The hydrogen storage potential of magnesium and calcium cages (Mg _n and Ca _n ; n = 8–10) along with that of trigonal alkali-metal cationic clusters (Li₃ ⁺ and Na₃ ⁺) were explored by Giri et al. (2011a) with a CDFT approach. The stability of 1H₂-trapped Mg _n and Ca _n complexes increases with increase in n. It is, however, interesting to discover that these bare cages could not be stabilized i.e., before trapping the H₂ molecule within them. Again, in the cases of H₂-bound Li₃ ⁺ and Na₃ ⁺ systems, the stability is found to increase with the increase in the number of bound H₂ molecules. Upon binding with the clusters, most of the H₂ retains their molecular identity, except in a few of the nH₂Li₃ ⁺ systems where one of the H₂ molecules dissociates and binds itself in the atomic form. This behaviour is also observed in the case of H₂-trapped Ca₁₀ cage (Figure 1). The planarity of the Li₃ ⁺ and Na₃ ⁺ clusters remained intact in the H₂-bound complexes. Further analysis of the changes in the CDFT based reactivity indices, viz., electronegativity (χ) hardness (η) and electrophilicity (ω), revealed a gradual decrease in the ω values with an increase in the number of H₂ molecules.

The NICS (0, 1) values calculated for the top and bottom M₄ rings (M = Mg, Ca) of the H₂-encapsulated Mg _n and Ca _n cages are found to be negative, indicating the existence of diatropic ring current at the said positions. Similarly, negative NICS_zz (0) values for the poly-hydrogenated trigonal clusters also established the aromatic stability with gradual H₂ uptake. Further, from a thermodynamic point of view, the negative values of the reaction energy (∆E _b, kcal/mol) for the sequential H₂ binding on the Li₃ ⁺ and Na₃ ⁺ systems provide some theoretical justification towards their possible usage as hydrogen storage materials (Table 1).

The aromaticity of all-metal Al₄ ²⁻ system was previously reported (both theoretically and experimentally) (Li et al., 2001), followed by that of Be₃ ²⁻ and Mg₃ ²⁻ systems (Kuznetsov and Boldyrev, 2004; Roy and Chattaraj, 2008; Giri et al., 2010). All these systems owe their aromatic behaviour to the presence of delocalized π-electrons. The motivation for using these systems with the alkali metal counterion M⁺ (M = Li, Na, and K) (Srinivasu et al., 2012) is backed by the logic that due to high polarization, the M centers will be highly electropositive and hence can serve as a suitable site for hydrogen adsorption. The optimized geometries of the systems under study are provided in Figure 2, and their hydrogen adsorbed structures are depicted in Figure 3. The positive charges carried by the M centers were found to be proportional to the difference in electronegativity values between the two types of metal species in the complex. This difference is lower in Mg₃M₂ as compared to that in Be₃M₂ and Al₄M₂, which causes a lower charge transfer from M to the Mg₃ ring compared to the others. This, in turn, results in poor H₂ adsorption in the Mg₃M₂ complexes (interaction energy of −0.5 kcal/mol per H₂, compared to the same ranging between −1.8 to −3.1 and −2.7 to −3.2 kcal/mol per H₂ for Be₃M₂ and Al₄M₂, respectively). Now, from the perspective of the alkali metals, a high ionic radius and low charge density (i.e., low ionic potential) on the potassium atom results in a very weak interaction with the K atom containing systems (as low as −0.6 kcal/mol per H₂). Both Be₃Li₂ and Be₃Na₂ are found to adsorb six hydrogen molecules each (three per alkali metal atom), whereas Al₄Li₂ and Al₄Na₂ are capable of binding eight molecules each (four H₂ per alkali metal atom). The gravimetric weight percentage of hydrogen adsorption for the former two are 22.64 and 14.12, those for Al₄Li₂ and Al₄Na₂ are 11.59 and 9.4, respectively. Evidently, Be₃Li₂ is preferred to Al₄Li₂ in terms of the gravimetric density, whereas with respect to the binding energy per H₂ molecule, Al₄Li₂ is preferred as a better hydrogen storage material.

