Improved H₂ uptake capacity of transition metal doped benzene by boron substitution

Abstract

The effect of boron substitution on hydrogen storage capacity of transition metal (TM) doped benzene is studied using density functional theory and the second order Møller–Plesset method with aug-cc-pVDZ basis set. Out of the six carbon atoms in a benzene ring, two are substituted by boron atoms. The structures considered here are C₄B₂H₆TM (TM = Sc, Ti, V). Four, four and three H₂ molecules can be adsorbed on unsubstituted C₆H₆Sc, C₆H₆Ti and C₆H₆V complexes, respectively, whereas upon boron substitution one additional H₂ molecule gets adsorbed on each of these complexes. The H₂ uptake capacity of C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V obtained is 7.71, 7.54 and 5.99 wt%, respectively. Gibbs free energy corrected adsorption energies show that H₂ adsorption on C₄B₂H₆Sc is energetically unfavorable whereas it is favorable on C₄B₂H₆Ti and C₄B₂H₆V at ambient conditions. Various interaction energies for the H₂ adsorbed complexes are obtained using a many-body analysis technique. The H₂ desorption temperature for boron substituted TM doped benzene is lower than that for TM doped benzene for all the three systems. Molecular dynamics simulations show that loosely bonded H₂ molecules in C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) complexes fly away during the simulation, thereby showing lower H₂ uptake capacity of these complexes than that obtained by electronic structure calculations.

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Introduction

Hydrogen is one of the best alternatives to fossil fuels. Obtaining suitable materials for storing hydrogen with high uptake capacity is the big obstacle for the hydrogen economy to be a reality.^1,2 Materials that can store hydrogen with high gravimetric and volumetric density, exhibiting fast hydrogen sorption kinetics and that operate under ambient thermodynamic conditions are essential for practical applications, in particular for the transportation sector. Therefore, the search for promising hydrogen storage systems has attracted great attention. Practical hydrogen storage for vehicular applications requires materials with high hydrogen capacity, low decomposition temperature and fast adsorption/desorption kinetics. Hydrogen can be stored either in gaseous or in liquid forms in cryogenic tanks. The gaseous hydrogen storage requires high pressure tanks and liquid hydrogen storage requires very low temperature about −252.8 °C. During the required liquefaction process a significant amount of energy is consumed. Continuous efforts are made to store hydrogen at ambient conditions using solid state materials. Among the present hydrogen storage options, solid-state storage would satisfy the market requirement.^3,4 Till date, no reversible materials are currently known that possess all mentioned attributes.

Organometallic complexes are increasingly important in the hydrogen storage and hydrogen fuel cell sector. Recent research has demonstrated that some transition metal (TM) based organic materials can store hydrogen at levels exceeding those found in most materials currently being evaluated for hydrogen storage applications. Hydrogen storage on several small organometallic complexes have been tested. Hydrogen storage on transition metal–acetylene^5–9 and transition metal–ethylene organometallic complexes^8,10–20 has been studied thoroughly. Wadnerkar et al. have compared the hydrogen uptake capacity and equilibrium isotope effect from theory and experiment for the Ti:C₂H₄ organometallic complex.¹⁹ They have shown that Ti:C₂H₄ organometallic thin films can be synthesized in an ultra-high vacuum chamber using the method of reactive pulsed laser deposition. The equilibrium isotope effect calculated using vibrational frequencies and H₂ uptake capacity of Ti:C₂H₄ from quantum chemical calculations is in excellent agreement with the experimental determinations.¹⁹ Phillips et al. have reported hydrogen adsorption on nanoscale titanium–benzene complex formed through reactive pulsed laser deposition in an ultra-high vacuum chamber.²¹ This has encouraged the researchers to study the H₂ uptake capacity of different small organometallic complexes.

Several investigations have also been made on hydrogen storage capacity of TM–C_nH_n rings and TM–C_nH_m (ref. 21–30) complexes. The H₂ uptake capacity of these complexes is as per the target set by the U.S. Department of Energy (US DOE). Though small organometallic complexes show high H₂ uptake capacity satisfying the target set by US DOE, their H₂ uptake capacity may be lower in bulk due to clustering of transition metal atoms. Therefore, continuous efforts are made to increase the H₂ uptake capacity of small organometallic complexes containing single TM atom so that even if in bulk it decreases due to clustering of TM atoms it satisfies the target set by US DOE. From this point of view instead of transition metal atom alkali or alkaline earth metal atom decorated complexes are considered. However, it is observed that H₂ adsorption on such complexes is energetically unfavorable at ambient conditions.^8,9 Hence TM doped complexes are the best options for hydrogen storage, but we have to increase their H₂ uptake capacity. Some efforts are made earlier to increase the hydrogen uptake capacity or metal binding energy by boron substitution. Lu et al. have investigated the effect of boron substitution in aromatic rings of graphyne for Li and H2 binding using Density Functional Theory (DFT), first principles molecular dynamics and grand canonical ensemble Monte Carlo method.³¹ Wang et al. have constructed three dimensional B-doped graphene-interconnected framework and reported 5.9 wt% hydrogen storage capacity of Li decorated material at 298 K and 100 bars.³² Using first principles calculations Lee et al. have reported hydrogen uptake capacity of Ca decorated zigzag graphene nanoribbon as 5 wt%.³³ They concluded that on the zigzag edge and B-doped armchair edge of graphene Ca clustering is suppressed. Rao et al. using DFT calculations have shown that in porous graphene nanotube and B-substituted porous graphene nanotube both, the curvature effect and B substitution strengthen the Li, Ca and Na metal binding and prevent the metal atoms from clustering.³⁴ Lu et al. have obtained the hydrogen uptake capacity of 6.4 and 6.8 wt% for two boron substituted Li decorated porous graphene and two boron substituted Ca decorated porous graphene respectively.³⁵ Kalamse et al. have studied interaction of molecular hydrogen with Li and Ti functionalized boron substituted and unsubstituted naphthalene using DFT method and concluded that Ti containing complexes are superior over Li containing complexes for hydrogen storage.³⁶ Zou et al. also observed suppressing of Sc, Ti and Ca clustering on covalent organic frameworks after boron doping.³⁷ This work is another effort to predict hydrogen storage properties of a metal decorated boron substituted material at ambient conditions.

