We study the adsorption of hydrogen molecules on a titanium atom supported by a benzene molecule using generalized gradient corrected Density Functional Theory (DFT). This simple system is found to bear important analogies with titanium adsorption sites in (8, 0) titanium-coated single-walled carbon nanotubes (SWNTs) (T. Yildirim and S. Ciraci, 2005) In particular, we show that up to four H2 molecules can coordinate to the metal ion center, with adsorption patterns similar to those observed in Ti-SWNTs and no more than one molecule dissociating in the process. We analyze in detail the orbital interactions responsible for Ti-benzene binding and for the electron transfer responsible for the H2 dissociation. We find the latter to involve a transition from a triplet to a singlet ground state as the hydrogen molecule approaches the adsorption site, similar to what has been observed in Ti-SWNTs. The total Ti-H2-binding energy for the first dissociative addition is somewhat inferior (~0.4โ€‰eV) to the value estimated for adsorption on Ti-SWNTs. We analyze in detail the orbital interactions responsible for the H2 binding.

1. Introduction

Developing safe, cost-effective, and practical means of storing hydrogen is crucial for the advancement of hydrogen and fuel-cell technologies [1โ€“3]. In this context, titanium-decorated organic compounds have received attention for their potential use as high-capacity hydrogen storage materials [4โ€“9]. More in specific, studies based on generalized gradient DFT and first-principle molecular dynamics simulations have indicated that a single-titanium atom supported on an insulating (8,0) SWNT can bind up to four hydrogen molecules [10]. Since high titanium coverages on SWNTs are achievable in experimental conditions, these materials could provide means to reach, or even exceed, the minimum hydrogen storage capacity required for technological applications.

Adsorption of one H2 molecule to a titanium site was found to proceed with a vanishing activation energy and to involve interactions between carbon atoms, titanium, and the hydrogen molecule which are essentially short ranged and localized at the absorption site. It was proposed that the mechanism responsible for the H2 bonding involves d orbitals of the Ti atom, the antibonding ๐œŽ๐‘ข of a H2 molecule, and p orbital at carbon sites.

In this paper we present a DFT study that elucidates the catalytic role played by the Ti atom in the dissociation of the H2 molecule and in the bonding mechanism of the Ti atom and the four hydrogen molecules, characterized as โ€œan unusual combination of chemisorption and physisorptionโ€ [10]. According to the results presented here, the same number of hydrogen molecules can be stored in essentially the same configuration introducing a different support for the Ti catalyst, the benzene molecule. The benzene molecule thus offers a hexagonal ring as support for Ti which is electronically very similar to the (8,0) SWNT, so that bonding of H2 molecules can be studied in detail using well-established molecular energy decomposition techniques and programs [11].

The paper is organized as follows. Details about the calculations are given in Section 2. The adsorption and dissociation of a H2 molecule on benzene-supported titanium is analyzed in Section 3.1, and the possible addition patterns for two and four molecule additions are studied in Section 3.3. Our results are briefly summarized in Section 4.

2. Computational Details

Calculations have been performed using the Amsterdam Density Functional program (ADF) [12โ€“14]. The molecular orbitals (MOs) were expanded in large uncontracted sets of Slater-type orbitals containing diffuse functions of TZ2P quality. A small frozen core (1s for C, 1sโ€“2p for Ti) was used in the present calculations. Equilibrium structures were optimized using analytical gradient techniques, with geometries and energies calculated at the OLYP [15, 16] level of theory. Our choice for the functional is motivated by its superior performance for the relative energies of different spin states of various transition-metal complexes in the gas phase, in particular when high-spin states are involved [17โ€“19]. Interactions between H2 molecules and the C6H6-Ti complexes were analyzed using the molecular fragment method that is a standard tool in energy decomposition methods for interactions between molecules, as detailed in Reference [11]. We use here primarily the description of the orbitals of the overall system expressed as linear combinations of fragment orbitals. The obvious fragments here are Ti, benzene and H2 molecules. The orbitals of these fragments are obtained (in the exact geometry they have in the total system) in separate calculations. These orbitals are then used as basis functions in the overall calculation. This affords an analysis of the overall orbitals in terms of percentages of the contributing fragment orbitals.

