Molecular hydrogen binding affinities of metal cation decorated substituted benzene systems: insight from computational exploration

Abstract

The binding affinity of hydrogen molecules towards Li⁺ and Mg²⁺ decorated C₆H₅X (X = −CH₃, −NH₂, −CN, −COOH) systems has been investigated theoretically with special emphasis on the nature of the interaction between metal cations and H₂ molecules. Our calculations show that binding of H₂ over C₆H₅X−M (where M = Li⁺, Mg²⁺) is improved on moving from Li⁺ to Mg²⁺. For both C₆H₅X−M complexes the electron donating substituents weaken the H₂ binding energy considerably whereas electron withdrawing substituents slightly strengthen the interaction relative to the C₆H₆−M complex. The interaction of H₂ molecules with the metal centers in Li⁺ and Mg²⁺ decorated C₆H₅X systems has been explored in the light of AIM formalism, NBO analysis and LMOEDA analysis. The polarization and the charge transfer together stabilize the system whereas the pairwise steric exchange interaction renders destabilization of the system. In the case of Mg²⁺ decorated systems, the amount of charge transfer from the bonding orbital of the hydrogen molecule to the antibonding lone pair orbital of the metal cation and thereby the polarization factor is much higher than that found in corresponding Li⁺ decorated systems.

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1. Introduction

Use of hydrogen as a practical fuel in the transportation sector is one of the challenging issues because of its safe and efficient storage related difficulties. Extensive efforts are in progress for designing materials with high hydrogen adsorption/desorption characteristics under ambient conditions. Whereas a very weak interaction would lead to lower H₂ sorption at reasonable temperature, a very strong interaction, on the other hand, might be irreversible or require extreme conditions to release H₂.¹ A quasi-molecular type of binding which is intermediate between physisorption and chemisorption is ideal for hydrogen storage under ambient temperatures and pressures.²

Microporous metal organic frameworks (MOFs) are one of the most promising class of hydrogen storage materials because their extremely high surface area helps in reversible H₂ uptake and release and also in fast H₂ desorption kinetics.^3–11 The two main adsorptive sites for H₂ on the MOF are the metal oxide center and the organic linker unit. This phenomena is proved by both experimental^5,12,13 and various theoretical studies.^11,14–17 The more positive H₂ binding energy, the stronger hydrogen is bound. The strength of the H₂ binding interaction should be in the range of ∼5–10 kcal mol⁻¹ for reversible sorption and desorption of H₂ at room temperature and at moderate pressures.¹ This range of interaction may not be achievable by choosing only the neutral surface. There are number of ways through which the binding energy of H₂ to MOFs can be increased. Dopants directly enhance the hydrogen binding energy of the carbon substrate, and in addition they can act as H₂ binding centers. Because of the weak van der Waals interaction between H₂ and the carbon support, the binding of hydrogen is very weak. To increase the binding, addition of electrostatic interaction is required and in order to cause this charging, the carbon systems could be doped with highly electropositive Group I and Group II metals. Alkali metal doping onto the organic linker part of MOFs and on carbon based systems have been studied widely and they are proved to be good candidates for this purpose. Han et al. first proposed Li-doped MOFs as a practical hydrogen storage material using an ab initio based GCMC simulation.¹⁸ Lochan et al. in their computational study established that strong H₂ sorption site can be obtained in MOFs by incorporating open transition metal sites (Cr, Mo, V⁻, Mn⁺) on the organic linkers.¹⁹ Using DFT calculation Blomqvist et al. showed significant H₂ adsorption properties of Li-decorated MOF-5.²⁰ Mavrandonakis et al. showed that Li atom is preferably located on the organic linker part rather than the metal oxide part of MOF.²¹ However, Dalach and coworkers reported that in Zn₂-based MOFs, the Li associates strongly with the metal oxide part and less with the organic linker part.²² In another theoretical work, Kolmann et al. investigated the interaction of one, two and three hydrogen molecules with Li⁺-doped benzene which acts as a model for lithium-doped carbon-based and metal organic framework materials.²³ The interaction of hydrogen molecules with alkali and alkaline earth metal cations (Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, Ca²⁺) in MH₁₆ complexes was studied by Chandrakumar et al.²⁴ By detailed energy decomposition analysis (EDA), they showed that both the electrostatic and charge transfer components play significant role in stabilizing those complexes. The polarization component also contributes significantly to the binding energy. In our earlier works we investigated the nature of interaction of different cation−H₂ complexes by using symmetry adapted perturbation theory (SAPT).^25,26 Srinivasu et al. in their work studied the effect of electron donating and electron withdrawing groups on hydrogen adsorption energy of Li⁺ doped and Na⁺ doped benzene ring respectively.²⁷ They also concluded that ionic surface with a significant curvature would enhance the hydrogen adsorption significantly. In another work they further investigated the H₂ adsorption properties of Na-doped C_nH_n systems (n = 4–6, 8).²⁸ The effect of metal ions (Li⁺, Na⁺, Be²⁺, Mg²⁺ and Al³⁺) on hydrogen adsorption of benzene system was studied by Maark et al.²⁹ The authors showed that Mg²⁺ ion-decorated MOF-5 has the most suitable binding energy for the practical H₂ storage applications in comparison to other metal cations. Bodrenko et al. studied the hydrogen storage capacity in alkali and alkaline-earth metal decorated aromatic carbon ring based molecular materials.³⁰ In a very recent work of Huang et al., the authors showed that alkali metal cation decorated carbon based molecular complexes with B- and N-substitution enhances the hydrogen storage capacity.³¹

