Theoretical study of the interaction between molecular hydrogen and [MC₆₀]⁺ complexes

Abstract

In this work we present a density functional theory study of the interaction between a positively charged exohedral metallofullerene and several hydrogen molecules. For this purpose we have chosen Li⁺, Ti⁺, V⁺ and Cu⁺ as the metal cations, since they represent a good sample of ionic or covalent interactions with the carbon cage. We have found that the interaction between the hydrogen molecules and the metal cation strongly depends on the type of interaction between the metal cation and the fullerene. Furthermore, the hydrogen saturation around the metal is also determined by the nature of the metal.

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Introduction

Hydrogen is both by mass and number the most abundant element in the known universe, and has become in the last years a candidate to replace fossil fuels. Hydrogen presents significant advantages over petroleum-derivative fuels, the most important being that hydrogen does not contribute to global warming, does not produce toxic pollutants, and has a very high energy content. One of the greatest challenges is to find out materials that can effectively store this promising non-contaminant fuel in a reversible way. According to the US Department of Environment (DOE) the target is to obtain a hydrogen storage capacity of 6.5 wt%. Many storage methods have been already proposed, for instance liquid hydrogen,¹ cycloalkanes as chemical hydrides,² Metal-Organic Frameworks (MOF)^3,4 or carbon nanotubes.^5–9 Though carbon nanotubes were at first the best option, due to their high surface-to-volume ratio, other studies^10–12 have shown that the adsorption potential for hydrogen on this kind of materials is less than for an array of idealized slit pores geometries.

On the other hand, following this line of carbon structures, fullerenes have also been studied as promising hydrogen storage devices. A first approach mainly considered their capacity to store H₂ inside the cage. For instance, C₁₁₀ fullerene was found to encapsulate up to 19 H₂ molecules;¹³ these hydrogen atoms cannot be attached to the inner wall of the structure and therefore they exist in their molecular form. Other studies¹⁴ have investigated, by molecular dynamics simulations, the possibility of H₂ storage in carbon clusters (as well as in boron nitride clusters) finding out that H₂ molecules are able to abide stable in a C₆₀ fullerene at 298 K and 0.1 MPa, however it has been confirmed that pressures up to 5 MPa are needed to store H₂ molecules in the C₆₀ cage.

Recent studies^5,15 propose to decorate carbon structures with metals, for instance titanium-decorated fullerenes⁵ or carbon nanotubes,¹⁶ as efficient materials to store H₂. It was shown how a titanium atom coated on a single-walled nanotube or to a fullerene binds up to four hydrogen molecules, thus offering an efficient storage material for practical applications. Y. Zhao et al.¹⁶ showed by means of Density Functional Theory calculations that C₆₀Sc₁₂ could bind up to 5 hydrogen molecules per transition metal; with binding energy between 0.26 and 0.45 eV/H₂ and storage density of 7 wt%. The main inconvenience using transition metals is that the former tend to cluster on the fullerene outer shell. Thus, an alkaline-earth metal as calcium,^15,17 which binds directly to the hexagonal and pentagonal faces, without forming droplets, would be more suitable for the final goal of hydrogen storage. C₆₀Ca₃₂ can adsorb up to 62 H₂ in two different layers. The first of them with an average binding energy of 0.45 eV/H and the second one, 0.11 eV/H₂, which makes Ca coated C₆₀ a practical hydrogen storage material at near ambient temperatures. Other promising elements to store hydrogen are alkaline metals such as lithium,¹⁸ since they enhance the H₂ adsorption capacity of fullerenes; this effect is more pronounced for Na, with a hydrogen adsorption capacity of 9.5 wt%,¹⁹ than for Li. Other experimental studies²⁰ have shown how a Li doped fullerene can reversibly desorb up to 5 wt% (at 270 °C), which is significantly less than the desorption temperature of an hydrogenated fullerene (C₆₀H_x) (500–600 °C).