The stability of these hydrogenated systems is established in terms of higher energy gaps (5.17–6.40 eV) between their respective HOMO and LUMO. The variation in total energy (E), χ, η, and ω also serve as good descriptors for judging the reactivity and stability of the molecular species. A uniform decrease in E, and decrease in ω values with increasing H₂ adsorption describes the stabilization of the metal clusters upon hydrogenation. η also shows a gradual increase in most of the cases. The aromaticity of Be₃M₂ and its hydrogenated species calculated in terms of NICS values at 0, 0.5, and 1 are highly negative and show very low variation with the number of H₂ molecules loaded. For the Al₄M₂ cluster, however, most of the NICS values are found to be positive, even though it is an established fact that the Al₄ ²⁻ species has aromatic stability. The variation of aromaticity with the number of adsorbed H₂ molecule is also found to be quite random and significantly high. Clearly, NICS is not a good indicator for the Al₄M₂ clusters.

Several non-metallic aromatic/anti-aromatic clusters are also explored to understand the influence of aromaticity on their hydrogen adsorbing or trapping potential. Replacing the H atoms from planar hydrocarbon rings like C₄H₄, C₅H₅ ⁻, and C₆H₆ with Li atoms results in the formation of star-shaped molecular clusters since the Li atoms prefer to bind two adjacent C atoms via a bridging bond (Figure 4) (Giri et al., 2011c). The partial positive charges on the Li centers enable them to readily adsorb H₂ molecules. Each Li atom in C₅Li₅ ⁻ can efficiently bind with only one H₂ (binding energy of −2.1 kcal/mol per H₂), whereas those in the neutral clusters (i.e., in C₄Li₄ and C₆Li₆) can bind up to two H₂ molecules with binding energies ranging within −2.5 to −3.3 kcal/mol per H₂. A thorough analysis of the NICS-scan (0–5 Å) plots (Figure 5) for each of the studied species provides useful information regarding the variation in the degree of aromaticity/anti-aromaticity with gradual hydrogen loading. The antiaromatic nature of C₄H₄ is found to be enhanced in its lithium analogue. It further increases in the 4H₂@C₄Li₄ system, followed by a decrease in 8H₂@C₄Li₄ where the NICS (0) value falls below those of the parent moieties (Figure 5A). Since the C₄Li₄ species is more likely to exist in the 8H₂-bound form, it can be arguably stated that hydrogen adsorption on C₄Li₄ reduces its antiaromatic nature, which is favourable in terms of explaining the stability of these clusters. In the case of the aromatic C₅H₅ ⁻ ring, lithiation increases its aromatic nature as evident from Figure 5B. The 5H₂-bound C₅Li₅ ⁻ complex follows the same trend as the parent moieties while moving from NICS (4) to NICS (1), i.e., they gradually decrease with decreasing distance from the ring center. However, unlike the parent moieties, 5H₂@C₅Li₅ ⁻ shows an unexpected rise in NICS (0) value rendering it anti-aromatic. Again, unlike in C₅-species, the aromaticity reduces in the lithium analogue of C₆H₆ complex. Although all the species maintain their aromatic behaviour, the degree of aromaticity initially decreases with hydrogen loading (i.e., in 6H₂@C₆H₆) with a final increase in the 12H₂@C₆H₆ species (Figure 5C). These plots provide ample evidence regarding the dominant π-ring current in the C₆ species compared to that in the C₅ complexes, which results in an enhanced H₂-trapping ability in the former.

The H₂ binding ability of a series of lithium ion complexed hydrocarbons (Li⁺ above and below the planar ring), viz., C₆H₆, C₁₀H₈, and C₁₄H₁₀ are explored in the same study (Giri et al., 2011c), along with that of an F⁻ ion stabilized tropylium complex. Each Li atom in these systems can store up to four H₂ molecules (Figure 6A). The same is true for the C₇H₇F system, even though, unlike the Li⁺-complexed hydrocarbons, C₇H₇ ⁺ loses its planarity and hence aromaticity on complexation with F⁻. Other 3D molecular star-like systems like C₅Li₇ ⁺ (π-aromatic and σ-nonaromatic) and its Si analogue (σ- and π-aromatic) can bind up to a maximum of 21 H₂ molecules (three per Li center) with a gravimetric wt% of 28.0 and 18.3, respectively (Pan et al., 2012; Perez-peralta et al., 2011; Tiznado et al.,2009) (Figure 6B). The Ge analogue has a maximum capacity of 19 H₂ molecules with 9.3 wt% of H₂ (Contreras et al., 2013). It is a well-known fact that temperature and pressure can act as tuning parameters in various adsorption/desorption processes. An interesting study performed on a series of Li clusters (BLi₆ ⁺, O₂Li₅ ⁺, N₂Li₇ ⁺, B₂Li₁₁ ⁺, OLi₃ ⁺, C₂Li₉ ⁺, F₂Li₃ ⁺, and FLi₂ ⁺) was reported by Pan et al. (2012) where they have achieved enhanced interaction between Li and H₂ by applying an external electric field. By gradually varying the field in the range 0.001–0.005 au, the negative ∆E value increases indicating improved interaction.