In this work, first we have studied hydrogen storage capacity of C₆H₆TM (TM = Sc, Ti, V) complexes viz. C₆H₆Sc, C₆H₆Ti, C₆H₆V using quantum chemical methods. We then studied C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V complexes obtained by substituting two boron atoms in place of two carbon atoms in a benzene ring and studied their H₂ uptake capacity. The aim of this substitution is to study whether boron substitution enhances the H₂ uptake capacity of unsubstituted organometallic complexes. The Gibbs free energy corrected adsorption energies are obtained at different temperatures and pressures to know at what temperature and pressure range H₂ adsorption on these complexes is energetically favorable. Molecular dynamics (MD) simulations were also carried out using atom centered density matrix propagation (ADMP). H₂ desorption temperatures from these complexes are obtained using Van't Hoff equation.³⁸ Many-body analysis technique has been used to study various interaction energies in H₂ adsorbed complexes.^39–43

Computational details

We optimized the geometries of unsubstituted TM doped benzene and boron substituted TM doped benzene using second order Møller–Plesset method and DFT with PBEPBE and B3LYP functionals along with aug-cc-pVDZ basis set. We then added H₂ molecules one by one on each of these complexes and optimized the geometries. Molecular dynamics simulations were carried out using atom centered density matrix propagation.⁴⁴ The time step (Δt) of ADMP–MD simulations was set at 0.2 fs. The temperature was maintained using the velocity scaling method during the ADMP-MD simulations. All calculations were performed using the Gaussian suite of programs.⁴⁵

The averaged adsorption energy without zero point energy correction (ΔE) is calculated as

ΔE = {E[OM] + (n × E[H₂]) − E[OM(nH₂)]}/n

here E[X] is the total energy of X without zero point energy correction and OM is either C₄B₂H₆Sc, C₄B₂H₆Ti, C₄B₂H₆V, C₆H₆Sc, C₆H₆Ti or C₆H₆V complex.

The averaged adsorption energy with zero point energy correction (ΔE_ZPE) is calculated as

ΔE_ZPE = {E_ZPE[OM] + (n × E_ZPE[H₂]) − E_ZPE[OM(nH₂)]}/n

where E_ZPE[X] is the total energy of X with zero point energy correction.

The averaged adsorption energy with Gibbs free energy correction (ΔE_G) is calculated as

ΔE_G = {E_G[OM] + (n × E_G[H₂]) − E_G[OM(nH₂)]}/n

where E_G[X] stands for the total energy of X with Gibbs free energy correction.

Various interaction energies for H₂ adsorbed complexes are obtained using many-body analysis technique. All the energies reported here are corrected for the basis set superposition error.

Results and discussion

Fig. 1 shows optimized structures of hydrogen adsorbed transition metal (TM) doped benzene and hydrogen adsorbed boron substituted TM doped benzene at MP2/aug-cc-pvdz level of theory. Four, four and three H₂ molecules can be adsorbed on C₆H₆Sc, C₆H₆Ti and C₆H₆V organometallic complex respectively. When two of the carbon atoms in a benzene ring are substituted by boron atoms, these complexes adsorb one extra H₂ molecule. The energy required to substitute two boron atoms in a benzene ring is found to be −8.5, −9.1 and −9.2 eV at PBEPBE, B3LYP and MP2 method respectively with aug-cc-pvdz basis set. The negative values indicate that substitution of boron in benzene is endothermic process and requires energy for substitution.

Fig. 1 Optimized structures of (a) C₆H₆Sc(4H₂) (b) C₆H₆Ti(4H₂) (c) C₆H₆V(3H₂) (d) C₄B₂H₆Sc(5H₂) (e) C₄B₂H₆Ti(5H₂) (f) C₄B₂H₆V(4H₂) at MP2/aug-cc-pvdz level.