In the present work, we have explored the viability of improving H₂ binding energy by incorporating open metal sites over the organic linkers of MOF and on the carbon based nanomaterials. For this purpose we have used two metal cations, one is from alkali metal family (Li⁺) and the other one is from alkaline earth metal family (Mg²⁺). Inspired by the work of Maark et al., as discussed earlier, we choose C₆H₆–Mg²⁺ complex, where the benzene moiety acts as a model representing doped BDC linker of MOF-5 and doped polyaromatic carbon-based materials. We have also investigated how different substituents alter the interaction when several electron donating (−CH₃, −NH₂) and electron withdrawing (−CN, −COOH) groups are introduced in the benzene system. A comparative study between ab initio and different DFT functionals with various basis sets to determine the most appropriate density functional to describe H₂ binding energy on the Li⁺ and Mg²⁺ decorated benzene and substituted benzene systems has been carried out. The most appropriate density functional, B2PLYPD in conjunction with 6-311+G(d,p) basis set is then used to investigate the binding energies for multiple hydrogen molecules. The interaction between the metal cation and hydrogen molecules is further studied critically employing natural bond orbital (NBO) analysis, topological analysis of charge density and localized molecular orbital energy decomposition analysis (LMOEDA).

2. Computational details

All electronic structure and frequency calculations, NBO analysis are performed using Gaussian 09,³² suite of quantum chemistry program. The DFT functionals considered for the systems under investigation are namely B3LYP,^33,34 and B2PLYPD.^35,36 Whereas hybrid B3LYP exchange correlation functional is the most widely used density functional, Grimme's dispersion corrected density functional B2PLYPD is known to work well for systems containing long range dispersion interactions. The double hybrid density functional B2PLYPD includes a second-order perturbation correction for nonlocal correlation effect which is comparable to the replacement of semi-local GGA exchange by the exact Hartree–Fock (HF) exchange, as in conventional hybrid functionals. The extension “D” stands for the long range dispersion-corrections that represent the van der Waals interaction. In order to provide benchmark results for comparison, we have also performed ab initio second-order Moller–Plesset perturbation theory (MP2)^37–39 calculation.

All the ab initio and DFT calculations associated with the binding of one H₂ molecule on the C₆H₆−M and C₆H₅X−M complexes are carried out using Pople's 6-31G(d),⁴⁰ 6-311+G(d,p),^41,42 basis sets and Ahlrichs' TZVP triple-ζ basis set.⁴³ The adsorption of multiple H₂ molecules over these systems has been analyzed by only B2PLYPD functional in conjunction with 6-311+G(d,p) basis set as this level of calculation is expected to provide most promising results as proposed by Grimme and co-workers.^35,36 The binding energy (ΔBE) of molecular hydrogen to the system is calculated from the energy difference between the H₂ bonded complex, i.e., C₆H₅X−M with adsorbed hydrogen molecules and the monomers (C₆H₅X−M and relevant number of hydrogen molecules). The effect of basis-set superposition error (BSSE) has been estimated by the counterpoise (CP) procedure.⁴⁴ Charge on the metal cation has been obtained at B2PLYPD level by applying natural population analysis (NPA). To assess the feasibility of adding hydrogen molecules one by one on the Li⁺ decorated system, we have calculated the incremental first-order energy difference by using the following equation

Δ₁E(n) = E[(C₆H₅X–Li⁺)(H₂)_n] − E[(C₆H₅X–Li⁺)(H₂)_n−1] − E[H₂]

The above equation is also applicable for Mg²⁺ containing systems.

The nature of interaction between the metal cation and hydrogen molecule of each optimized structure is calculated using the topological analysis of atoms in molecule formalism employing AIMAll program.⁴⁵ For evaluating the strength of this interaction, two important parameters, namely electron density (ρ) and its Laplacian (∇²ρ) at the bond critical point (BCP) are calculated. In order to get a more vivid depiction about the nature of this type of bonding, we have employed natural bond orbital (NBO) analysis by using NBO 6.0 program,⁴⁶ which is implemented in Gaussians 09. The donor–acceptor (bond–antibond) charge transfer interaction,^47–49 say i → j, is evaluated by the delocalization correction energy (ΔE_CT) calculated using second-order perturbation theory

In the above equation, F(i, j) is the off-diagonal Fock matrix element expressed in the NBO basis, q_i is the donor orbital occupancy and ε_i and ε_j are the respective orbital energies.

