Journal of Molecular Modeling

, 24:307 | Cite as

Improvement in hydrogen binding ability of closo-dicarboranes via functionalization and designing of extended frameworks

  • Sudip PanEmail author
  • Lili ZhaoEmail author
  • Gabriel MerinoEmail author
Original Paper
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday


Neutral closo-dicarboboranes are reported to have very low H2 binding ability. Herein, we report an improvement in H2 binding energy (Eb) of C2B4H6 by substituting H atoms with different functional groups like X = F, Cl, Br, and XY = BO, CN and NC via quantum-chemical density functional theory based computations. In going from B6H62− to C2B4H6, the Eb value is reduced from 14.6 kJ mol−1 to 2.7 kJ mol−1. C2B4X6 and C2B4(XY)6 systems, which can bind a total of eight H2 molecules, with one H2 molecule occupying at each B-B-C face, possess an Eb value per H2 in the range of 4.5 kJ mol−1 for X = F, 3.9 kJ mol−1 for X = Cl, 5.9 kJ mol−1 for X = Br, 6.8 kJ mol−1 for XY = BO, 5.8 kJ mol−1 for XY = CN and 5.2 kJ mol−1 for XY = NC. The improvement in Eb value is found to be the highest in case of C2B4(BO)6, which has the ability to bind 6.6 gravimetric wt% of H2. The situation can be made more favorable by applying an external electric field. Energy decomposition analysis reveals that although the dispersion interaction (ca. 55–65%) has significant role in binding H2 with such types of molecules, contribution from electrostatic and orbital interaction is also considerable. Further, we modeled an extended system by linking C2B4(BO)n through ‘C ≡ C’ units for H2 storage purpose. The energy difference between the highest occupied and the lowest unoccupied molecular orbitals gradually lessens with the increase in molecular length. Therefore, it can be tuned gradually by controlling the chain length, which may further open up their potency in the field of electronics.

Graphical abstract

C2B4X6 (X = F, Cl, Br) and C2B4(XY)6 (XY = BO, CN, NC) show enhanced H2 binding ability from C2B4H6. Further, 1D, 2D and 3-D frameworks can be built by joining C2B4(BO)n units via ‘C ≡ C’ linkage.


Hydrogen storage Binding energy Energy decomposition analysis HOMO-LUMO energy gap 


Hydrogen is one of the brightest names among the possible clean energy alternatives to fossil fuel [1, 2, 3]. Its abundance in nature, high energy density and the liberation of only water vapor upon combustion make it a very promising candidate for use in this field. However, the main difficulty for practical usage is storage as, being a gas at ambient temperature, hydrogen needs large volumes for storage. Use of hydrogen in liquid state is also not feasible as it requires very low temperature and high pressure, which cannot be provided in daily life. The alternative is to use hydrogen storing materials. For that purpose, all types of materials that can bind hydrogen through either chemisorption or physisorption, or a combination thereof, have been tested [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. Each system has its own advantages and disadvantages. This motivates scientists to explore new hydrogen storing templates that are better than existing ones.

Dienberg et al. [24] recently studied the possibility of hydrogen storage by physisorption on B12H122−, which was corroborated by experimental studies on Cs2B12H12. Further, Srinivasu et al. [25] combined two Li+ ions with the B6H62− system to make it electronically neutral and then studied the hydrogen-binding ability of Li centers in B6H6Li2. Even without considering the overall charge neutrality, the hydrogen storing ability of B6H6Li22− was also investigated [26]. Other metals like Mg [27, 28] and Ti [29] can also be doped or substituted in the closo-boranes, and their efficacy in binding hydrogen was tested. Therefore, there is no doubt that one can neutralize the closo-boranes with several metal ions, and that they indeed act as effective hydrogen trapping materials.

In addition to the use of metal as counterion, another approach is the replacement of two B atoms with two C atoms to make a closo-borane neutral. The starting material is now a closo-dicarborane. Gopalsamy et al. [30] showed that in going from B12H122− to CB11H12 to C2B10H12 and Al12H122− to CAl11B12 to C2Al10H12, the hydrogen binding energy decreases gradually. In fact, in C2B10H12 and C2Al10H12, the binding energy per H2 molecule becomes quite small and is only 2.4 kJ mol−1 and 1.9 kJ mol−1, respectively, in contrast to 8.8 kJ mol−1 in B12H122− and 4.4 kJ mol−1 in Al12H122− computed at the M05-2X/6–31 + G(d,p) level. Therefore, neutralization of boranes or alanes through the replacement of B by C incurs a cost in the form of H2 binding energy.