In this work we present a thorough study of the binding energies and geometries of a series of complexes of the form [C₆₀M(H₂)_n]⁺, where M is Li, Ti, V or Cu and n = 1–5 hydrogen molecules. The choice of charged clusters is relevant since recent mass spectrometry experiments have allowed characterization of the sequential absorption of H₂ molecules on C₆₀ fullerenes²¹ as well as other molecules.²² Furthermore, Rao and Jena have shown^23–25 that positively charged atoms would be able to bind a large amount of H₂ molecules due to the charge polarization effect, which is in fact the main interaction mechanism we found between a metal cation and the fullerene cage in a previous work.²⁶ All [M–C₆₀]⁺ interactions are mainly governed by an ion-induced dipole interaction due to the positively charged metal and the large polarizability of the C₆₀ cage. Concerning Li⁺ and Cu⁺ ions, our conclusion was that they present a larger ionic and covalent character, respectively; while for Ti⁺ and V⁺, the interaction between the metal and the carbon cage presented a shared character between ionic and covalent. Thus, in contrast with previous works we present four different metals (i.e. Li⁺, Cu⁺, Ti⁺ and V⁺), which interact distinctly with the C₆₀ carbon cage (i.e. covalently, ionically or with a mixed character) and that present different abilities to storage H₂ molecules, according to their type of interaction. We thus, provide a simple guide to predict the behavior of other metals coating the fullerene for their ability to storage H₂.

Computational details

We have performed self-consistent field calculations for all the geometry optimizations in the framework of Density Functional Theory (DFT). In particular we have used the hybrid B3LYP functional, which combines the B3 non-local hybrid exchange potential proposed by Becke²⁷ with the non-local gradient corrected correlation functional of Lee, Yang and Parr²⁸ and the M06-2X hybrid meta-exchange correlation functional,²⁹ which includes dispersion forces, that are in principle expected to play some role in the interaction of H₂ with the fullerene cage and with neighboring H₂ molecules. In both cases the 6-31G* Pople basis set has been used. In the case of the M06-2X functional, further optimizations have been performed using the 6-311++G(d,p) basis. Previous studies have compared the performance of the M06-2X functional with wavefunction methods, as the perturbative MP2 one, showing not only comparable but identical results.³⁰ In addition, we have performed a zero point vibrational energy correction (ZPE) for all calculations. The optimization of the fullerene cage leads to a length of 1.39 Å for the bond between two hexagons (hh bond) and 1.45 Å for the one between a pentagon and a hexagon (hp bond). These results are in good agreement with previous theoretical works, e.g. R_hh = 1.38 Å, R_hp = 1.43 Å,³¹ R_hh = 1.40 Å, R_hp = 1.46 Å (ref. 32) and with electron diffraction measurements, R_hh = 1.40 Å, R_hp = 1.45 Å.³³ Concerning the basis set, the 6-31G* in combination with the B3LYP functional has shown to give accurate results in comparison with those obtained with perturbational theory (MP2) in fullerenes.³⁴ Comparison between 6-31G* and 6-311++G(d,p) allows to check the importance of including diffuse functions for a correct description of the weak H₂⋯M⁺ interaction.

Calculations were carried out with the Gaussian 09 program package.³⁵ In order to determine the most stable isomer, we considered in our previous work²⁶ 5 types of initial geometries with the metal atom interacting with the fullerene external surface: the hexagonal (h) and pentagonal (p) rings, the double (hh) and single (hp) bonds and on top of a carbon atom (C). Furthermore, several spin multiplicities were also computed for the ground state. According to these results, we present here only the interaction between the most stable isomer for each [MC₆₀]⁺ complex and the H₂ molecules. This is for [C₆₀Li]⁺ the h isomer with singlet spin multiplicity, for [C₆₀Ti]⁺ the h isomer with quadruplet spin multiplicity, for [C₆₀V]⁺ the h isomer with quintuplet spin multiplicity and the hh isomer with singlet spin multiplicity for [C₆₀Cu]⁺.

The hydrogenation energy has been determined as follows:

E_Hyd = E[C₆₀M(H₂)_n⁺] − (E[C₆₀M(H₂)_n−1⁺] + E[H₂])

where E[C₆₀M(H₂)_n⁺] is the total energy of the hydrogenated complex, E[C₆₀M(H₂)_n−1⁺] is the energy of the hydrogenated complex with one less H₂ molecule and E[H₂] is the energy of one single hydrogen molecule. The hydrogenated energy is thus the energy needed to add one more hydrogen molecule to the previous hydrated complex.

We have as well calculated the adsorption energy per H₂, defined as

where E[C₆₀M(H₂)_n⁺] is the total energy of the hydrogenated complex, E[C₆₀M⁺] is the energy of the metallofullerene complex and E[H₂] is the energy of a single hydrogen molecule. Thus, negative values of the E_Ads will show stable adsorbed complexes and therefore the hydrogenation process would be an exothermic course.