The H₂ uptake capacity of C₆H₆Sc, C₆H₆Ti, C₆H₆V, C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V complexes is found to be 6.15, 6.02, 4.48, 7.71, 7.54 and 5.99 wt% respectively. Thus boron substitution has enhanced the H₂ uptake capacity of C₆H₆Sc, C₆H₆Ti, C₆H₆V complexes by about 1.56, 1.52, and 1.51 wt% respectively. Substituting boron for carbon in benzene ring introduces new states above the highest occupied molecular orbital as shown in Fig. 2. This is in agreement with what observed by Park et al.⁴⁶ They have shown that in boron substituted graphene-like structure, new states appear above the valence band maximum. This electron deficient structure accepts extra electrons and suppresses TMs clustering by increasing metal binding energy. Hindering metal clustering is one of the important issues for hydrogen storage on transition metal decorated materials because it not only affects the surface stability but reduces the surface area for hydrogen adsorption. Here, it is difficult to observe metal clustering because we are using only one TM atom on hexagonal site of C₆H₆ and C₄B₂H₆ as a H₂ interacting species. But, the multiple TM decorated complexes are more than likely to form cluster during synthesis. One way to understand the metal clustering thermodynamically is to compare metal binding energy on surface with its cohesive energy in bulk. In Table 1, we have compared Sc, Ti and V binding energy on C₆H₆ and C₄B₂H₆ before and after H₂ adsorption. The binding energy of Sc, Ti and V to C₆H₆(C₄B₂H₆) is found to be 0.91(3.63), 1.39(4.8) and 1.72(5.57) eV respectively before H₂ adsorption. It indicates that the TM atom bound strongly to boron substituted benzene than benzene. The binding energy of Sc, Ti and V to C₄B₂H₆ in H₂ adsorbed complexes is found to be 3.28, 4.38 and 3.87 respectively and little lower than that before H₂ adsorption.

Fig. 2 Introduction of new states after boron substitution in benzene.

Table 1 Calculated metal binding energy (in eV) on C₆H₆ and C₄B₂H₆ before and after H₂ adsorption at MP2/aug-cc-pVDZ level of theory

Metal	C6H6	C4B2H6^a	C4B2H6^b	Cohesive energy in bulk^c
a Before H2 adsorbed.b After H2 adsorbed.c C. Kittel, Introduction to Solid State Physics, 7th edn, Wiley, 1996.
Sc	0.91	3.63	3.82	3.90
Ti	1.39	4.80	4.38	4.85
V	1.72	5.57	3.87	5.31

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Calculated TM binding energies on C₆H₆ are much lower than the cohesive energy of TM in bulk. Consequently clustering of TM on C₆H₆ is likely to be happened. On the other hand, boron substituted benzene shows significant enhancement in TM binding energy as compared with un-substituted benzene. Calculated binding energies of TM on C₄B₂H₆ before and even after H₂ adsorption are found to be very close to their cohesive energy in bulk. Therefore, it can be concluded that B-substitution not only enhances hydrogen uptake but also helps to prevent the metal clustering. This is due to the fact that boron has one less valence electron than that for the carbon and when we substitute two of the carbon atoms with boron, C₄B₂H₆ becomes an electron deficient surface with respect to C₆H₆. This forces TM to give some extra electron to C₄B₂H₆ compared with C₆H₆. Table 2 shows calculated NBO charges for the H₂ adsorbed complexes at MP2/aug-cc-pVDZ level.

Table 2 NBO charge on transition metal decorated C₆H₆ and C₄B₂H₆ complexes before and after H₂ adsorption at MP2/aug-cc-pVDZ level. The values in parenthesis are NBO charges after H₂ adsorption

Complex	C	B	Metal
C6H6Sc	−0.41(−0.33)	—	0.84(0.37)
C6H6Ti	−0.28(−0.25)	—	0.60(−0.29)
C6H6V	−0.29(−0.25)	—	0.45(−0.40)
C4B2H6Sc	−0.70(−0.62)	0.20(0.28)	1.72(0.86)
C4B2H6Ti	−0.77(−0.59)	0.36(0.41)	1.63(−0.1)
C4B2H6V	−0.66(−0.55)	0.19(0.36)	1.56(0.04)

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It is found that substitution of two boron atoms in place of carbon in benzene ring not only shows a prominent effect on metal binding but also on hydrogen adsorption. Table 3 shows a comparison of structural parameters for TM doped benzene and boron substituted TM doped benzene before H₂ adsorption. As can be seen from Table 2, the C–C bond length gets little elongated on boron substitution for C₆H₆Sc and C₆H₆Ti whereas there is almost no change for the C₆H₆V complex. There is no large change in C–TM bond length before and after boron substitution. The C–B bond length is found to be 1.53 Å for all the three complexes. The B–TM bond lengths are longer than the C–TM bond lengths for all the three complexes. The B–TM and C–TM bond length decreases as we go from C₄B₂H₆Sc to C₄B₂H₆V complex.

Table 3 Structural parameter (Å) of C₄B₂H₆TM and C₆H₆TM (TM = Sc, Ti, V) at B3LYP/aug-cc-pVDZ level

Complex	Bond length (Å)
	C–C	C–B	C–TM	B–TM
C6H6Sc	1.41	1.53	2.35	2.47
C4B2H6Sc	1.44		2.35
C6H6Ti	1.44	1.53	2.14	2.38
C4B2H6Ti	1.48		2.15
C6H6V	1.44	1.53	2.10	2.32
C4B2H6V	1.43		2.14

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Structural parameters for H₂ adsorbed boron substituted TM doped benzene complexes at MP2/aug-cc-pVDZ, B3LYP/aug-cc-pVDZ and PBEPBE/aug-cc-pVDZ levels are compared in Table 4. The structural parameters at PBEPBE/aug-cc-pvdz level are comparable with those obtained at MP2/aug-cc-pvdz level. The C–C bond lengths in H₂ adsorbed TM doped benzene complexes before and after boron substitution are equal. Similarly C–B bond lengths in boron substituted TM doped benzene before and after maximum H₂ adsorption are also equal. There is large change in the C–TM bond lengths before and after H₂ adsorption for unsubstituted as well as boron substituted TM doped benzene for all the three cases. The elongation of C–TM bond lengths after H₂ adsorption indicates weakening of the C–TM bond after maximum H₂ adsorption. The C–TM bond lengths for H₂ adsorbed boron substituted TM doped benzene are longer than those for the H₂ adsorbed unsubstituted TM doped benzene. The bond between boron and transition metal also becomes weak after the maximum number of H₂ adsorption.