The steric calculations are carried out using Badenhoop–Weinhold procedure,^50–52 implemented in NBO 6.0. The pairwise steric exchange interactions between H₂ molecule and metal cation as well as among the H₂ molecules correspond to the classical “steric hindrance” and is mainly responsible for destabilizing the system. Different contributions to the interaction energy are obtained by using the localized molecular orbital energy decomposition analysis (LMOEDA),⁵³ by using GAMESS electronic structure code.⁵⁴ The LMOEDA calculations are performed at the B2PLYPD level using the triple-ζ TZV basis set. The instantaneous interaction energy (ΔE_int) between two fragments i.e. between hydrogen molecules and C₆H₅X−M complex under investigation can be decomposed into the terms described in the following equation:

ΔE_int = E_elec + E_ex-rep + E_pol + E_disp

The classical Coulomb interaction between the occupied orbitals on two fragments is described by electrostatic term E_elec, and E_ex-rep is the repulsive exchange component resulting from the Pauli exclusion principle. E_pol and E_disp correspond to polarization and dispersion terms respectively. The polarization term is expressed as the orbital relaxation energy that includes both polarization and charge transfer interactions.

3. Results and discussion

In this present investigation, we choose to employ three different basis sets namely 6-31G(d), 6-311+G(d,p) and TZVP with ab initio MP2 and density functionals B3LYP and B2PLYPD in order to calibrate the most suitable level of theory. Table S1 and S2 in the ESI† contain all the detailed hydrogen binding energy values of the investigated systems i.e. C₆H₆−M and C₆H₅X−M complexes. As hydrogen binds weakly to the metal center, an accurate treatment of dispersion correction to measure long range interaction is very vital for studying the present systems.^27,28 Therefore as outlined in the computational section, Grimme's dispersion corrected density functional B2PLYPD in conjunction with 6-311+G(d,p) basis set is expected to be the most suitable combination in describing the energetics of all the systems under investigation. The following discussions are based on the B2PLYPD/6-311+G(d,p) geometries and energies, unless otherwise stated.

3.1 Interaction of hydrogen with C₆H₆–M complexes

While analyzing the interaction of hydrogen with C₆H₆–Li⁺ complex, we considered the possible maximum number of hydrogen molecules that can be adsorbed on the complex in accordance with the existing theoretical investigations.^23,27,29 As illustrated in Fig. 1(a), Li⁺ ion can accommodate maximum three hydrogen molecules. This is also reflected in their Δ₁E(n) values shown in Table 1. On addition of H₂ molecules from one to three, the stability of the complexes increases with respect to their lower homologue. But 4_li–ben, containing four hydrogen molecules, is destabilized by an amount of 0.31 kcal mol⁻¹ energy as compared to 3_li–ben, implying that further addition of hydrogen is energetically not favorable. As the number of hydrogen molecules increases from one to three, the arrangement of H₂ around Li⁺ changes in order to accumulate additional H₂ molecules having average Li⁺−H₂ distance in the range 1.9 Å and 2.0 Å in all the cases. When the fourth hydrogen molecule is attached to the complex it moves away from the system by making a distance of ∼3.7 Å from the Li⁺ cation. According to Srinivasu et al.,²⁷ smaller ionic radius and high effective charge density of the lithium ion is responsible for the steric crowding occurring among the hydrogen molecules around it and for this reason Li⁺ cannot accommodate more than three hydrogen molecules. As evident from the optimized geometries of 1_li–ben, 2_li–ben, 3_li–ben and 4_li–ben of Fig. 1(a), the increased Li⁺−H₂ distance is an indication of gradual weakening of interaction with increased number of hydrogen molecules. The molecular hydrogen binding energy is −4.05 kcal mol⁻¹ in 1_li–ben complex while the NPA charge of Li⁺ is found to be 0.915 a.u. With the gradual increase of the number of hydrogen molecules the interaction becomes weaker, the value of average H₂ binding energy being −2.88 kcal mol⁻¹, −2.10 kcal mol⁻¹ and −1.50 kcal mol⁻¹ in 2_li–ben, 3_li–ben and 4_li–ben, respectively. Charge on the metal cation accordingly decreases in these complexes in the range 0.884 a.u. to 0.857 a.u., which is consistent with the decreasing order of ΔBE value.

Fig. 1 Optimized geometries of C₆H₆–Li⁺(H₂)_n (a) and C₆H₅X–Li⁺(H₂)_n [(b)–(e)] complexes where n = 1–4. D_Li–H2 represents the average bond length between Li⁺ and H₂ molecules. All the bond lengths are given in Å unit.

Table 1 B2PLYPD BSSE corrected H₂ binding energy (ΔBE) and incremental first-order energy difference [Δ₁E(n)] values (kcal mol⁻¹) of Li⁺ decorated systems and charge on the cation (a.u.)

