)6-5 has the highest stability and shows the highest number of 4 BH...HN interactions per monomer. Therefore this growth pattern of the cluster is assumed as the most preferred for maximising the non-covalent dihydrogen interactions. Hence, we studied the formation of large NH3BH3 clusters by extending (NH3BH3)6-5 in the three directions. Figure 6 shows the sidewise expanded hexamer clusters (NH3BH3)12-1 and (NH3BH3)18-

1, the end-on-wise expanded (NH3BH3)12-2, and the side- and end-on-wise expanded (NH3BH3)36-1, (NH3BH3)48-1 and (NH3BH3)54-1. For all these clusters, the energetic parameters are presented in Table 1. The ordered pair of (Estb, ∆G) for (NH3BH3)18-1, (NH3BH3)36-1, (NH3BH3)48-1 and(NH3BH3)54-1 are (270.4, -47.9), (615.9, -155.9), (853.0, -234.7) and (961.6, 264.1) kcal/mol respectively. This data clearly indicate that the stabilizing interaction energy per monomer (Em) steadily increases from a value 7.94 kcal/mol for the dimer to 17.81 kcal/mol for the 54mer. In 54mer, Em is increased by 2.24 fold compared to the dimer and suggests very high amount of cooperativity in the formation of large clusters. The increasing energetic stabilization of the clusters with increase in monomers is also reflected in free energy lowering. For instance, the free energy change per monomer, ∆Gm for the dimer -2.29 kcal/mol is changed to -4.89 kcal/mol for 54mer indicating a substantial 2.14 fold lowering and a spontaneous cluster formation process.

MESP analysis of NH3BH3 clusters How do we account for the large cooperativity observed in NH3BH3 cluster? The MESP distribution of NH3BH3 (Figure 2) gives a clear demarcation between positively charged ammonia moiety (red) and negatively charged borane moiety (blue) and confirms the zwitterionic character of the molecule. The value of the most negative MESP point (referred to as Vmin) in the BH3 unit can be used as measure of the electron rich character of the anionic end of the zwitterion. In the NH3BH3 monomer, Vmin is -41.16 kcal/mol and the most stable dimer, (NH3BH3)2-1 shows Vmin -33.51 kcal/mol. It may be noted that Vmin is present for both the monomers in the dimer. Hence, the total decrease in Vmin accounted by both the monomers and relative to the Vmin of monomer is 15.3 kcal/mol. This quantity is abbreviated as Σ∆Vmin. The significant decrease in the magnitude of Vmin in the dimer can be attributed to the utilization of the accumulated electron density at BH3 end of the monomer to establish intermolecular interaction with NH3 end of the other monomer. In fact, a clear visualisation of the charge distribution in terms of MESP can be obtained by plotting MESP on a space filling model of the molecule. Such a figure for all the (NH3BH3)n clusters are shown in Figure 7. In the trimer (NH3BH3)3-1, NH3BH3 in the middle looses more electron density to interact with the other two monomers. In cyclic trimer, the symmetry allows the monomers to acquire a balanced distribution of electron density. Similarly, in larger clusters, for instance, for those having hexagonal arrangements (hexamer, dodecamer, 18mer, 36mer, 48mer and 54mer), increase in the number of interactions around BH3 units by NH3 units decreases the overall negative character of MESP at that region which is evident from the fading blue colour there. A visual inspection is not adequate to find a quantitative relationship between MESP and interaction energy. Since electrostatics dominates in the intermolecular interactions of zwitterionic monomers, a correlation between the MESP parameter Σ∆Vmin and interaction energy could be expected. To explore this, Vmin value of every monomer in the cluster has to be obtained. The magnitude of Vmin in the cluster is expected to decrease due to interaction of the electron rich site with the electron deficient site. Unfortunately, observing a distinct Vmin for all the monomers in the cluster is not always possible, especially for cyclic configurations with multiple layered arrangements as in the case of 54mer. In such cases,



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(NH3BH3)12-1

(NH3BH3)18-1

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(NH3BH3)12-2

(NH3BH3)36-1

(NH3BH3)48-1

Figure 6. Optimized structures of ammonia borane hexamers.


(NH3BH3)54-1

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Figure 7. MESP plotted on the space filling model the cluster geometries of NH3BH3. Color coding ( 20.0 to 20.0 kcal/mol.


) from blue to red is -


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Table 1. Energy parameters for ammonia borane clusters. All values in kcal/mol.