Herein, we describe our efforts to improve H2 binding energy starting with a closo-dicarborane, taking C2B4H6 [31] from the closo-dicarborane family as a case study. We note that the H2 binding energy reduces from 14.6 kJ mol−1 in B6H62− to 2.7 kJ mol−1 in C2B4H6. Now, to improve the binding energy, we substituted the H atoms of C2B4H6 by -F, -Cl, -Br, -BO, -CN and -NC groups and studied their H2 binding energy. In fact, Dreuw et al. [32, 33] adopted this technique of the substitution of H atoms by these groups to provide electronic stability to B6H62− and B4H42− systems with respect to spontaneous emission of electrons. Further, the B6X62− (X = Cl, Br, I) systems were already characterized by 11B-NMR and vibrational spectroscopy [34, 35]. However, the synthesis of B6F62− is appeared to be a difficult task due to the acidic character or strong oxidation power of the common fluorinating agents. So far, Thomsen et al. [36] reported the successful preparation of only monofluoro derivatives, [B6FH5Hfac] and [B6FH5]2−. Further study showed that [B6(CN)H5]2− and cis-[B6(CN)2H4]2− can be prepared by the reaction of B6H62− and (CN)2 [37]. Therefore, such dicarborane derivatives can indeed be prepared in the laboratory. The present results show that the improvement in H2 binding energy is 67% for F, 44% for Cl, 119% for Br, 152% for BO, 115% for CN and 93% for NC substitution with respect to that in C2B4H6. We further analyzed the nature of binding via an energy decomposition analysis (EDA) [38] and modeled extended frameworks by joining C2B4(BO)n units through a C ≡ C linkage.

Computational details

Full geometry optimizations and subsequent frequency computations of B6X62−, B6(XY)62−, their dicarborane analogues and the corresponding hydrogen bound systems were carried out at the M05-2X/6–31 + G(d,p) level [39, 40] via the Gaussian 09 program package [41]. The M05-2X functional is parameterized in such a way that it is adequate to describe the medium-range electron correlation [39]. Hence, this functional can be recommended for the study of non-covalent interactions [39, 42, 43]. For the extended systems, we reduced the basis set to 6-31G(d) due to their large sizes.

Average binding energy per H2 molecule (Eb) was calculated as follows:
$$ {E}_b=\left(1/n\right)\;\left[\;\left({E}_{C_2{B}_4{X}_6/{C}_2{B}_4{(XY)}_6}+n\;{E}_{H_2}\right)-{E}_{n{H}_2@{C}_2{B}_4{X}_6/{C}_2{B}_4{(XY)}_6}\right] $$

EDA [38] was carried out at the BLYP-D3/TZ2P//M05-2X/6–31 + G(d,p) level using the program package ADF 2013.01 [44, 45]. In EDA, the total interaction energy (ΔEint) between two fragments is divided into four energy terms, viz., the electrostatic interaction energy (ΔVelstat), Pauli repulsion energy (ΔEPauli), orbital interaction energy (ΔEorb) and dispersion interaction energy (ΔEdisp).

So, ΔEint can be expressed as
$$ \Delta {E}_{\mathrm{int}}=\Delta {E}_{\mathrm{Pauli}}+\Delta {V}_{\mathrm{elstat}}+\Delta {E}_{\mathrm{orb}}+\Delta {E}_{\mathrm{disp}} $$

This technique was reported as a very elegant tool to describe the nature of bonding in various types of systems [46, 47, 48, 49, 50, 51, 52, 53]. For further details about this method, some comprehensive reviews are recommended [54, 55].


Hydrogen storage in B6X6 2−/B6(XY)6 2− vs C2B4X6/C2B4(XY)6

Representative structures of 1,2- and 1,6- positional isomers of C2B4X6 and C2B4(XY)6 (X = F, Cl, Br and XY = BO, CN, NC) are given in Fig. 1. Except for the 1,6-C2B4F6 system, which adopts D2h symmetry, all other 1,6-analogues correspond to the D4h symmetry, whereas the geometries of all 1,2-analogues belong to the C2v point group. In all cases, the 1,6-isomers were found to be energetically more stable (by 10.3–38.0 kJ mol−1) than the corresponding 1,2-analogues. Hence, 1,6-analogues only were considered for further analysis.
Fig. 1