A discussion on hydrogen storage warrants the inclusion of boron hydrides. Metal borohydrides like LiBH₄ and NaBH₄ are reported to be good hydrogen storage materials (Kojima et al., 2002; Züttel et al., 2003; Liang et al., 2010). The effect of aromaticity on the structural preference of both neutral and ionic boron hydrides with the general formula B₃H _n (n = 3–9) was reported by Korkin et al. (1995). A similar study (Bandaru et al., 2012) was performed on several boron-lithium complexes with the general formula B _x Li _y (x = 2–6; y = 1, 2) where the cationic species show a higher H₂ binding capacity than their neutral counterparts owing to the greater net positive charge on the Li centers in the former. Among various boron hydrides, B₃H₃ ²⁻ can be considered as the iso-electronic boron-analogue of the aromatic cyclopropenium ion (Garratt, 1986; Minkin et al., 1994). A theoretical study on B₃H₃ ²⁻ and its various Li doped species performed by Pan et al. (2011) investigates the H₂ storage process via an interaction that lies somewhere between physisorption and chemisorption. The aromaticity of these systems is evident from the negative values of NICS (0) (ranging within −3.32–−29.38) and NICS (1) (varies from −7.48 to −17.91). The parent moiety itself is capable of adsorbing a maximum of 11 H₂ molecules. Here, the importance of the dispersion interaction is clearly reflected from the interaction energy values obtained before and after including the dispersion corrected terms in the theoretical calculations. For example, the interaction energy per H₂ molecule in the maximum H₂-loaded systems ranges within −1.2–−1.9 kcal/mol, which changes to a range of −2.6–−5.6 kcal/mol after dispersion correction. Although judging by parameters like the H₂ binding capacity, and gravimetric wt% of H₂, the B₃H₃ ^2- system seems to be a preferable choice, it is yet to be experimentally realized. In that regard, B₃ (μ-Li)₃H₃ ⁺ species is a better alternative with high aromatic stability. The H₂ molecules are mostly bound by weak interaction and most of the adsorption process shown here is energonic in nature. Thus an optimal condition for these processes to be feasible would be that of high pressure (P) and low temperature (T). A T-P phase diagram (Figure 7) for the adsorption of 6 H₂ molecules on B₃ (μ-Li)₃H₃ ⁺ depicts the variation of free energy change with the change in T and P, where black markers indicate regions of favourable adsorption and red markers indicate that of favourable desorption.

A study (Duley et al., 2011) reported on the aromaticity and hydrogen storage in the inorganic analogues of cyclobutadiene and benzene rings, i.e., N₄ ²⁻ and N₆ ⁴⁻ reveals the anti-aromatic and aromatic natures, respectively. The NICS-scan plots of all four systems are provided in Figure 8 where it can be clearly seen that the NICS variation of N₆ ²⁻ follows a similar trend as that of the benzene, whereas this is not the case for N₄ ²⁻ and cyclobutadiene. The otherwise antiaromatic N₄ ²⁻ ring shows aromaticity at a distance of 1 Å above the molecular plane, and gradually decreases away from the ring. Thus, a positive NICS (0) value and a negative NICS (1) value makes it σ-antiaromatic and π-aromatic. These anionic clusters are stabilized by complexation with lithium and calcium counterions to form N₄Li₂ and N₆Ca₂ (optimized structures provided in Figure 9). Each Li center is found to bind with up to four H₂ (∆E = −1.2 kcal/mol) and each Ca center adsorbs up to six H₂ molecules (∆E = −1.3 kcal/mol).