Figure 8. MESP isosurface (orange) -18.0 kcal/mol plotted for (NH3BH3)12-2. Points corresponding to MESP minima Vmin-a and Vmin-b are assigned for boron centers labeled as 'a' and 'b', respectively. 0.00

Estb = -0.824 ( Σ∆Vmin ) - 9.262 R² = 0.999

-200.00

-400.00

Estb -600.00

-800.00

-1000.00

-1200.00 0

200

400

600

800

1000

1200

1400

Σ∆V Σ∆ min

Figure 9. Correlation between MESP parameter covalent binding energy. All values in kcal/mol.

and non-

the MESP regions appear united for a group of symmetrically identical monomers, giving rise to localization of MESP in the interior region of the cyclic cluster. An illustration of this feature is given in Figure 8 for (NH3BH3)12-2. For such cases, Vmin observed in the interior region is assigned commonly for all the symmetrically identical monomers. For instance, in Figure 8, the value of Vmin-b is assigned to all the symmetrically equivalent boron centers labeled as 'b'. In Table 2, Σ∆Vmin of all the clusters is depicted (see ESI for all Vmin values). As depicted in Figure 9, Σ∆Vmin correlates linearly with Estb.

Cluster

Estb

∆G

Em

∆Gm

EBSSE

(NH3BH3)2-1

15.87

-4.59

7.94

-2.29

0.56

(NH3BH3)3-1

28.68

-5.59

9.56

-1.86

1.11

(NH3BH3)3-2

27.18

-5.33

9.06

-1.78

1.08

(NH3BH3)3-3

27.60

-5.08

9.20

-1.69

1.12

(NH3BH3)4-1

42.17

-7.64

10.54

-1.91

1.68

(NH3BH3)4-2

42.61

-7.83

10.65

-1.96

1.74

(NH3BH3)4-3

48.83

-10.97

12.21

-2.74

1.93

(NH3BH3)4-4

45.75

-9.14

11.44

-2.28

1.93

(NH3BH3)4-5

41.27

-5.89

10.32

-1.47

1.70

(NH3BH3)6-1

79.09

-14.13

13.18

-2.35

3.41

(NH3BH3)6-2

76.01

-15.27

12.67

-2.54

3.48

(NH3BH3)6-3

77.46

-15.96

12.91

-2.66

3.99

(NH3BH3)6-4

79.36

-16.11

13.23

-2.68

3.64

(NH3BH3)6-5

81.62

-18.24

13.60

-3.04

3.49

(NH3BH3)12-1

175.67

-37.23

14.64

-3.10

7.82

(NH3BH3)12-2

187.66

-43.67

15.64

-3.64

9.16

(NH3BH3)18

270.42

-47.91

15.02

-2.66

13.39

(NH3BH3)36

615.90

-155.91

17.11

-4.33

28.15

(NH3BH3)48

852.97

-234.66

17.77

-4.89

37.99

(NH3BH3)54

961.57

-264.10

17.81

-4.89

42.91

This strong correlation indeed suggests that the interaction energy of the cluster is largely governed by electrostatics. In recent studies, Suresh et al. have successfully used MESP Vn analysis to study non-covalent intermolecular interactions in a large variety of complexes and obtained a single linear relationship between change in Vn during complex formation (∆Vn) and the interaction energy.56,57,59 Such a relationship proposed that the stability of a complex is proportional to the amount of electron density donated from one molecule to another and the complexes are classified as electron donoracceptor (eDA) complexes. In the present case, when NH3BH3 changes from monomer state to the cluster state, significant changes in Vn of N and B atoms occur. Quantifying these changes is very easy as a Gaussian09 output for MESP calculation list the values of that property at all the nuclei. The MESP at the nucleus of N (VN) and at B (VB) of NH3BH3 is 18.3155 and -11.5222 a.u. respectively. During cluster formation, VN becomes more negative while VB becomes less negative. This indicates that the excess electron density at BH3 unit is utilized for developing non-covalent interactions with NH3 unit of other monomers. The VN and VB values of all the monomers in a cluster are determined and the change in VN (∆VN) and change in VB (∆VB) with respect to N and B nuclei of NH3BH3 monomer is calculated (ESI). Further, ∆VN and ∆VB for all the monomers in a cluster is summed up to obtain total MESP change at N nuclei (Σ∆VN) and


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Table 2. MESP parameters for ammonia borane clusters. All values in kcal/mol.