Table 4 Different bond length (Å) in C₄B₂H₆Sc(5H₂)^a, C₄B₂H₆Ti(5H₂)^b and C₄B₂H₆Ti(4H₂)^c complexes. The values in parenthesis are corresponding bond length in isolated C₄B₂H₆TM (TM = Sc, Ti and V) complexes with respective method and aug-cc-pVDZ basis set

Method		Bond length (Å)
		C=C	C–B	C–TM	B–TM	TM–H2
PBEPBE	a	1.43(1.45)	1.54(1.53)	2.45(2.30)	2.55(2.43)	2.20(top), 2.14, 2.09, 2.08, 2.25
	b	1.43(1.50)	1.54(1.54)	2.38(2.10)	2.50(2.35)	2.12(top), 1.86, 1.86, 1.89, 1.89
	c	1.42(1.43)	1.54(1.53)	2.29(2.24)	2.40(2.33)	1.78, 1.78, 1.81, 1.81
B3LYP	a	1.42(1.44)	1.53(1.53)	2.46(2.34)	2.56(2.47)	2.30(top), 2.17, 2.13, 2.13, 2.31
	b	1.42(1.47)	1.52(1.52)	2.37(2.13)	2.51(2.37)	2.37(top), 1.89, 1.89, 1.93, 1.93
	c	1.41(1.43)	1.53(1.53)	2.32(2.24)	2.43(2.32)	1.85, 1.83, 1.86, 1.83
MP2	a	1.43(1.45)	1.53(1.53)	2.44(2.39)	2.55(2.51)	2.36(top), 2.17, 2.23, 2.09, 2.15
	b	1.43(1.50)	1.54(1.54)	2.36(2.10)	2.50(2.36)	2.13(top), 1.88, 1.88, 1.83, 1.83
	c	1.41(1.44)	1.53(1.54)	2.32(2.24)	2.43(2.34)	1.86, 1.83, 1.86, 1.83

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Boron substitution not only affects the bond length, but also the orientation of adsorbed H₂ molecules. In case of C₆H₆Sc all the four H₂ molecules are adsorbed with H–H bond parallel to the plane of benzene ring. Boron substitution results in adsorption of an extra H₂ molecule which adsorbs on top of the Sc atom. Out of five adsorbed H₂ molecules including the H₂ molecule adsorbed on top of Sc atom three are having their H–H bond parallel to the plane of boron substituted benzene ring. For the remaining two, the H–H bond is perpendicular to the plane of boron substituted benzene ring. In case of C₆H₆Ti all the four H₂ molecules are adsorbed with their H–H bond inclined to the plane of benzene ring. Upon boron substitution all the five H₂ molecules are adsorbed with their orientation parallel to the plane of boron substituted benzene ring. For C₆H₆V complex all the three H₂ molecules are adsorbed with their orientation parallel to the plane of benzene ring whereas upon boron substitution the adsorbed H₂ molecules are with their orientation inclined to the boron substituted benzene ring. The H₂ molecules are adsorbed at a little longer distance in boron substituted TM doped benzene than that for the TM doped benzene. This indicates weak interaction between H₂ molecules and boron substituted TM doped benzene than that between H₂ molecule and TM doped benzene.

Table 4 shows that for C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) complexes one of the five H₂ molecules is adsorbed at a longer distance as compared to the remaining four adsorbed H₂ molecules. It indicates that the fifth H₂ molecule is loosely bonded to these complexes. For C₄B₂H₆V complex all the four adsorbed H₂ molecules are adsorbed at equal distance. The H–H bond lengths of adsorbed H₂ molecules are longer than that for the isolated H₂ molecule for all the H₂ adsorbed complexes. The H–H bond length for the isolated H₂ molecule is found to be 0.75 Å at MP2/aug-cc-pvdz level whereas it is found to be in a range of 0.78–0.79, 0.79–0.86 and 0.83–0.85 for C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂) and C₄B₂H₆V(4H₂) complexes respectively. The elongation in H–H bond length upon adsorption indicates that there is Kubas interaction between H₂ molecules and TM atom. It also indicates that there is a charge transfer from d orbitals of TM atom to the H₂ molecules. More the charge transfer more is the elongation. Number of H₂ molecules adsorbed depends on number of empty d orbitals of TM. The charge transfer between sigma bonding orbitals of H₂ to d orbitals of TM plays an important role in H₂ interaction. Natural bond orbital analysis shows that boron substituted benzene ring gains extra 0.25, 0.35 and 0.1 electrons from Sc, Ti and V respectively as compared to that for the unsubstituted benzene ring. This is in agreement with earlier findings.⁴⁶ This results in more empty d orbitals of TM to interact with one extra H₂ molecules for boron substituted TM doped benzene.