3. Results and Discussion

3.1. Orbital Interactions and Bonding in C6H6-Ti

The structure of the C6H6-Ti complex has been theoretically [20โ€“27] and experimentally [28] studied on the basis of DFT calculations and laser evaporation methods. Experimental evidence indicates the ground state to be a triplet in a planar C6๐‘ฃ configuration. We show in Figure 1 the orbital interaction diagram of the benzene molecule and the Ti atom obtained at the OLYP level of theory for the optimized triplet C6๐‘ฃ configuration. In this analysis, the C6H6-Ti (C6๐‘ฃ) compound was divided in two fragments: the isolated Ti atom and the benzene support, their geometries fixed to the relaxed interacting configuration. From now on, we will take the ๐‘ฅ๐‘ฆ-plane as the plane parallel to C6H6. When interacting with the planar C6H6, the 3d set of the metal atomic orbitals (AOs) are split into three levels of E2, A1, and E1 symmetry, the 3da1 (d๐‘ง2) orbital, two 3e2 (d๐‘ฅ๐‘ฆ and Ti-3d๐‘ฅ2โˆ’๐‘ฆ2), and two 3eโˆ—1 (d๐‘ฅ๐‘ง and d๐‘ฆ๐‘ง) orbitals, respectively. The important bonding interaction is between the benzene ๐œ‹ orbitals of E1 symmetry and the Ti-3d๐‘ฅ๐‘ง,๐‘ฆ๐‘ง orbitals, which is understandable considering the relatively large overlap between these favorably oriented orbitals. This leads to significant stabilization of the bonding combination and destabilization of the antibonding combination. There is a weaker interaction between the ๐œ‹ orbitals of E2 symmetry and the Ti-3d๐‘ฅ๐‘ฆ and Ti-3d๐‘ฅ2โˆ’๐‘ฆ2 orbitals, which are parallel to the benzene plane and little interaction of the 3d๐‘ง2 with the much lower lying C6H6-๐œ‹ orbital of A1 symmetry. The 3da1 (Ti-3d๐‘ง2) AO is somewhat stabilized by the small hybridization with the 4s and 4p of the same symmetry. The orbital pattern for the d orbitals is reminiscent of the one for sandwich complexes, but a peculiarity of the C6H6-Ti system is the presence of a low-lying 4s orbital, hardly displaced from its atomic position [26, 29]. This is related to Ti being coordinatively very unsaturated; in highly coordinated (hexa- or penta-coordinated) metal complexes the 4s is invariably very much destabilized by the orthogonality requirement on the occupied ligand orbitals.

The four d electrons of Ti are available to go into the C6H6Ti-de2 and -da1 orbitals. Because there is only a small gap between these orbitals, the โ€œhigh-spinโ€ configuration (e2)3 (da1)1 results, leading to a triplet ground state of E2 symmetry. This is Jahn-Teller distorted, so that the degeneracy of the e2 MO is lifted. Our OLYP calculations predict a triplet-C2๐‘ฃ configuration as ground state of the C6H6-Ti compound, with the quintet-C6๐‘ฃ (e2)2 (da1)1 (4s)1 and triplet-C6๐‘ฃ (e2)3 (da1)1 (4s)0 configurations lying higher in energy by 0.372 and 0.242โ€‰eV, respectively. Previously, both triplet-C2๐‘ฃ [20, 24, 26] and quintet-C6๐‘ฃ [21โ€“23, 25, 27, 28] states have been theoretically predicted as possible ground states. However, a quintet-C6๐‘ฃ ground state was predicted only by the B3LYP method, and previous studies on the reaction products formed between group 5 transition metals (V, Nb, Ta) and benzene revealed the B3LYP method to calculate the correct ground state only for the C6H6-Nb complex [29]. It was already suggested that triplet-C2๐‘ฃ is the real ground state of the C6H6-Ti complex [26] at DFT-PBW91 level of theory, and our OLYP evidence leads us to agree with such suggestions. Conclusive evidence from experimental data on the ground state of the C6H6-Ti complex is, however, still lacking.