Results

Taking the most stable isomer of each [C₆₀M]⁺ species (M = Li, Ti, V, Cu),²⁶ hydrogen molecules have been then placed on a top configuration, i.e. forming an angle of 180° between the center of the fullerene, the metal and the center of the H₂ molecule, since it is well known from previous works¹⁵ that this is the most favorable arrangement if one wants to maintain the hydrogen atoms in their molecular form. Thus, one single H₂ molecule is initially placed on top of a metal cation (Li⁺, Ti⁺, V⁺ and Cu⁺) with H–H distance set to 0.743 Å, which was found to be the equilibrium distance for an isolated H₂ molecule after optimization. In order to study the interaction with more than one H₂ molecule we have placed sequentially 2, 3, 4 and 5 H₂ molecules following the most symmetric configuration with respect to the metal atoms. Starting from these initial configurations the geometry of the complexes were fully optimized. Fig. 1 shows the optimized structures for [C₆₀Li(H₂)_n]⁺ and [C₆₀Cu(H₂)_n]⁺.

Fig. 1 Optimized structures for [C₆₀Li(H₂)_n]⁺ and [C₆₀Cu(H₂)_n]⁺, n = 1–5, with M06-2X/6-311++G(d,p).

The result shows that the four systems present a certain limit number of hydrogen molecules that can be attached to the metal, i.e. there is a saturation limit. This limit is four hydrogen molecules for [C₆₀Cu(H₂)_n]⁺, three H₂ molecules for the [C₆₀Li(H₂)_n]⁺ and [C₆₀Ti(H₂)_n]⁺ systems and two H₂ molecules for the [C₆₀V(H₂)_n]⁺ (see Fig. 2). This behavior is observed at the three different levels of theory considered in this work. In fact the differences between the H₂-cage distances, when H₂ molecules are adsorbed to the metallofullerene system (i.e. when the saturation limit is not reached yet) is in the order of 0.5–2%. Although the three theory levels show similar trends, differences increase significantly (up to ∼30%) for those distances corresponding to H₂ molecules weakly bound by the system. On the other hand, the H–H bond distances of H₂ molecules in [C₆₀Li]⁺ are 0.74 Å until saturation is reached (i.e. up to three hydrogen molecules), then it decreases (0.73 Å for [C₆₀Li(H₂)₄]⁺ and [C₆₀Li(H₂)₅]⁺). For [C₆₀Ti]⁺, it changes from 0.76 Å to 0.73 Å in [C₆₀Ti(H₂)₄]⁺ and [C₆₀Ti(H₂)₅]⁺. For [C₆₀V]⁺ it decreases from 0.76 Å when the complex is not saturated to 0.73 Å from the third H₂ molecule onwards. And finally, for [C₆₀Cu]⁺ it changes from 0.76 Å up to saturation of the complex to 0.75 Å in [C₆₀Cu(H₂)₃]⁺ and 0.73 Å in [C₆₀Cu(H₂)₄]⁺ and [C₆₀Cu(H₂)₅. Hence, the H–H distance increases when the H₂ molecule is interacting with the metal cation.

Fig. 2 Optimized M–H₂ distances (M = Li, Ti, V, Cu) at the three levels of theory.

This is a consequence of the H–H bond disruption by the metal; similar results were obtained by previous works⁵ on C₆₀Ti₁₂ where it was described that each Ti atom was able to bind 4 H₂ molecules, but the first one was attached as a single H atom to Ti. Thus, the metal cation prefers to attach one single H atom, and form the hydride.

Fig. 3 shows the hydrogenation energy and the total adsorption energy per H₂, as defined before. Among the four studied metals, Li shows the lowest adsorption energies and its saturation limit is reached almost at 3 H₂ molecules. The interaction is caused by a polarization of the hydrogen molecule by the Li⁺ cation, which results in an electrostatic interaction between the metallofullerene and the H₂ molecule.

Fig. 3 Hydrogenation energy, E_Hyd., and adsorption energy, E_Ads., in kcal mol⁻¹, for [C₆₀Li(H₂)_n]⁺, where M = Li, Ti, V, Cu and n = 1–5.