Calculated averaged H₂ adsorption energies without (ΔE), with zero point energy correction (ΔE_ZPE) and with Gibbs free energy correction (ΔE_G) at 298.15 K and 1 atm pressure are presented in Table 5 for maximum H₂ adsorbed complexes. As can be seen from Table 5, H₂ adsorption on C₆H₆Sc and C₄B₂H₆Sc complexes is energetically unfavourable at ambient conditions whereas it is favourable on C₆H₆Ti, C₄B₂H₆Ti, C₆H₆V and C₄B₂H₆V complexes. It can also be seen from Table 5 that the zero point energy correction for adsorption energy is significant and not negligible. The H₂ adsorption energies for boron substituted TM doped benzene are lower than that for the TM doped benzene for all the three systems indicating weak interaction of H₂ molecules with the former than the latter. Similar to the structural parameters H₂ adsorption energies obtained by PBEPBE/aug-cc-pVDZ level are comparable with those from MP2/aug-cc-pVDZ level.

Table 5 Calculated averaged H₂ adsorption energy without (ΔE), with zero point energy correction (ΔE_ZPE) and with Gibbs free energy correction (ΔE_G) in eV at 298.15 K for C₄B₂H₆TM(nH₂) where (TM = Sc, Ti, V and n = 1–5) using different level of theory with aug-cc-pVDZ basis set

Complex	PBEPBE			B3LYP			MP2
	ΔE	ΔEZPE	ΔEG	ΔE	ΔEZPE	ΔEG	ΔE	ΔEZPE	ΔEG
C6H6Sc(4H2)	0.48	0.34	0.05	0.36	0.22	−0.07	0.34	0.18	−0.12
C4B2H6Sc(5H2)	0.37	0.23	−0.06	0.29	0.16	−0.12	0.33	0.18	−0.09
C6H6Ti(4H2)	0.73	0.55	0.26	0.64	0.45	0.16	0.76	0.59	0.29
C4B2H6Ti(5H2)	0.59	0.41	0.13	0.47	0.31	0.01	0.70	0.53	0.23
C6H6V(3H2)	0.89	0.73	0.44	0.78	0.60	0.31	1.49	1.27	0.96
C4B2H6V(4H2)	0.77	0.56	0.26	0.56	0.39	0.08	0.73	0.52	0.21

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Since adsorption of five H₂ molecules on C₄B₂H₆Sc is energetically unfavorable at ambient conditions we have calculated H₂ adsorption energies at different temperatures and pressures to know the suitable temperature and pressure range over which H₂ adsorption on C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V is energetically favorable. For obtaining H₂ adsorption energies at different temperatures, the pressure is kept constant as 1 atm. For calculating H₂ adsorption energies at different pressures, the temperature is kept constant as 298.15 K. Fig. 3 and 4 show temperature and pressure dependent H₂ adsorption energies respectively for C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂) and C₄B₂H₆V(4H₂) complexes. As observed earlier for structural parameters and H₂ adsorption energies, temperature and pressure dependent H₂ adsorption energies at PBEPBE/aug-cc-pVDZ and MP2/aug-cc-pVDZ levels are comparable. Fig. 3 shows that H₂ adsorption on C₄B₂H₆Ti and C₄B₂H₆V complexes is energetically favorable at all the temperatures considered here at MP2/aug-cc-pVDZ as well as PBEPBE/aug-cc-pVDZ level. H₂ adsorption on C₄B₂H₆Sc is possible below 200 and 250 K at MP2/aug-cc-pVDZ and PBEPBE/aug-cc-pVDZ levels respectively. H₂ adsorption on C₄B₂H₆Ti and C₄B₂H₆V is possible for a wide range of temperature than that on C₄B₂H₆Sc. Fig. 4 shows that maximum number of H₂ adsorption on C₄B₂H₆Ti and C₄B₂H₆V complexes is possible at all the pressures considered here at MP2/aug-cc-pVDZ and PBEPBE/aug-cc-pVDZ levels. The Gibbs free energy corrected H₂ adsorption energies are higher at lower temperature and 1 atm pressure. Similarly H₂ adsorption energies are higher at higher pressure and room temperature. Higher Gibbs free energy corrected H₂ adsorption energies at lower temperature and higher pressure indicates stronger interaction of H₂ molecules with respective organometallic complex.

Fig. 3 Temperature dependent Gibbs free energy corrected adsorption energies for C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂), and C₄B₂H₆V(4H₂) at different levels.

Fig. 4 Pressure dependent Gibbs free energy corrected adsorption energies for C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂), and C₄B₂H₆V(4H₂) at different levels.

The stability of H₂ adsorbed complexes is confirmed by vibrational frequencies and the gap between Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO). The HOMO–LUMO gap with successive adsorption of H₂ molecules for all the three complexes is shown in Fig. 5. It can be seen that the HOMO–LUMO gap for the maximum number of H₂ adsorbed complex is greater than 6.5 eV at MP2/aug-cc-pVDZ level indicating that these complexes are kinetically stable. Also there are no soft vibrational modes for all the three H₂ adsorbed complexes indicating quantum mechanically stable complexes. Also HOMO–LUMO gap for the H₂ adsorbed complexes is higher than that for the respective isolated organometallic complexes at MP2/aug-cc-pVDZ level indicating more kinetic stability of former than the latter.