System	ΔBE	Δ1E(n)	Charge on cation
1li–ben	−4.05	—	0.915
2li–ben	−2.88	−1.70	0.884
3li–ben	−2.10	−0.56	0.857
4li–ben	−1.50	0.31	0.857
1li–aniline	−3.71	—	0.916
2li–aniline	−2.79	−1.87	0.883
3li–aniline	−2.14	−0.84	0.855
4li–aniline	−1.50	0.43	0.855
1li–methyl	−3.96	—	0.916
2li–methyl	−2.82	−1.68	0.885
3li–methyl	−2.11	−0.69	0.858
4li–methyl	−1.49	0.36	0.858
1li–cyano	−4.24	—	0.921
2li–cyano	−3.42	−2.60	0.887
3li–cyano	−2.63	−1.06	0.857
4li–cyano	−1.89	0.33	0.858
1li–benzoic	−4.15	—	0.919
2li–benzoic	−3.14	−2.13	0.886
3li–benzoic	−2.38	−0.86	0.857
4li–benzoic	−1.67	0.44	0.857

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C₆H₆–Mg²⁺ complex on the other hand, can accommodate a number of maximum four hydrogen molecules (Fig. 2(a)). The Δ₁E(n) values of these complexes depicted in Table 2 also support this observation. There is a negligible amount of energy decrement (∼−0.11 kcal mol⁻¹) on going from 4_mg–ben to 5_mg–ben. Upon adsorption of up to four H₂ molecules on the metal site, the average Mg²⁺−H₂ distance increases in the range of 2.1 Å and 2.2 Å and the residual charge on the Mg²⁺ decreases (Table 2). On the other hand, addition of fifth hydrogen causes its distance ∼3.8 Å away from the metal center. The average binding energies of H₂ to 1_mg–ben, 2_mg–ben, 3_mg–ben, 4_mg–ben and 5_mg–ben are −13.60 kcal mol⁻¹, −10.99 kcal mol⁻¹, −9.47 kcal mol⁻¹, −7.65 kcal mol⁻¹ and −6.14 kcal mol⁻¹ respectively. The increasing order of metal−H₂ distance as well as the decreasing order of residual charge values with the addition of multiple hydrogen molecules signifies that they hold same correlation with the decreasing trend of binding energy values.

Fig. 2 Optimized geometries of C₆H₆–Mg²⁺(H₂)_n (a) and C₆H₅X–Mg²⁺(H₂)_n [(b)–(d)] complexes where n = 1–5. D_Mg–H2 represents the average bond length between Mg²⁺ and H₂ molecules. All the bond lengths are given in Å unit.

Table 2 B2PLYPD BSSE corrected H₂ binding energy (ΔBE) and incremental first-order energy difference [Δ₁E(n)] values (kcal mol⁻¹) of Mg²⁺ decorated systems and charge on the cation (a.u.)

System	ΔBE	Δ1E(n)	Charge on cation
1mg–ben	−13.60	—	1.786
2mg–ben	−10.99	−8.40	1.742
3mg–ben	−9.47	−6.43	1.701
4mg–ben	−7.65	−2.19	1.672
5mg–ben	−6.14	−0.11	1.675
1mg–aniline	−12.27	—	1.764
2mg–aniline	−9.83	−7.40	1.732
3mg–aniline	−8.60	−6.13	1.696
4mg–aniline	−6.86	−1.65	1.671
5mg–aniline	−5.49	−0.01	1.675
1mg–methyl	−12.91	—	1.789
2mg–methyl	−10.55	−8.20	1.746
3mg–methyl	−9.10	−6.20	1.706
4mg–methyl	−7.31	−1.93	1.678
5mg–methyl	−5.85	−0.02	1.683
1mg–cyano	−14.00	—	1.793
2mg–cyano	−11.70	−9.40	1.744
3mg–cyano	−10.17	−7.11	1.700
4mg–cyano	−8.28	−2.61	1.670
5mg–cyano	−6.68	−0.29	1.673

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3.2 Interaction of hydrogen with C₆H₅X–M (X = −NH₂, –CH₃, –CN, –COOH) complexes