As a consequence of the Jahn-Teller distortion, the planar C6๐‘ฃ C6H6 structure undergoes a deformation, characterized by a ruffling of the C6 ring (up or down displacement of the C atoms along the ๐‘ง-axis), Figure 1. Also, an elongation of all the Cโ€“C bonds in the C6H6-Ti compound of up to 4% is observed, because of the charge donation from the C6H6 bonding e1 states to the metal atom. The C6๐‘ฃ planar configuration may distort in two different ways towards a C2๐‘ฃ configuration, one characterized by a displacement along the ๐‘ง-axis of two para carbon atoms towards Ti, labeled as [4 + 2], the other one by displacement of the other four carbon atoms towards Ti, labeled as [2 + 4] configuration. In both cases, the distance along the ๐‘ง-axis between the Ti and the displaced C atoms is reduced from the C6๐‘ฃ value of 1.66โ€‰ร… to 1.56 and 1.59โ€‰ร… values of the [2 + 4] and [4 + 2] C2๐‘ฃ configurations, respectively. Energies reported in Figure 2 are relative to the C6๐‘ฃ structure with planar C6H6.

Figure 3 shows the electronic structure of the C6H6Ti (C2๐‘ฃโ€“ [2 + 4]) complex. The Jahn-Teller distortion from the planar C6๐‘ฃ to the [2 + 4] distorted C2๐‘ฃ structures causes a splitting of the degenerate C6H6Ti de2 levels (Figure 1) into the 8a1 and 3a2 states as shown in Figure 3. These now lie lower in energy than the Ti-3d๐‘ง2 (he 9a1 in Figure 3) with 3da1 (Figure 1) parentage. In the corresponding [2 + 4] configuration of the benzene, the e2 LUMO splits into an a2 and an a1 orbital, which stabilize the 8a1 (Ti-3d๐‘ฅ2โˆ’๐‘ฆ2) and 3a2 (Ti-3d๐‘ฅ๐‘ฆ) MOs by admixing in a bonding fashion. The ๐‘ฅ-axis is perpendicular to the direction of the 2โ€‰C atoms of the [2 + 4] structure (and again the 2โ€‰C atoms of the [4 + 2] structure). The triplet C2๐‘ฃ โˆ’ [2 + 4] configuration is thus characterized by a doubly occupied 8a1-Ti-3d๐‘ฅ2โˆ’๐‘ฆ2 state and singly occupied 9a1-Ti-3d๐‘ง2 and 3a2-Ti-3d๐‘ฅ๐‘ฆ states. In the alternative C2๐‘ฃ โˆ’ [4 + 2] Jahn-Teller configuration, the splitting of the e2 is reversed, the 3a2-Ti-3d๐‘ฅ๐‘ฆ state lies lower in energy, while the Ti-3d๐‘ฅ2โˆ’๐‘ฆ2 lies in higher position. Thus, the electron configuration in the distorted [4+2] geometry is characterized by a doubly occupied 3a2-Ti-3d๐‘ฅ๐‘ฆ state of the metal atom and a singly occupied Ti-3d๐‘ฅ2โˆ’๐‘ฆ2. However, in both configurations, the 3d๐‘ง2 state is singly occupied (9a1 state in both [2 + 4] and [4 + 2] configurations). In all cases the empty Ti-4s (10a1) is present, which potentially could act as acceptor orbital for electrons from the approaching H2.

3.2. H2 Dissociative Adsorption on C6H6-Ti

Taking the triplet C2๐‘ฃโ€“ [2 + 4] as the representative electronic ground state of the C6H6-Ti compound, we now turn to investigate the role played by the Ti addition in the adsorption of the four H2 molecules on the C6H6-Ti compound reported by Yildirim and Ciraci [10]. The first H2 addition proved to lead to dissociation of the corresponding hydrogen molecule, while an additional three molecules could be weakly bonded to the Ti atom on the SWNT surface. We therefore obtain here, for the C6H6-Ti compound, the same H2 adsorption pattern observed in the (8,0) Ti-SWNT studied in Reference [10].