Fig. 5 HOMO–LUMO gap with successive addition of H₂ molecules on C₄B₂H₆Sc, C₄B₂H₆Ti, and C₄B₂H₆V complex.

Estimation of H₂ desorption temperature from C₆H₆Sc, C₄B₂H₆Sc, C₆H₆Ti, C₄B₂H₆Ti, C₆H₆V and C₄B₂H₆V complexes is obtained using the Van't Hoff equation³⁸ written in terms of ΔE_ZPE

T_D = (ΔE_ZPE/k_B)(ΔS/R − ln P)⁻¹

here k_B is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹), R the gas constant (8.31 J K⁻¹ Mol⁻¹), ΔS the change in the H₂ entropy from gas to liquid phase and P the equilibrium pressure P (1 atm). It is observed that H₂ desorption temperature is lower for the boron substituted TM doped benzene than that for the TM doped benzene. This is due to the fact that the H₂ molecules interact weakly with the former than the latter. Using ΔS from ref. 47 and ΔE_ZPE calculated at MP2/aug-cc-pVDZ level of theory H₂ desorption temperature from C₆H₆Sc, C₆H₆Ti, C₆H₆V, C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V is found to be 231, 757, 1630, 231, 680 and 667 K respectively.

Many-body analysis technique has been used here to obtain various interaction energies in H₂ adsorbed complexes and are presented in Table 6. As can be seen from Table 6 two body interactions of adsorbed hydrogen molecules with all the three organometallic (OM) complexes are attractive whereas all the H_i–H_j two body interactions are repulsive. Here H_i and H_j are i^th and j^th hydrogen molecules in a complex respectively as shown in Fig. 1. The interaction energy depends on how far the hydrogen molecule is adsorbed in a complex. In case of C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) complexes the fifth and fourth hydrogen molecule is loosely bonded respectively to the respective OM complex and shows lower OM–H_i interaction energy as compared to that for the remaining hydrogen molecules within the same complex. In case of C₄B₂H₆V(4H₂) complex two hydrogen molecules are adsorbed at 1.842 Å and show equal OM–H_i interaction energy whereas the remaining two hydrogen molecules are adsorbed at 1.831 Å and the interaction energy for these two hydrogen molecules with C₄B₂H₆V is also equal. For C₄B₂H₆Sc(5H₂) complex, first and fourth hydrogen molecules are adsorbed at equal distance of 2.124 Å and there is no large difference between the OM–H_i interaction energy for these two molecules with OM complex. Second and third hydrogen molecules are adsorbed at 2.283 Å and 2.170 Å respectively and result in little higher interaction energy for the latter than the former with OM complex. In case of C₄B₂H₆Ti(5H₂) complex first and second adsorbed hydrogen molecules are at 1.891 Å and having equal interaction energy with C₄B₂H₆Ti complex. Similarly the third and fifth adsorbed hydrogen molecules are at equal distance of 1.926 Å and show equal two body interaction energy.

Table 6 Many-body interaction energies and binding energy (kcal mol⁻¹) for C₄B₂H₆SC(5H₂), C₄B₂H₆Ti(5H₂), C₄B₂H₆V(4H₂) complexes at MP2/aug-cc-pVDZ level. Here OM is organometallic complex and H_i is the i^th hydrogen molecule in a complex