In this section we investigated the effect of different electron donating groups (−NH₂, −CH₃) and electron withdrawing groups (−CN, −COOH) on the hydrogen binding capability of the Li⁺ decorated substituted benzene rings. Due to extremely high affinity of Mg²⁺ for the oxide, it is quite impossible to model Mg²⁺ decorated benzoic acid. Therefore, except the COOH group, we have studied the effect of other three substituents on the C₆H₅X–Mg²⁺ complexes. The study of Srinivasu and co-workers on the Na⁺ and Li⁺ doped substituted benzene revealed that the interaction of molecular hydrogen with it is always found to be stronger than that of benzene irrespective of the nature of the substituents.²⁷ Both Table 1 and Fig. 1(b)–(e) exemplify the effect of introducing the above mentioned substituents and also the effect of multiple hydrogen molecules adsorbed onto the C₆H₅X–Li⁺ complexes. Alike to the benzene system, the maximum number of hydrogen molecules adsorbed is three in all the four substituted benzene systems which is also revealed by their Δ₁E(n) values in Table 2. With increase of the number of adsorbed hydrogen molecules, ΔBE as well as the residual charge on the Li⁺ cation decreases, whereas Li⁺−H₂ distance increases accordingly. The varying trends of these geometrical parameters with the addition of multiple hydrogen molecules imply that these factors correlate themselves well with the decreasing binding energy values. As we move from an electron donating group (−NH₂, −CH₃) to an electron withdrawing group (−CN, −COOH), the charge on the alkali metal cation increases which in turn helps in increasing the binding energy of H₂ to some extent. The average binding energy of hydrogen molecule in the complexes 1_li–aniline, 1_li–methyl, 1_li–benzoic and 1_li–cyano are −3.71 kcal mol⁻¹, −3.96 kcal mol⁻¹, −4.15 kcal mol⁻¹ and −4.24 kcal mol⁻¹ while the residual charges on the Li⁺ are 0.916 a.u., 0.916 a.u., 0.919 a.u. and 0.921 a.u., respectively. The corresponding optimized geometries of these complexes are shown in Fig. 1.

Table 2 summarizes the average binding energy (ΔBE) of hydrogen and the charge on the metal cation of corresponding C₆H₅X–Mg²⁺ complexes. The estimated ΔBE values indicate that the electron donating substituents like 1_mg–aniline and 1_mg–methyl weaken the H₂ binding energy considerably relative to the benzene complex 1_mg–ben while the electron withdrawing substituent 1_mg–cyano slightly strengthens the interaction. The ΔBE values of 1_mg–aniline, 1_mg–methyl and 1_mg–cyano are −12.27 kcal mol⁻¹, −12.91 kcal mol⁻¹ and −14.00 kcal mol⁻¹ and the residual charges on cation are 1.764 a.u., 1.789 a.u. and 1.793 a.u., respectively. The number of maximum hydrogen molecules adsorbed remains the same relative to the C₆H₆–Mg²⁺ complex as confirmed by both the optimized geometries (Fig. 2(b)–(d)) and the incremental energy difference values Δ₁E(n) (Table 2). Keeping the substituent unaltered and by varying the number of hydrogen molecules from one to five, the order of ΔBE decreases. This change is consistent with the other structural changes mentioned in Fig. 2.

3.3 LMOEDA analysis

The LMOEDA analysis is executed by taking the interaction between the C₆H₅X−M system and the hydrogen molecules. Table 3 displays the four contributing energy terms of the instantaneous interaction energy (ΔE_int) which is outlined in the introduction section. Irrespective of the nature of the substituent, the electrostatic term E_elec is repulsive in nature when one hydrogen molecule gets adsorbed on C₆H₅X–Li⁺ complexes while for the multiple hydrogen adsorbed systems it becomes attractive in nature. For all the complexes investigated, the attractive term E_pol is higher than the repulsive terms as well as other attractive terms. Therefore, it has the major contribution to the interaction energy. Among the two attractive terms (E_pol and E_disp), the E_pol provides 82.6% whereas the dispersion term contributes only 17.4% to the total attractive energy of 1_li–ben complex. As evident from the Table 3 the extent of interaction energy increases with increase of the number of hydrogen molecules. In case of 2_li–ben, 3_li–ben and 4_li–ben the attractive polarization energy contributes 70.0%, 67.6% and 67.6% to their respective total attraction energy. In these three complexes, the other two attractive terms, i.e., electrostatic energy term and dispersion term varies between 10% to 12% and 20–20.5%, respectively. On going from electron donating group to electron withdrawing group polarization energy does not vary considerably. The value of E_pol for 1_li–aniline, 1_li–methyl, 1_li–cyano and 1_li–benzoic are −6.91 kcal mol⁻¹, −7.11 kcal mol⁻¹, −7.33 kcal mol⁻¹ and −7.33 kcal mol⁻¹, respectively.

Table 3 ΔE_int and its contributions in kcal mol⁻¹ for H₂ adsorbed C₆H₆–Li⁺ and C₆H₅X–Li⁺ complexes