C₁₂N₁₂ cage can have three possible isomers, viz., C₁₂N₁₂-A, C₁₂N₁₂-B, and C₁₂N₁₂-C with the optimized structures having D_6d, C₃, and C₂ point group symmetries, respectively (Figure 10A) (Mondal et al., 2013). Unlike isomers A and B, C is an open cage structure and hence is the most stable of the lot. Although the NICS (0) for all the isomers are found to be negative, isomers A and B do not obey the Spherical Aromaticity rule [2(N+1)² π-electrons], and isomer C does not follow the Open-Shell Spherical Aromaticity rule [(2N² + 2N + 1) π-electrons]. Although, the hydrogen may be expected to bind at three possible sites: N, C, and bridging C and N, the minimum energy structures are obtained only for the N-site adsorption. All the isomers are capable to bind 12 H₂ molecules providing a gravimetric wt% of 7.2 (Figure 10B). These clusters can have potential applications as high energy density materials (HEDMs) since they have high heat of formation values (∆H ⁰ _f ). These ∆H ⁰ _f values (1747.759, 1758.442, and 1813.864 kcal/mol for isomers A, B, and C, respectively) are calculated using the following isodesmic reaction: C 12 N 12 + 12 H 2 C = C H 2 + 3 N H 3 → 9 C 4 H 4 N H + 3 H 2 N − N H 2

The Ni-decorated analogue (Jana et al., 2020) of the cage can have three possible binding modes: bridging between C and N (denoted as X_CN isomer), between 2 C atoms (X_CC isomer), or between 2 N atoms (X_NN isomer) (Figure 11A). Higher numbers of Ni decoration (up to four) in the N-(μ-Ni)-N bridging mode reveals the variation in aromaticity and H₂-binding potential with the number of Ni atoms (Figure 11B). The reason for selecting N-(μ-Ni)-N bridging mode for this purpose is the highest amount of positive charge on the Ni center of the X_NN isomer. The isodesmic reactions used to determine the ∆H ⁰ _f of Ni-C₁₂N₁₂ (4,239.470 kcal/mol) and 4Ni-C₁₂N₁₂ (4,520.528 kcal/mol) are as follows: N i - C 12 N 12 + 12 H 2 C = C H 2 + 3 N H 3 → 9 C 4 H 4 N H + 3 H 2 N − N H 2 + N i 4 N i - C 12 N 12 + 12 H 2 C = C H 2 + 3 N H 3 → 9 C 4 H 4 N H + 3 H 2 N − N H 2 + 4 N i

Each Ni center on C₁₂N₁₂ is capable to adsorb up to three H₂ molecules (Figure 11C). In the single Ni-doped clusters, the aromaticity increases in the order X_CN < X_CC < X_NN, and in the case of multiple Ni-doping, the aromaticity increases uniformly with the number of Ni atoms.

The boron analogue of the C₁₂N₁₂ cage, i.e., B₁₂N₁₂ can trap hydrogen both endohedrally and exohedrally (Giri et al., 2011b). A total of 12 hydrogen molecules can be adsorbed in this cage system, the interaction energy per H₂ molecule varies from −11.5 to −12 kcal/mol. The change in the reactivity descriptors with the gradual hydrogen uptake validates the CDFT based electronic structure principles. The aromaticity in terms of NICS (0) values of all the nH₂@B₁₂N₁₂ (n = 0–12) species are plotted and presented in Figure 12. It is evident that among all the hydrogen-loaded species, the four, eight, and twelve numbers of H₂ loaded clusters have high aromatic stability.

In this report, we have described the influence of aromatic behaviour on the H₂ trapping potential of various all-metal and nonmetal systems where it is measured in terms of nucleus independent chemical shift (NICS) values. The effect of aromaticity is not uniform throughout all systems. In some systems, the variation of aromaticity with the number of adsorbed H₂ molecule is quite uniform and systemic, like in the cases of C₄Li₄, C₅Li₅ ⁻, and C₆Li₆ rings, N₄ ²⁻ and N₆ ⁴⁻ rings, the nNi-decorated C₁₂N₁₂ clusters. While for others, like that in the Al₄M₂ clusters, it is found to be quite random and significantly high. It deserves a careful scrutiny.