Interaction terms	Interaction energy (kcal mol^−1)
	C4B2H6SC(5H2)	C4B2H6Ti(5H2)	C4B2H6V(4H2)
Two body
OM–H1	−9.31	−20.86	−10.70
OM–H2	−6.37	−20.86	−12.22
OM–H3	−7.48	−17.83	−12.22
OM–H4	−9.48	−5.34	−10.70
OM–H5	−2.83	−17.82	—
H1–H2	0.28	0.14	2.06
H1–H3	0.24	1.72	4.52
H1–H4	0.06	1.34	0.25
H1–H5	1.19	1.72	—
H2–H3	0.05	1.73	0.16
H2–H4	1.21	1.34	4.51
H2–H5	0.53	1.73	—
H3–H4	0.29	2.04	2.05
H3–H5	1.70	0.14	—
H4–H5	0.58	2.05	—
Three body
OM–H1–H2	2.01	7.86	−4.61
OM–H1–H3	0.05	−0.18	−2.82
OM–H1–H4	2.30	−1.97	1.62
OM–H1–H5	−1.70	−0.23	—
OM–H2–H3	1.62	−0.23	−0.46
OM–H2–H4	−0.73	−1.97	−2.80
OM–H2–H5	0.66	−0.19	—
OM–H3–H4	−0.25	−2.10	−4.61
OM–H3–H5	−3.09	7.55	—
OM–H4–H5	−1.75	−2.10	—
H1–H2–H3	−0.03	−0.25	−0.37
H1–H2–H4	−0.05	−0.13	−0.50
H1–H2–H5	−0.18	−0.25	—
H1–H3–H4	−0.03	−0.65	−0.50
H1–H3–H5	−0.13	−0.25	—
H1–H4–H5	−0.08	−0.66	—
H2–H3–H4	−0.05	−0.66	−0.37
H2–H3–H5	−0.06	−0.25	—
H2–H4–H5	−0.20	−0.65	—
H3–H4–H5	−0.17	−0.14	—
Four body
OM–H1–H2–H3	−1.57	−2.22	−3.01
OM–H1–H2–H4	−0.13	1.47	−3.36
OM–H1–H2–H5	−1.35	−2.22	—
OM–H1–H3–H4	−0.75	2.49	−3.35
OM–H1–H3–H5	1.20	−2.22	—
OM–H1–H4–H5	−1.05	2.47	—
OM–H2–H3–H4	0.20	2.48	−3.01
OM–H2–H3–H5	0.02	−2.22	—
OM–H2–H4–H5	1.31	2.49	—
OM–H3–H4–H5	1.13	3.92	—
H1–H2–H3–H4	0.03	0.22	0.79
H1–H2–H3–H5	0.03	0.48	—
H1–H2–H4–H5	0.06	0.22	—
H1–H3–H4–H5	0.03	0.22	—
H2–H3–H4–H5	0.06	0.22	—
Five body
IOM–H1–H2–H3–H4	−0.11	−2.62	5.70
IOM–H1–H2–H3–H5	0.70	−0.15	—
IOM–H1–H2–H4–H5	−0.86	−2.61	—
IOM–H1–H3–H4–H5	0.34	−3.89	—
IOM–H2–H3–H4–H5	−1.13	−3.89	—
H1–H2–H3–H4–H5	−0.02	−0.11	—
Six body
IOM–H1–H2–H3–H4–H5	0.75	3.89	—
Sum of 2-body	−29.31	−68.77	−32.29
Sum of 3-body	−1.88	2.56	−15.42
Sum of 4-body	−0.79	7.81	−11.95
Sum of 5-body	−1.07	−13.26	5.70
Sum of 6-body	0.75	3.89	—
Relaxation energy	−1.09	10.92	1.93
Additive energy	−29.31	−68.77	−32.29
Non additive energy	−2.98	1.01	−21.67
Binding energy	−33.39	−56.84	−52.03
BSSE corrected total energy (Hartree)	−972.40	−1061.18	−1154.52

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Similar to OM–H_i two body interaction energies, the H_i–H_j interaction energies within the same complex are also dependent on distance between H_i and H_j for all the three complexes. In C₄B₂H₆Sc(5H₂) complex the fifth hydrogen molecule is adsorbed on top of Sc atom. H₁ is adsorbed on one side of Sc and H₄ on another. Similar is the case for H₂ and H₃. The distance between H₁–H₂, H₁–H₃, H₁–H₄, H₁–H₅, H₂–H₃, H₂–H₄, H₂–H₅, H₃–H₄, H₃–H₅ and H₄–H₅ is found to be 2.272, 2.655, 4.118, 2.083, 4.128, 2.411, 2.441, 2.603, 2.322 and 2.255 Å respectively. The repulsive interaction energies between H₁–H₄ and H₂–H₃ molecules are almost negligible than that for other pairs of hydrogen molecules.

In case of C₄B₂H₆Ti(5H₂) complex, H₁ and H₂ adsorbed on opposite side of Ti. Similar is the case for H₃ and H₅. Two-body repulsive interaction energies for these two pairs are negligible as compared to other H_i–H_j interaction energies within the same complex. The distance between H₁–H₂, H₁–H₃, H₁–H₄, H₁–H₅, H₂–H₃, H₂–H₄, H₂–H₅, H₃–H₄, H₃–H₅ and H₄–H₅ is found to be 3.557, 1.932, 2.290, 1.932, 1.930, 2.289, 1.932, 2.389, 3.539, 3.539 and 2.388 Å respectively. As compared to C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) complexes, the H_i–H_j distances are shorter in C₄B₂H₆V(4H₂) complex and show higher H_i–H_j two body repulsive interaction energies. Here also H₁ and H₄ are adsorbed on opposite side of V. Similar is the case for H₂ and H₃. These two interaction energies are negligible as compared to other H_i–H_j two-body repulsive interaction energies within the same complex.

Total two-body interaction energy contributes about 87.8, 120.9 and 62.1% attractively to the binding energy of C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂) and C₄B₂H₆V(4H₂) complex respectively. The OM–H_i two-body interaction energies have 121, 120 and 142% attractive contribution whereas H_i–H_j interaction energies have 21, 20 and 42% repulsive contribution to the total two-body interaction energy for C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂) and C₄B₂H₆V(4H₂) complex respectively.

Not only two-body interaction energies but higher energies viz. three-body, four-body etc. and relaxation energies are also contributing significantly to the binding energy of a respective complex. For total three-body, total four-body, total five-body and total six-body energies, contribution from many-body energies containing OM complex as one of the many-body terms is more as compared to that from the terms containing only hydrogen molecules. The attractive% contribution from total three body, total four body and total five body energy to the binding energy of C₄B₂H₆Sc(5H₂) complex is 5.63, 2.4 and 3.2% respectively where as the only six body energy for this complex contributes about 2.2%.

For C₄B₂H₆Ti(5H₂) complex the repulsive% contribution from total three-body, total four-body and total six-body energy to its binding energy is 4.5, 13.7 and 6.84% respectively whereas total five body energy has 23.3% attractive contribution. In case of C₄B₂H₆V(4H₂) complex, total three body and total four body has about 29.6 and 22.9% attractive contribution to its binding energy whereas total five body energy contributes repulsively by about 11%. The binding energy of C₄B₂H₆Sc(5H₂), C₄B₂H₆Ti(5H₂) and C₄B₂H₆V(4H₂) complex is found to be 33.39, 56.84 and 52.03 kcal mol⁻¹ respectively.