Figure 4 shows the total energies of the C6H6TiH2 complex as a function of the distance between the metal atom and the center of mass of the approaching H2. All energies are relative to the value of the triplet curve at large distance, that is, the chosen energy zero is the sum of the energies of isolated ground state H2 and ground state triplet C6H6Ti[2+4]. For each value of the constrained Ti-H2 distance a full geometry optimization was carried out in both triplet and singlet states by relaxing to equilibrium all unconstrained degrees of freedom. The H2 approach turns out to be with the center of mass on the ๐‘ง-axis and the H2 bond axis perpendicular to the ๐‘ง-axis and in the direction of the two equivalent C atoms of the [2 + 4] configuration, which is the ๐‘ฅ-axis. Similar to the H2 adsorption on a SWNT [10] we find the C6H6Ti-H2 complex to be in a triplet ground state at large Ti-H2 distances and to undergo a transition to the singlet at 1.72โ€‰ร…. At variance with the barrierless dissociative adsorption of H2 on the (8,0) Ti-SWNT studied in Reference [10], a finite barrier (0.17โ€‰eV) is computed here for the H2 addition to C6H6Ti, given by the difference between the energy at the spin transition and the energy at the minimum of the triplet spin surface. The absence of a barrier for H2 dissociation in the (8,0) Ti-SWNT is likely to arise from a selective stabilization of the singlet state relative to the triplet in the Ti-SWNT compared to C6H6Ti. In Figure 4 this would result in the singlet curve joining smoothly the triplet one at Ti-H2 distances lower than ~2โ€‰ร….

The H2 lowest unoccupied orbital (LUMO) 1๐œŽ๐‘ข has B1 symmetry in C2๐‘ฃ, so it cannot mix with the de2 orbitals (8a1 and 3a2 in Figure 3) or with the 3d๐‘ง2 or 4s (both A1), but it mixes very strongly with the eโˆ—1-derived Ti-3d๐‘ฅ๐‘ง (the 6b1 of the C6H6Ti fragment). This orbital is a typical frontier orbital which is hybridized with the 4p๐‘ฅ and thereby acquires a large amplitude towards the incoming H2. The strong interaction of 1๐œŽ๐‘ข and 3d๐‘ฅ๐‘ง results in a low-lying stabilized strongly mixed C6H6TiH2-6b1 level (Tables 1 and 2 and Figure 5). As the H2 molecule approaches the C6H6Ti compound, this level stabilizes so much that it becomes successively occupied with two (spin-paired) electrons, which may be pictured as coming from the originally singly occupied 9a1๐›ผ and next 3a2๐›ผ of C6H6Ti[2 + 4] of Figure 3. This is a typical example of a bond-breaking reaction, where the initially empty strongly Hโ€“H-antibonding orbital becomes occupied. The stabilization of the 1๐œŽ๐‘ข which makes the mixing with 3d๐‘ฅ๐‘ง very strong is of course concomitant with the stretching of the H2 molecule (the bond breaking). The whole process only requires a very low barrier of 0.17โ€‰eV.

The interaction of H2 with a transition metal is often weak, because occupied metal orbitals have Pauli repulsion with the occupied 1๐œŽ๐‘” orbital of H2, preventing H2 from coming so close that the interaction of a metal d orbital with the H2โ€‰โ€‰1๐œŽ๐‘ข orbital can become strong. Typically another occupied metal d orbital then interacts only weakly with the high-lying H21๐œŽ๐‘ข, resulting in weak backdonation. In the present case the coordinatively unsaturated Ti atom, with relatively few d electrons (as an early transition metal in the 3d series), offers a route to strong interaction and H2 bond breaking. The 1๐œŽ๐‘” mixes (allowed by symmetry) with the 4s and the 3d๐‘ง2 states (9a1 and 10a1 of the C6H6Ti fragment) but not with the 3d๐‘ฅ2โˆ’๐‘ฆ2 (8a1), see Table 2. The antibonding combination of 3d๐‘ง2 and 1๐œŽ๐‘”, embodying the Paul repulsion, is destabilized in the process and loses its electron to the downwards moving 6b1. The loss of the electron from the antibonding orbital implies disappearance of the Pauli repulsion, and the H2 can approach unhindered to optimize the interaction of 1๐œŽ๐‘ข with 3d๐‘ฅ๐‘ง in the now fully occupied 6b1, which leads to the bond breaking. At the same time, there is a low-lying bonding combination of the (mostly) 1๐œŽ๐‘” orbital with the Ti-3d๐‘ง2, resulting in the orbital 8a1, which remains fully occupied (with the original two electrons of 1๐œŽ๐‘”). This orbital is further stabilized by favorable mixing with the Ti 4s (10a1) and the Ti-3d๐‘ฅ2โˆ’๐‘ฆ2 (note the percentages of 12% and 15%, resp. in the 8a1, Table 2). This contributes to the force pulling H2 to Ti. So ultimately the two electrons of H2 end up in the Ti-1๐œŽ๐‘”(H2) bonding orbital 8a1 and out of the four Ti electrons two go into the Ti-1๐œŽ๐‘ข(H2) bonding orbital 6b1 (Hโ€“H bond breaking), while the two remaining ones reside in the largely nonbonding Ti-3d๐‘ฅ2โˆ’๐‘ฆ2 (9a1). The final resulting electron configuration has only doubly occupied orbitals, that is, it is a singlet state. The transition from the triplet to the singlet state occurs at a distance of 1.72โ€‰ร… between the Ti atom and the incoming H2 molecule.