M05-2X/6–31 + G(d,p) structures of the 1,6- and 1,2-C2B4X6 and C2B4(XY)6 systems. The relative energies are given in kJ mol−1

Now, let us see the change in H2-binding energy in going from the dianionic boranes to the neutral dicarboranes. The corresponding values for the H2-binding energy are given in Table 1. A marked change in H2 orientation is noted in moving from dianionic to neutral species. While in the former H2 is oriented itself in an end-on fashion, in the latter H2 has a side-on orientation (see Fig. 2). The H2 molecule carries an electric quadrupole moment of 0.38 × 10−16 cm2, with positive and negative charges at two ends and at the bonding region, respectively [56]. This leads to a charge–quadrupole interaction providing an end-on orientation of H2 for the negatively charged dianion species. Note that the side-on orientation would result larger van der Waals contact than the end-on one. Therefore, for cases where the interaction is greatly supported by dispersion, they would prefer side-on orientation as in the present neutral systems.
Table 1

H2 binding energy (Eb, kJ mol−1) in single H2 bound B6X62−, B6(XY)62− and their corresponding dicarborane analogues at the M05-2X/6–31 + G(d,p) level


E b


E b





























Fig. 2

Pictorial depiction of the orientation of the single H2 molecule bound with B6X62−, B6(XY)62−, C2B4X6 and C2B4(XY)6 systems studied at the M05-2X/6–31 + G(d,p) level. X = H, F, Cl, Br and XY = BO, CN and NC

B6H62−, which is unstable with respect to spontaneous dissociation of electrons, binds H2 with a large binding energy, Eb, of 14.6 kJ mol−1, which diminishes to 2.7 kJ mol−1 in C2B4H6. B6F62− also possesses quite a high Eb value of 12.5 kJ mol−1. In moving from B6F62− to C2B4F6, the Eb value reduces less than that in B6H62−. The other dianions are reported to be stable against dissociation of electrons. B6Cl62− and B6Br62− bind H2 with Eb values of 8.3 kJ mol−1 and 9.2 kJ mol−1, respectively, which drops by almost 50% in neutral analogues. The B6(XY)62− species have lower H2 binding ability with Eb value of 4.9–6.1 kcal mol−1 lower than their halogen congeners. There are also no marked changes in H2 binding ability in moving from the dianionic species to the corresponding dicarboranes. Therefore, from these results it is obvious that by substituting H with these functional groups, H2 binding ability improves.

Now, since there are eight such B-B-C faces, we extended our study to the maximum limit of H2 molecules bound in such fashion in dicarborane derivatives. Figure 3 depicts the structures of 8H2 bound systems, and the related results are tabulated in Table 2. For the results of intermediate systems, please see supporting information (Figs. S1, S2 and Tables S1S6). The average distance from the center of the B-B-C face and the H2 molecule gradually increases from F to Br because of the larger sized substitutent. Still quite comparable Eb values suggest that the interaction occurs mainly with the substitutent, not with the B-B-C moiety, and the H2 takes this position to enhance the stability by making interaction with maximum number of substitutents. On the other hand, in BO, CN or NC substituted systems, this distance is quite comparable.
Fig. 3

M05-2X/6–31 + G(d,p) structure of 8H2@C2B4X6 and 8H2@C2B4(XY)6 (where X = F, Cl, Br; XY = BO, CN, NC)

Table 2

Average binding energy per H2 molecule (Eb, kJ mol−1), HOMO–LUMO energy gap (ΔH-L, eV) and the range of the distances from the center of B-B-C face and bound H2 (r(H2), Å) of the C2B4X6 and C2B4(XY)6 systems and their 8H2-bound analogues studied at the M05-2X/6–31 + G(d,p) level


E b



















































Each H2 molecule interacts with the C2B4X6, having an average Eb value of 4.5 (F), 3.9 (Cl) and 5.9 (Br) kJ mol−1, whereas with C2B4(XY)6, the same becomes 6.8 (BO), 5.8 (CN) and 5.2 (NC) kJ mol−1. Note that there is no marked fluctuation in Eb value per H2 molecule upon gradual cluster growth from 1H2 to 8H2 bound systems (except for C2B4Br6, where, for the first H2 molecule, the corresponding Eb value is slightly lower). This might be because the interaction is supported mainly by the van der Waals interaction and, for a given system, the degree of van der Waals contact at each B-B-C face would be similar (vide infra). Therefore, in comparison to that in C2B4H6, an improvement in H2 binding energy by 67% for F, 44% for Cl, 119% for Br, 152% for BO, 115% for CN and 93% for NC can be attained because of the substitution and the maximum improvement is noted for C2B4(BO)6.