ADMP-MD simulations have been performed to confirm whether boron substituted TM decorated benzene complexes can adsorb hydrogen molecules at finite temperature. The minimum energy structures obtained using the electronic structure calculations have been used as initial geometries for the ADMP-MD simulations. The trajectories of H₂ at 300 K for the three complexes are shown in Fig. 6–8. The TM–H₂ distances in all the H₂ adsorbed complexes studied here are shown in Table 4. The TM–H₂ distance oscillation range (1.7–2.3 Å) in the MD simulations is reasonable to compare with optimized distance by different level of theory. No H₂ molecule is oscillating far from their maximum distance observed in optimized structure. The labile H₂ molecules leave very early (around 50 fs) from Sc and Ti decorated C₄B₂H₆ complexes by leaving more space for other H₂ molecules to interact with TM. This is true for other systems studied earlier as well.^7,20,30 Other hydrogen molecules remain adsorbed on a complex during the simulation of 1000 fs or even longer. To confirm this we have performed ADMP-MD simulation for longer than 1000 fs for C₄B₂H₆Ti(5H₂) system upto 1600 fs and results are shown in Fig. 7. It can be concluded that the H₂ molecules which are having a tendency to leave the complex, fly away very early and 1000 fs simulation time seems to be long enough.

Fig. 6 Trajectories of H₂ molecules (R_H2 in Å) during ADMP-MD simulations for C₄B₂H₆Sc(5H₂).

Fig. 7 Trajectories of H₂ molecules (R_H2 in Å) during ADMP-MD simulations for C₄B₂H₆Ti(5H₂).

Fig. 8 Trajectories of H₂ molecules (R_H2 in Å) during ADMP-MD simulations for C₄B₂H₆V(4H₂).

From Fig. 6 and 7 out of five adsorbed H₂ molecules in initial structure of C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) at least four hydrogen molecules are retained on Sc/Ti atom during the simulations. One of the five hydrogen molecules which was loosely bonded to the OM complex gets desorbed during the ADMP-MD simulations. During ADMP-MD simulations the four adsorbed hydrogen molecules on C₄B₂H₆Sc(5H₂) and C₄B₂H₆Ti(5H₂) oscillate at a distance in a range of 1.7 to 2.3 Å. In Fig. 7, it is observed that the first hydrogen molecule shows minor oscillations for Ti–H₂ distance upto 500 fs after which that begins to grow in magnitude till 1000 fs. To confirm whether this hydrogen molecule remain adsorbed on C₄B₂H₆Ti complex or not, we have performed ADMP-MD simulations for longer than 1000 fs up to 1600 fs. It is observed that Ti–H₂ distance for this hydrogen molecule becomes shorter after 1000 fs. It indicates that it remain adsorbed on C₄B₂H₆Ti complex during entire simulation period of 1600 fs and does not leave the complex.

In case of C₄B₂H₆V(4H₂) all the four molecules are remain adsorbed during the ADMP-MD simulations as can be seen in Fig. 8. This is due to the fact that all the four molecules are strongly bonded to the C₄B₂H₆V complex and there is no loosely bonded hydrogen molecule for C₄B₂H₆V(4H₂) complex. From ADMP-MD simulations each of the complex C₄B₂H₆Sc, C₄B₂H₆Ti and C₄B₂H₆V can retain four hydrogen molecules during the simulations thereby showing hydrogen uptake capacity of 6.26, 6.13 and 5.99 wt% respectively. The predicted hydrogen uptake capacity of boron substituted TM doped benzene from electronic structure calculations as well as ADMP-MD simulations for all the three complexes is satisfying the target set by US DOE.

Conclusions

Second order Møller–Plesset method, density functional theory with PBEPBE and B3LYP functionals and aug-cc-pVDZ basis set have been used to study the effect of boron substitution on hydrogen uptake capacity of Sc, Ti and V doped benzene. Boron substitution enhances the hydrogen uptake capacity of C₆H₆Sc, C₆H₆Ti and C₆H₆V by about 1.5 wt%. Electronic structure calculations show that five, five and four hydrogen molecules get adsorbed on C₆B₂H₆Sc, C₆B₂H₆Ti and C₆B₂H₆V complex respectively. However ADMP-MD simulations show that four hydrogen molecules are remain adsorbed on C₆B₂H₆Sc, C₆B₂H₆Ti and C₆B₂H₆V complexes during the simulation with respective hydrogen uptake capacity of 6.26, 6.13 and 5.99 wt%. Hydrogen desorption temperature is found to be lowered for the boron substituted TM doped benzene than that for the TM doped benzene. Two-body interaction energies show that hydrogen molecules interact strongly with C₄B₂H₆Ti than C₄B₂H₆Sc and C₄B₂H₆V complexes. The hydrogen uptake capacity predicted here for the boron substituted TM doped benzene complexes is satisfying the target set by US DOE.

Acknowledgements

Financial support from CSIR, New Delhi, India (Grant No: 03(1223)/12/EMR-II) is thankfully acknowledged.

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