Figure 5 shows the orbital interactions between the C6H6Ti complex and the adsorbed H2 molecule in the singlet equilibrium geometry. For analysis the systems was divided into two fragments: the C6H6Ti C2๐‘ฃ โˆ’ [2 + 4] complex described before and the hydrogen molecule with the Hโ€“H distance lengthened to the dissociated value (2.61โ€‰ร…). At such a long Hโ€“H distance the 1๐œŽ๐‘” (A1 symmetry in C2๐‘ฃ) and 1๐œŽ๐‘ข (B1 symmetry) orbitals have little bonding/antibonding character left and are almost degenerate. As described above, these two H2-based orbitals enter the orbital energy diagram as the states 8a1 and 6b1, below the 3d orbitals, with a good deal of mixing of these H2 orbitals and the metal orbitals. The internal caption in the figure shows the composition of the C6H6TiH2 C2๐‘ฃ โˆ’ [2 + 4] 8a1 and 6b1 MOs.

3.3. Adsorption of Two and Four H2 Molecules

Turning now to the addition of two H2 molecules, we observe that Figure 6 shows two adsorption patterns, one in which one of the H2 molecules is dissociated (Figure 6(a)) and one in which purely molecular adsorptions are observed (Figure 6(b)). In the dissociative configuration (a) the distance between the centers of mass of the first and the second H2 molecule and the Ti is predicted to be 0.76 and 1.81 ร…, respectively, with a lengthened 0.84โ€‰ร… bond for the second nondissociated molecule and a Hโ€“H distance of 3.22โ€‰ร… for the dissociated one. The Hโ€“H distance in a free H2 molecule is 0.74โ€‰ร…. In the configuration (b), the two H2 molecules were added in a position other than the on-top adsorption site of the Ti. The optimized geometry predicted a displacement between the center of mass of the two H2 molecules and the Ti atom of 0.98โ€‰ร… and 1.77โ€‰ร… along the ๐‘ง-axis and the ๐‘ฅ๐‘ฆ-plane, respectively. The adsorbed H2 bond length was calculated to be 0.78โ€‰ร…. The first configuration is energetically favored by 0.38โ€‰eV over the second.

Table 3 shows the composition of the MOs involved in the donation/backdonation bonding mechanisms. In the configuration (a), the system was divided again in two fragments: C6H6TiH2 and the second undissociated H2 molecule. In the configuration (b), the system was divided into a C6H6Ti and two H2 fragments. In both configurations, the added H2 molecules bind weakly to the Ti and do not dissociate with bonding energies of 0.10 and 0.20โ€‰eV per H2 molecule, respectively.

In the configuration (a), the dissociation of the second H2 molecule is hindered by the double occupancy of the C6H6TiH2-8a1 orbital, which prevents the second H2 molecule from approaching the adsorption site by the Pauli repulsion (occupied-occupied orbital repulsion of 1๐œŽ๐‘” with 8a1). Strong mixing of the high-lying H2โ€‰โ€‰1๐œŽ๐‘ข with a suitable occupied metal fragment orbital is therefore blocked, and significant stabilizing mixing between the 1๐œŽ๐‘” and the empty 10a1-3d๐‘ง2 and the 11a1-4s is also prevented. Charge donation from the C6H6Ti complex to the 1๐œŽ๐‘ข of the second H2 molecule is thus avoided, (which could take place in the first dissociative H2 addition and caused the Hโ€“H bond breaking). The empty 10a1 and 11a1 orbitals, with large 3d๐‘ง2 and 4s character, do act to some extent as acceptor orbitals (cf. the 7% 10a1 mixing with the 1๐œŽ๐‘” in Table 3), but bond breaking would require the antibonding 1๐œŽ๐‘ข orbital to be filled.