System	ΔEint	Eelec	Eex-rep	Epol	Edisp
1li–ben	−3.44	0.30	4.13	−6.50	−1.37
2li–ben	−5.17	−1.63	11.05	−11.36	−3.23
3li–ben	−6.49	−2.83	16.97	−15.87	−4.76
4li–ben	−6.97	−2.90	17.38	−16.46	−4.99
1li–aniline	−3.33	0.66	4.35	−6.91	−1.43
2li–aniline	−5.44	−1.98	12.37	−12.19	−3.64
3li–aniline	−6.88	−3.28	18.34	−16.67	−5.27
4li–aniline	−7.41	−3.68	19.67	−17.49	−5.91
1li–methyl	−3.39	0.98	4.11	−7.11	−1.37
2li–methyl	−5.01	−1.11	11.45	−12.00	−3.35
3li–methyl	−6.36	−2.37	17.43	−16.47	−4.95
4li–methyl	−6.84	−2.47	17.91	−17.08	−5.20
1li–cyano	−3.76	0.66	4.32	−7.33	−1.41
2li–cyano	−6.03	−1.18	11.06	−12.56	−3.35
3li–cyano	−7.63	−2.25	16.82	−17.28	−4.92
4li–cyano	−8.20	−2.39	17.45	−18.04	−5.22
1li–benzoic	−3.61	0.85	4.27	−7.33	−1.40
2li–benzoic	−5.82	−1.33	11.78	−12.77	−3.50
3li–benzoic	−7.54	−2.64	17.98	−17.68	−5.20
4li–benzoic	−8.32	−3.22	19.90	−18.98	−6.02

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It is noteworthy that for all of the C₆H₅X–Mg²⁺ complexes, as described in Table 4, the electrostatic energy term is negative in nature and the absolute value of E_pol is the largest one. The contribution of the polarization term to the total attraction energy is about 78.4% for the complex 1_mg–ben and the electrostatic energy term has no such significant contribution in this respect. Similar to the Li⁺ decorated complexes here also the interaction energy increases with increase in the number of hydrogen molecules. The interaction energy values are −11.47 kcal mol⁻¹, −18.48 kcal mol⁻¹, −24.00 kcal mol⁻¹, −26.81 kcal mol⁻¹ and −28.06 kcal mol⁻¹ for the complexes from 1_mg–ben to 5_mg–ben, respectively. Among the three attractive terms (E_elec, E_pol and E_disp), percentage of polarization energy of these complexes varies from 71.5 to 78.4%, the electrostatic energy term varies from 10.7% to 15.7% and the dispersion term is only 10.9–13.1% of the total attraction energy. Similar to the lithium analogues, here also the E_pol does not change considerably on going from electron donating to electron withdrawing group. The values of E_pol are −14.15 kcal mol⁻¹, −14.87 kcal mol⁻¹ and −15.45 kcal mol⁻¹ in 1_li–aniline, 1_li–methyl and in 1_li–cyano, respectively.

Table 4 ΔE_int and its contributions in kcal mol⁻¹ for H₂ adsorbed C₆H₆–Mg²⁺ and C₆H₅X–Mg²⁺ complexes

System	ΔEint	Eelec	Eex-rep	Epol	Edisp
1mg–ben	−11.47	−1.98	7.01	−14.48	−2.02
2mg–ben	−18.48	−5.04	14.93	−24.40	−3.97
3mg–ben	−24.00	−7.17	21.81	−32.97	−5.67
4mg–ben	−26.81	−8.18	28.14	−39.62	−7.15
5mg–ben	−28.06	−8.79	29.06	−40.86	−7.47
1mg–aniline	−10.51	−1.47	7.11	−14.15	−2.00
2mg–aniline	−16.83	−4.56	15.29	−23.66	−3.90
3mg–aniline	−22.38	−7.33	23.05	−32.28	−5.82
4mg–aniline	−25.10	−8.81	29.77	−38.53	−7.53
5mg–aniline	−26.35	−9.46	30.75	−39.78	−7.86
1mg–methyl	−11.10	−1.21	6.98	−14.87	−2.00
2mg–methyl	−17.86	−4.32	15.04	−24.63	−3.95
3mg–methyl	−23.14	−6.57	22.17	−32.99	−5.75
4mg–methyl	−25.93	−7.85	28.93	−39.64	−7.37
5mg–methyl	−27.20	−8.45	29.75	−40.80	−7.70
1mg–cyano	−11.95	−1.67	7.25	−15.45	−2.08
2mg–cyano	−19.88	−4.91	15.34	−26.14	−4.17
3mg–cyano	−25.96	−7.21	22.53	−35.26	−6.02
4mg–cyano	−29.52	−8.16	28.68	−42.45	−7.59
5mg–cyano	−31.07	−9.02	30.62	−44.37	−8.30