The gravimetric wt% of H2 in 8H2@C2B4X6 or 8H2@C2B4(XY)6 was found to be 8.2 for X = F, 5.4 for X = Cl, 2.9 for X = Br, 6.6 for XY = BO, and 6.7 for XY = CN and NC. Therefore, in terms of gravimetric wt% of H2, B4C2F6 is the best candidate among the other systems; however, in terms of H2 binding ability, C2B4(BO)6 is preferable.

The energy gap (ΔH–L) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) represents the stability and reactivity of a system, as a large ΔH–L value indicates that the systems neither easily accept an electron in the LUMO nor easily donate an electron from the HOMO. This is also connected with the maximum hardness principle [57, 58]. The parent moieties in the present cases possess quite high ΔH-L values (7.59–8.80 eV), reflecting their high stability. Remarkably, there were no notable changes in ΔH-L values upon H2 binding.

Further, we checked the effect of external electric field in improving H2 binding ability, taking 1H2@C2B4(BO)6 as an example. Previously, Zhou et al. [59] reported improvement in the hydrogen storage properties of easily polarizable substrates upon application of an electric field. Thereafter, Sun et al. [60] also adopted this technique to enhance the H2 binding ability of mesoporous metal oxides. This method also turned out to be successful in strengthening the bond with a noble gas [61, 62]. Since the H2 molecule in the considered system is placed toward the x-axis, we applied the electric field along that direction. The corresponding Eb value becomes 7.4 kJ mol−1 at 0.001 au, 9.0 kJ mol−1 at 0.002 au, and, finally, 11.1 kJ mol−1 at 0.004 au. Therefore, from these results, it is obvious that an external electric field would be helpful in enhancing H2 storing ability in the systems studied here. This can also be used to control the adsorption–desorption kinetics.

Energy decomposition analysis

We performed EDA on 1H2@C2B4X6 and 1H2@C2B4(XY)6, taking H2 as one fragment and C2B4X6 or C2B4(XY)6 as another at the BLYP-D3/TZ2P//M05-2X/6–31 + G(d,p) level (see Table 3). There were some differences (both in magnitude and in trend) between the ΔEint values obtained compared with the Eb values, particularly in the case of C2B4X6. This is because of the different functionals used in EDA computations, as the M05-2X functional cannot be coupled with –D3 correction to get the dispersion contribution in ADF. Nevertheless, the present results provide, at least qualitatively, the nature of interaction therein. Moreover, similar to Eb, C2B4(BO)6 carries the largest ΔEint value among the systems tested.
Table 3

Energy decomposition analysis (EDA) results of 1H2@C2B4X6 and 1H2@C2B4(XY)6 systems studied at the BLYP-D3/TZ2P//M05-2X/6–31 + G(d,p) level. All energy terms are in kJ mol−1









H2 + C2B4F6



−3.1 (28.9%)

−1.4 (13.4%)

−6.1 (57.7%)


H2 + C2B4Cl6



−2.6 (23.0%)

−1.3 (11.9%)

−7.4 (65.0%)


H2 + C2B4Br6



−3.2 (22.3%)

−2.1 (14.7%)

−9.0 (63.1%)


H2 + C2B4(BO)6



−4.3 (23.7%)

−3.8 (21.0%)

−10.1 (55.3%)


H2 + C2B4(CN)6



−4.0 (25.0%)

−2.7 (16.6%)

−9.4 (58.4%)


H2 + C2B4(NC)6



−3.8 (24.3%)

−2.0 (12.4%)

−10.0 (63.3%)

aPercentage values in parentheses show the contribution toward the total attractive interaction, ΔVelstat + ΔEorb + ΔEdisp

Most importantly, the interaction is not noted to be exclusively van der Waals in nature; rather, the ΔEdisp term accounts for 55–65% of the total attraction. The remaining attractive part originated from ΔVelstat (ca. 22–29%) and ΔEorb (ca. 12–21%). In other words, EDA shows that, although the dispersion interaction plays the most significant role in stabilizing such hydrogen loaded complexes, essentially reflecting the physisorption nature of the interaction, the contributions from electrostatic and orbital interactions are also not negligible. It may be noted that, in moving from C2B4X6 (except Br) to C2B4(XY)6, all the attractive energy terms increase; however, the Pauli repulsion is also greater in the latter cases than in the former, which nullifies part of the attractive privilege.