Ti hydrated complexes also show a saturation limit of 3 H₂ molecules, though adsorption energies are larger (∼5 kcal mol⁻¹) compared to [C₆₀Li(H₂)_n]⁺. [C₆₀V(H₂)_n]⁺ shows a saturation limit of two hydrogen molecules, and the third H₂ molecule releases ∼7 kcal mol⁻¹ to be adsorbed. Among all the studied metals, Cu has the lowest H₂ adsorption capability; [C₆₀Cu(H₂)]⁺ releases almost 10 kcal mol⁻¹ to attached a second H₂ molecule. All the studied complexes show an electrostatic interaction due to polarization. However, the adsorption energies are significantly larger for Ti, V and Cu, than for Li, especially for the adsorption of the first H₂ molecule (5.56 kcal for TiC₆₀⁺, 8.77 kcal for VC₆₀⁺ and 10.10 kcal for CuC₆₀⁺). Furthermore, if we take into account our previous conclusions on the type of interaction between these cations and the fullerene cage,²⁶ we can establish a relation between the pure interaction M⁺–C₆₀ and the adsorption energies H₂–MC₆₀⁺: Cu interacts with the carbon cage with larger covalent character and therefore presents a stronger M–C binding. This feature involves stable adsorption of the hydrogen molecules as well as high adsorption energy. On the other hand, Ti⁺ and V⁺ present a shared character, in between ionic and covalent, in their interaction with the fullerene. The double character of the M⁺–C₆₀ binding will enhance this polarization and consequently the adsorption energies will be higher when more than one H₂ molecule is adsorbed by the metallofullerene. The enhancement of the adsorption energy is due to the polarization that the positive metal exerts on the H₂ molecule.

In order to give a deeper insight on the interaction, we have also evaluated the charge, in the framework of the Mulliken population analysis, on the metal cation after the interaction, as well as the charge on each H₂ molecule after adsorption to the hydrated complex (see Fig. 4). The metal cation is initially charged with one single positive charge. The interaction between the metal cation and the fullerene cage involves the polarization of the latter by the former and, thus a gain of electron density (reducing the charge on the metal). This leads to a very localized reactivity, which results in the involvement of the closest carbon atoms in the interaction with the metal cation.

Fig. 4 Charge localized on the metal cation and the surrounding hydrogen molecules, with the Mulliken approach.

When hydrogen molecules are added to the MC₆₀⁺ complex, positive charge decreases on the metal and increases in some of the hydrogen molecules. This loss of neutrality by the H₂ molecules, once attached to the complex, is the signature of the induced polarizability and thus, of induced dipole type of interaction between the metal and the H₂ molecule. The charge in the metal is reduced and also shows a limit similar to the saturation limit.

Conclusions

In this work we have presented a DFT study on the interaction between cationic metallofullerenes and several hydrogen molecules (from one up to five). For this purpose we have chosen to study Li⁺, Ti⁺, V⁺ and Cu⁺. Each of these metal cations presents a different kind of interaction with the carbon cage (i.e. ionic or covalent-like). Despite the different interactions, all metallofullerenes exhibit a rather similar saturation limit for the adsorption of H₂ molecules, which is around three H₂ molecules. However, adsorption energies differ significantly from one system to the other (for instance, [CuC₆₀]⁺ shows the largest ones) due to the different nature of the interaction between the metal atoms and the fullerene cage. These differences are also important for the reversibility of the H₂ adsorption. We can thus conclude that in the case of M⁺…C₆₀ interactions with ionic/dipolar character a larger charge remains in the metal atom, giving rise to a stronger adsorption of the H₂ molecules. Where as for M⁺…C₆₀ interactions with covalent character, the opposite behavior is observed.

This study provides important new insight into the adsorption of hydrogen molecules in exohedral metalofullerenes cationic complexes, showing the importance of the charge and the correct choice of a metal for hydrogen storage at the nanoscale.

Acknowledgements

We acknowledge the generous allocation of computer time at the Centro de Computación Científica at the Universidad Autónoma de Madrid (CCC-UAM). This work was partially supported by the projects CTQ2013-43698 P and FIS2013-42002 R (MINECO), and NANOFRONTMAG (CAM), and the European COST Action XLIC. M. R. acknowledges the FPI grant associated with the project CTQ2010-17006 of the Spanish Ministerio de Economía y Competitividad. S. D.-T. gratefully acknowledges the “Ramón y Cajal” program of the Spanish Ministerio de Educación y Ciencia.

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