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3.4 NBO analysis

The results of NBO analysis reflect a strong charge transfer interaction between the bonding orbital of hydrogen molecule and the antibonding lone pair orbital of lithium cation. Table 5 depicts the amount of charge transfer among the participating NBOs (‘BD’ for 2-centre bond, ‘LP’ for 1-centre valence lone pair). Forward donation from H₂ to metal is described by the second-order stabilization energy (ΔE_CT) which varies between 8.85 kcal mol⁻¹ and 11.72 kcal mol⁻¹ for the C₆H₆–Li⁺ complexes. For lithium decorated aniline, methyl benzene, cyano benzene and benzoic acid systems this charge transfer energy value varies between 8.53 kcal mol⁻¹ and 12.09 kcal mol⁻¹. For each of the complexes when the fourth hydrogen molecule gets attached to the system the amount of charge transferred from H₂ to metal drastically decreases. The values are 0.35 kcal mol⁻¹, 0.22 kcal mol⁻¹, 0.38 kcal mol⁻¹, 0.50 kcal mol⁻¹ and 0.56 kcal mol⁻¹ for 4_li–ben, 4_li–aniline, 4_li–methyl, 4_li–cyano and 4_li–benzoic systems respectively. The total pairwise steric exchange energy (ΔE_steric) consists of contribution arising from the interaction among the H₂ molecules (ΔE_H2–H2) as well as between the Li⁺ cation and H₂ molecule (ΔE_Li–H2). Upon adsorption of up to three hydrogen molecules over C₆H₅X–Li⁺ systems the ΔE_Li–H2 value varies between 2.6 kcal mol⁻¹ and ∼4.0 kcal mol⁻¹ while ΔE_H2–H2 term is in the range of ∼2.0–2.3 kcal mol⁻¹. The absence of pairwise steric exchange energy between Li⁺ and the fourth H₂ molecule in both unsubstituted and substituted benzene systems implies that the fourth hydrogen molecule is oriented away from the system. The value of ΔE_steric considerably increases with increase in the number of hydrogen molecules around the metal cation for all the unsubstituted and substituted benzene systems. The ΔE_steric energy terms being more or less same in both the 3_li–ben and 4_li–ben complexes indicate that the steric repulsion is relieved in 4_li–ben by placing its fourth hydrogen molecule far apart from the system. The same correlation of ΔE_steric energy term is seen in the presence of both electron donating and electron withdrawing groups.

Table 5 Second order energy correction (ΔE_CT) and pairwise steric exchange energy (ΔE_steric) associated with H₂ to Li⁺ charge transfer interaction in Li⁺ decorated complexes

System	Type of interaction	ΔECT	ΔEsteric
1li–ben		8.85	3.95
2li–ben		10.63	9.03
		10.63
3li–ben		11.72	15.50
		11.71
		11.72
4li–ben		11.50	15.91
		11.39
		0.35
		11.45
1li–aniline		8.53	3.95
2li–aniline		10.91	8.58
		10.26
3li–aniline		11.88	14.46
		11.37
		11.86
4li–aniline		11.70	15.42
		11.15
		0.22
		11.68
1li–methyl		8.90	3.69
2li–methyl		10.78	8.84
		10.42
3li–methyl		11.75	14.78
		11.73
		11.36
4li–methyl		11.48	15.49
		0.38
		11.07
		11.40
1li–cyano		8.91	3.87
2li–cyano		10.85	8.74
		10.87
3li–cyano		12.01	14.90
		11.98
		12.09
4li–cyano		11.65	15.45
		11.71
		11.70
		0.50
1li–benzoic		8.87	3.97
2li–benzoic		10.51	8.62
		10.84
3li–benzoic		12.08	14.55
		11.94
		11.67
4li–benzoic		11.71	16.09
		11.76
		11.38
		0.56

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For C₆H₅X–Mg²⁺ complexes the amount of charge transferred from H₂ bonding orbital to metal antibonding orbital is found to be much higher than the analogous Li⁺ decorated systems indicating stronger interaction in case of Mg²⁺ decorated complexes. The detailed NBO analysis of the participating donor (H₂) and acceptor (Mg²⁺) NBOs in charge transfer interaction are illustrated in Table 6. The ΔE_CT values fluctuate in between 13.88 kcal mol⁻¹ and 18.43 kcal mol⁻¹ for all the unsubstituted and substituted Mg²⁺ containing systems. Due to the extremely larger distance of the fifth hydrogen molecule from the metal center, the charge transfer interaction drastically decreases. It is interesting to note that similar to the charge transfer interaction, ΔE_steric values in Mg²⁺ containing systems (Table 6) are much higher than the Li⁺ containing equivalent systems. Parallel to the Li⁺ decorated systems the ΔE_steric energy term increases with increase in the number of hydrogen molecules. The pairwise steric exchange energy terms between Mg–H₂ (ΔE_Mg–H2) and H₂–H₂(ΔE_H2–H2) varies between 3.2–6.7 kcal mol⁻¹ and 0.1–3.4 kcal mol⁻¹ respectively up to the addition of fourth hydrogen molecule on C₆H₆–Mg²⁺ and C₆H₅X–Mg²⁺ complexes. But as the number of attached H₂ molecules changes from four to five the ΔE_Mg–H2 term between Mg²⁺ and the fifth hydrogen molecule vanishes indicating its inability to be remained cohesively attached to the Mg²⁺ cation.