In the configuration (b), the dissociation of the two H2 molecules does not occur since the orbital overlaps between the C6H6Ti and H2 remain too weak in this configuration. For instance, the calculated overlap between 9a1 and 1๐œŽ๐‘” was 0.114, while a 0.765 value was obtained for the C6H6Ti-H2 dissociative adsorption described before. The two H2 molecules should approach the C6H6Ti fragment more closely in order to build better overlaps but would then experience substantial repulsion. The first dissociation in configuration (a) occurs because the antibonding H2 orbital 1๐œŽ๐‘ข gets filled through its strong interaction with the exposed Ti-3d๐‘ฅ๐‘ง. In general, dissociation requires that electrons are dumped into the antibonding (bond-breaking) orbital. This does not occur in configuration (b) because of the repulsion between C6H6Ti-8a1 and 1๐œŽ๐‘”'s. In addition, bond breaking requires occupation of the 1๐œŽ๐‘ข orbitals. In the depicted configuration the 1๐œŽ๐‘ข orbitals cannot, however, establish strong interactions with unoccupied C6H6TiH2 orbitals and gain sufficient stabilization to bring about its occupation through the mechanism described above. A weak donation/backdonation mechanism is therefore responsible for the bonding between the Ti atom and the two H2 molecules also in this second configuration. Note that the C6H6Ti-6b1, 6a1 and 3a2 states indicated in the right panel of Table 3 consist mainly of the Ti-3d๐‘ฅ๐‘ง, a lower lying C6H6-e1 and the Ti-3d๐‘ฅ๐‘ฆ/C-p๐‘ง states, respectively.

We next consider the adsorption of four H2 molecules on the C6H6Ti complex. In this case, two stable four-H2 adsorption patterns were computed (Figure 7). We denote these two different configurations as TiH2 + 3H2 (Figure 7(a)) and Ti + 4H2 (Figure 7(b)). These equilibrium structures are clearly related to the corresponding geometries in the two-H2 addition patterns (Figure 6). In both cases, no more than one H2 molecule undergoes dissociative adsorption, and when dissociation occurs an additional undissociated molecule resides on top of the adsorption site. In the configurations of type (b), the on-top site is left vacant. Similar configurations were found to be stable when using SWNT support in place of C6H6 for the Ti catalyst [10]. The final optimized TiH2 + 3H2 structure is 0.32โ€‰eV lower than Ti + 4H2. In the very symmetric Ti + 4H2 configuration, all the four molecules stay intact, with an average Hโ€“H bond distance and bond energy of 0.82โ€‰ร… and 0.23โ€‰eV, respectively.