Modeling of the extended frameworks

Next, we modeled long extended frameworks by linking C2B4(BO)n units via ‘C ≡ C’ linkers. In this way, we designed a long chain of 1-D, 2-D and 3-D frameworks as depicted in Fig. 4. Their existence at the minima on the PES is also verified by harmonic frequency calculations. Note that here we have provided only the results of C2B4(BO)n. But with other C2B4Xn and C2B4(XY)n units, similar types of structures are also turned out as minima on PES. In addition to the outside surface, similar to the covalent organic frameworks [11, 12] the inner porous region of the 3-D frameworks may be suitable for H2 storage. In addition, based on these repeating units, one can modify these frameworks by introducing other cross-linkers as well. We further computed the variation in ΔH-L with the change in chain length for their probable utility as semiconductors. Note that ΔH-L is also roughly called bandgap as HOMO and LUMO are analogous to the valence and conduction bands of a material at solid state, respectively. The ΔH-L value in C2B4(BO)6 is 8.80 eV, but this value is found to decrease gradually with the increase in chain length. For example, in the 1-D chain given in Fig. S3, the ΔH-L values of structures 2, 3, 4 and 5 are 7.45, 6.94, 6.70 and 6.58 eV, respectively, whereas, in the case of the 2-D and 3-D frameworks given in Figs. S4 and S5, they range within 6.84–6.23 eV and 6.47–5.90 eV, respectively, with a gradual decrease with increasing chain length.
Fig. 4

Minimum energy structures of the n-D frameworks (n = 1, 2, 3) designed by joining C2B4(BO)n units via ‘C ≡ C’ linkage studied at the M05-2X/6-31G(d) level

A similar trend is also noted for other systems as well. So, one may tune the HOMO–LUMO energy gap just by changing the degree of chain length. The ΔH-L value for a large framework may eventually fall within the bandgap range of 2–4 eV to act as wide bandgap semiconductor [61]. Therefore, the present systems might show effective H2 storing ability as well as interesting optical properties, including semiconductor properties.


By substituting the –H of C2B4H6 by X = F, Cl, Br, and XY = BO, CN and NC, one can enhance the H2 binding ability of these compounds. The corresponding binding energy per H2 molecule can be increased from 2.7 kJ mol−1 in C2B4H6 to 4.5 kJ mol−1 for X = F, 3.9 kJ mol−1 for X = Cl, 5.9 kJ mol−1for X = Br, 6.8 kJ mol−1 for XY = BO, 5.8 kJ mol−1 for XY = CN and 5.2 kJ mol−1 for XY = NC. Each H2 molecules is located at each B-B-C face, and, therefore, a total of eight H2 molecules can be bound in such a manner. While in terms of gravimetric wt% of H2, B4C2F6 is the best candidate, C2B4(BO)6 would be preferable in terms of H2 binding ability. Further, H2 binding energy can be improved by applying an external electric field. EDA shows that, although the dispersion interaction (ca. 55–65%) plays a significant role in binding H2, electrostatic and orbital interactions are also important. We further designed n-D (n = 1, 2, 3) systems by joining C2B4(BO)n through ‘C ≡ C’ linkers; these can be used for H2 storage purposes. They might also have interesting optical and semiconducting properties, since the HOMO–LUMO energy gap gradually decreases with increasing chain length. Therefore, apart from metal decoration, the present results provide alternative ways to improve the H2 binding ability of carboranes in an experimentally realistic way.



SP thanks Nanjing Tech University for the postdoctoral fellowship and the High Performance Computing Center of Nanjing Tech University for supporting the computational resources. LZ acknowledges financial support from the Natural Science Foundation of Jiangsu Province (Grant no: BK20170964), the National Natural Science Foundation of China (grant no. 21703099), and a SICAM Fellowship from Jiangsu National Synergetic Innovation Center for Advanced Materials. The work in Mexico was supported by Conacyt (grant CB-2015-252356).

Supplementary material

894_2018_3827_MOESM1_ESM.docx (3 mb)
ESM 1 (DOCX 3083 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced MaterialsNanjing Tech UniversityNanjingChina
  2. 2.Departamento de Física AplicadaCentro de Investigación y de Estudios Avanzados, Unidad MéridaMéridaMexico

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