Table 6 Second order energy correction (ΔE_CT) and pairwise steric exchange energy (ΔE_steric) associated with H₂ to Mg²⁺ charge transfer interaction in Mg²⁺ decorated complexes

System	Type of interaction	ΔECT	ΔEsteric
1mg–ben		16.73	6.73
2mg–ben		17.81	13.22
		17.50
3mg–ben		17.78	21.11
		17.78
		17.78
4mg–ben		16.46	29.34
		16.45
		16.44
		16.47
5mg–ben		16.68	29.57
		15.68
		15.47
		16.78
		0.26
1mg–aniline		15.52	6.29
2mg–aniline		16.85	12.77
		16.25
3mg–aniline		17.04	15.82
		17.21
		16.93
4mg–aniline		14.52	26.82
		16.88
		16.63
		14.49
5mg–aniline		13.88	28.70
		16.75
		16.52
		14.11
		0.25
1mg–methyl		16.55	6.38
2mg–methyl		17.38	12.96
		16.83
3mg–methyl		17.53	20.49
		17.40
		16.98
4mg–methyl		15.70	27.57
		16.70
		16.55
		14.89
5mg–methyl		14.61	29.74
		16.77
		16.57
		14.15
		0.26
1mg–cyano		16.87	6.63
2mg–cyano		17.95	13.46
		17.73
3mg–cyano		17.86	20.87
		18.43
		18.22
4mg–cyano		16.25	28.49
		17.05
		17.13
		16.83
5mg–cyano		16.55	31.01
		16.84
		16.40
		16.74
		0.36

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3.5 AIM analysis

AIM analysis is carried out in order to get further insight into the H₂−metal cation interaction of the Li⁺ and Mg²⁺ decorated C₆H₅X systems. Table S3 and S4 in the ESI† depict the electron density and the Laplacian of charge density (∇²ρ) values at the respective hydrogen-metal cation BCP of each complex. The molecular graphs of 1_li–ben and 1_mg–ben are illustrated in Fig. 3. The charge shift type interaction between H₂ and metal center is realized by small positive value of ∇²ρ at the respective BCP. The electron density value along the (H₂)–Li⁺ BCPs and the ∇²ρ value in all the C₆H₆–Li⁺ and C₆H₅X–Li⁺ complexes lies within the range of 0.0120–0.0156 and 0.0664–0.0828, specifying that this interaction is stronger than the van der Waals interaction. In case of Mg²⁺ complexes, the value of electron density at the (H₂)–Mg²⁺ BCPs varies between 0.0125 and 0.0225 while ∇²ρ value lies in between 0.0538 and 0.1048 indicating stronger charge shift type interaction among H₂–Mg²⁺ complexes compared to the Li⁺-analogue.

Fig. 3 Electron density molecular graphs of (I) 1_li–ben and (II) 1_mg–ben. The green dot localized between the H₂ and the metal cation indicates the location of bond critical point of the electron density.

4. Conclusions

In this work we have systematically explored and analyzed the adsorption and thereby the binding affinities of hydrogen molecules on alkali (Li⁺) and alkaline earth metal (Mg²⁺) decorated benzene. Between these two metal cations the later one is found to bind greater number of hydrogen molecules than the former one. The binding energy of hydrogen molecule is much higher in C₆H₆–Mg²⁺ complex than the C₆H₆–Li⁺ complex. Addition of electron donating and electron withdrawing groups to the benzene moiety is also found to affect the hydrogen adsorption. The topological analysis of the electron density at the (H₂)−metal cation BCP (Li⁺, Mg²⁺) shows closed shell interaction. For this particular type of bond the contribution of polarization term is much more prominent than other attractive and repulsive terms of the instantaneous interaction energy, evident from the LMOEDA analysis. There is considerable amount of charge transfer from the bonding orbital of hydrogen molecule to the antibonding lone pair orbital of metal cation, found from the NBO analysis. In case of C₆H₅X–Mg²⁺ system, the amount of charge transfer is much higher than that found in C₆H₅X–Li⁺ system. This significant contribution of charge transfer in the interaction between H₂ molecule and the metal cation is also reflected in polarization term value in LMOEDA analysis. Substantial steric exchange interactions are also realized among the bound H₂ molecules and the metal center. Here also, these interactions are more pronounced in Mg²⁺ complexes compared to the analogous Li⁺ complexes. A strong correlation is found to exist between the charge transfer interaction and the total binding energy of the complex. In addition the contribution of polarization towards the binding energy is significantly high. The polarization and charge transfer interactions together help in stabilizing the system while the pairwise steric exchange interaction on the other hand, destabilizes the system, resulting decrease in binding energy of H₂. Our work is expected to provide crucial insight into the interaction between metal cation and hydrogen molecules and thereby provides fundamental basis of designing carbon nanomaterials, metal organic frameworks etc. for efficient hydrogen storage.

Acknowledgements

TB, TD and KS are grateful to the Council of Scientific and Industrial Research (CSIR), Government of India, for providing them research fellowships. AKD is grateful to the Department of Science and Technology (DST), Govt. of India, for a research grant under scheme number: SB/S1/PC-79/2012.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra09884j

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