Table 4 shows a comparison between the benzene and SWNT supports. It is important to notice that the results presented in this paper agree with the hypothesis of Yildirim and Ciraci [10] about the characteristic properties of a Ti atom supported by a hexagonal-carbon-based framework and its hydrogen adsorption properties. Also, our orbital analysis substantiates the picture of the Tiโ€“Cโ€“H2 interaction proposed by the authors for the SWNT support. There are nonetheless important differences between the two supports. In the first instance the adsorption energy of the first dissociative H2 addition is much reduced in the benzene support (from 0.83โ€‰eV to 0.37โ€‰eV). In addition, the dissociative addition is an activated process which suggests, according to the argument of Section 3.1, that the singlet state is stabilized in the SWNT compared to the benzene support. Furthermore, when four molecules are adsorbed, in the benzene-Ti system, one is dissociated, the others are not. In the SWNT none is dissociated. The very symmetric SWNT-Ti-4H2 configuration was found to lie lower in energy by 0.10โ€‰eV than the SWNT-TiH23H2 [10]. It may therefore be argued that the yield of molecular H2 adsorption in the C6H6-Ti system would be lower than in the SWNT (one need to recombine one molecule when releasing hydrogen). Finally, the average Ti-H2 adsorption energy decreases from 0.54โ€‰eV for the SWNT support to 0.23โ€‰eV for the C6H6. In conclusion, although the C6H6 support for the Ti addition qualitatively reproduces the dominant local contribution of the large gap (8,0) SWNT, the different boundary conditions of the two materials, finite system in the case of C6H6, infinite periodic in the case of the SWNT, lead to sizable differences in the adsorption energies. The result is a favored Ti + 4H2 configuration for the periodic SWNT support of the Ti atom and the more localized TiH2 + 3H2 as the favored pattern for C6H6. We stress that, in the TiH2 + 3H2 configuration, the first H2 adsorption is dissociative, while the other three are not. From a material modelling viewpoint, the C6H6-Ti complex can be seen as an โ€œalmost convergedโ€ model system for the SWNT-Ti with respect to cluster size. Nevertheless, C6H6-Ti can store the same number of H2 molecules per Ti atom, achieving a 6% weight percentage of stored hydrogen. Indeed, some electronic relationship between SWNT and C6H6 may be expected from the modern theory of the macroscopic polarization [30]. According to such theory, the quadratic spread of the manybody electronic wavefunction in condensed phase has an upper bound, in the presence of a finite gap ๐ธ๐‘”: โ„๐œ†<22๐‘š๐ธ๐‘”,(1) where ๐œ† is the so called localization length [30], defined by a unitary operator based on a Berry phase in place of the position operator, and ๐‘š is the electron mass. Qualitatively, (1) can be read as โ€œthe larger the gap, the more localized the electrons areโ€. Indeed, (8,0) SWNT is a large gap insulator nanotube, thus limiting the quadratic spread of the manybody electronic wavefunction. This means that, as normal for insulators, the interaction between Ti adatom and the SWNT may be expected to consist of a dominant local contribution from the C6 hexagon surrounding the metal atom. When we isolate the carbon hexagon support of the Ti atom, the C6H6 is obtained by hydrogen passivation of the dangling bonds. Benzene can be therefore provide the simplest model system in which the local effects occurring in the large gap insulator (8,0) SWNT may be represented.

4. Summary and Conclusions

We studied the adsorption of one, two, and four H2 molecules on a single titanium atom supported on a benzene molecule. In all cases we found one H2 molecule to adsorb dissociatively and the remaining one(s) to bind to the metal ion center through weak-charge transfer interaction. The dissociative addition was found to involve a transition from the triplet to the singlet energy surface, similar to what has been found in the adsorption of H2 on a titanium atom supported on a (8,0) SWNT. At variance with the latter, this was, however, found to be an activated process, with a barrier of 0.17โ€‰eV. The Tiโˆ’H2-binding energy was estimated to be ~0.4โ€‰eV lower than in the SWNT. The main emphasis of this work has been on a detailed analysis of the orbital interactions responsible for the H2 binding to Ti and for the dissociation of one H2 molecule. Typically, the coordination of H2 to a transition metal atom (or ion) is very weak, because the occupied 1๐œŽ๐‘” orbital will have Pauli repulsion with occupied metal orbitals. This prevents H2 from coming close and interacting strongly by way of its high-lying 1๐œŽ๐‘ข, which could lead to breaking of the Hโ€“H bond. In the Ti-benzene system, however, the situation is different due to the small number of d electrons and due to fact that the interaction with the benzene โ€œpreparesโ€ the Ti 3d orbitals for the interaction with H2. Notably, the Pauli repulsion, which is embodied in the antibonding interaction of the occupied 1๐œŽ๐‘” of H2 with an occupied mostly 3d๐‘ง2 orbital, is relieved by the loss of the two electrons from the rising antibonding combination of the 1๐œŽ๐‘” and 3d๐‘ง2. These electrons are transferred to an in-phase (bonding) combination of the (originally empty) Ti 3d๐‘ฅ๐‘ง and H2โ€‰โ€‰1๐œŽ๐‘ข orbitals, which comes down due to the stabilizing interaction. We also find that the empty Ti 4s orbital can interact favorably with H2, which adds to the force pulling the H2 in. In essence, Ti is specially favorable because the combination of the small number of four d electrons and the special orbital interactions with benzene lead to just the right electronic structure for easy dissociation of H2. Our results elucidate the electronic structure reasons for the high potential of Ti on carbon supports as new and efficient materials for hydrogen storage.


This work was supported by the Netherlands Organization for Scientific Research through the ACTS Programme for Sustainable Hydrogen. Computer resources were provided by the Netherlands' Scientific Research Council (NWO) through a grant from Stichting Nationale Computerfaciliteiten (NCF). Support was also given by the WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology of the Republic of Korea (Project no. R32-2008-000-10180-0).