1200

Cluster

Σ∆Vmin

Σ∆VN

Σ∆VB

1000

(NH3BH3)2-1

15.31

-17.67

17.18

800

(NH3BH3)3-1

26.98

-31.11

30.08

(NH3BH3)3-2

25.60

-36.43

23.88

(NH3BH3)3-3

28.87

-28.56

29.97

(NH3BH3)4-1

39.41

-45.69

44.14

(NH3BH3)4-2

56.85

-41.76

45.29

(NH3BH3)4-3

44.68

-50.06

52.00

(NH3BH3)4-4

41.67

-49.73

48.34

(NH3BH3)4-5

46.18

-41.27

46.79

(NH3BH3)6-1

73.17

-80.69

87.38

(NH3BH3)6-2

69.15

-88.84

74.45

(NH3BH3)6-3

62.88

-92.36

78.65

(NH3BH3)6-4

83.46

-103.27

50.43

(NH3BH3)6-5

76.05

-75.83

83.80

(NH3BH3)12-1

204.57

-192.74

170.56

(NH3BH3)12-2

204.44

-187.67

183.01

(NH3BH3)18

321.16

-300.37

261.35

(NH3BH3)36

758.28

-597.40

598.88

(NH3BH3)48

1019.58

-830.74

819.29

(NH3BH3)54

1157.00

-918.14

919.14

total MESP change at B nuclei (Σ∆VB), respectively. These two quantities are presented in Table 2. It may be noted that the magnitude of Σ∆VN is almost equal to the magnitude of Σ∆VB. Further, the value of Estb (Table 1) is very close to the magnitude of Σ∆VN or Σ∆VB. In fact, a strong linear correlation between Σ∆VN and Estb as well as that between Σ∆VB and Estb exists (Figure 10). These correlations indeed suggest that the dihydrogen bonding in ammonia borane clusters is governed by the eDA interaction of the ammonia unit to the borane unit. This leads to electron dense and electron deficient hydrogen centers in borane and ammonia units, respectively which in turn promote the eDA type BH...HN dihydrogen interactions between adjacent monomers. The total energetic contribution from such interaction increases with increase in the number of interactions around a monomer. A hexamer unit taken from the 54mer cluster (Figure 11) is useful to illustrate the substantial amount of Estb observed for this cluster. The innermost monomer unit is surrounded by the side-wise interacting three monomers and end-on wise interacting two more monomers. The side-wise interactions accounts for 12 BH...HN dihydrogen bonds and the end-on wise interaction accounts for the through-space electrostatic interaction between the positive and negative ends of the monomers.

CONCLUSIONS In ammonia borane, the electron donation from the nitrogen lone pair to boron gives a formal charge +1 to nitrogen and -1 to boron leading to polarization of the charge on N-H and B-H bonds. NH3BH3 is a zwitterionic molecule and the

Estb = -1.029Σ∆VN R² = 0.997

Estb = 1.043Σ∆VB R² = 0.999

600

Estb 400 200 0 -200 -1200

-700

-200

Σ∆V Σ∆ N

300

800

1300

or Σ∆V Σ∆ B

Figure 10. Correlation between MESP based parameters and noncovalent binding energy. All values in kcal/mol.

Figure 11. A portion of 54mer structure showing the interaction of the central monomer with nearby 5 monomers.

driving force for the formation of clusters is the tendency of the molecule to undergo charge delocalization through a large number of BH...HN dihydrogen interactions. Essentially, every nitrogen lone pair in the cluster is delocalized through the coordinated B-N bonds and the dihydrogen interactions. Up to hexamer, the side-on interacting hexagonally packed cluster is the most stable due to the formation of maximum 24 BH...HN dihydrogen interactions. Two dimensional expansion of the cluster by hexagonal structures further increases the interaction energy per monomer due to the formation of more number of dihydrogen interactions per monomer than hexamer. Moreover, expansion of the cluster in the Z-direction gives layered arrangement of NH3BH3 and the through space electrostatic interactions between positive and negative ends of adjacent layers contribute further to the interaction energy. The interaction energy per monomer (Em) steadily increases from a value 7.94 kcal/mol for the dimer to 17.81 kcal/mol for 54mer which indicates strong cooperativity in the cluster growth mechanism. The gradual increase in Em and steady decrease in free energy with increase in the cluster size indicate the importance of cooperativity in dihydrogen interaction and both factors contribute to the high melting solid state character of ammonia borane. In other words, the extended network of dihydrogen



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interactions and the positive cooperativity effect support the formation of stable large assembly of ammonia borane molecules and indicates its potential use as a hydrogen storage material. MESP analysis has provided a clear-cut description of the charge delocalization in the cluster. The MESP based analysis also provides a quantitative way to interpret the charge delocalization in terms of Vmin, VB and VN. The total change observed in each of these quantities during cluster formation with respect to a free monomer is strongly linearly related with the total non-covalent interaction energy. Such correlations suggest that ammonia borane cluster formation is largely controlled by electrostatics of dihydrogen interactions.

ASSOCIATED CONTENT Supporting Information. Thermodynamic parameters, correlation plots, MESP data and coordinates of optimized geometreis are provided. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]; Ph: +91- 471-2564751; [email protected]; Ph. +91-471-2515472

Author Contributions The manuscript was written through equal contributions from all authors.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The author KPV acknowledges Director, VSSC for his support and Dr. Benny K. George, Group Director, ASCG, VSSC for fruitful discussions. This work is also supported by CSIR project CSC0129 to CHS.

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SYNOPSIS TOC (Word Style “SN_Synopsis_TOC”).

DFT studies show that cluster growth mechanism of ammonia borane is largely controlled by electrostatics of dihydrogen interactions.

TOC Graphic

13


Ammonia Borane Clusters: Energetics of Dihydrogen Bonding

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