# Titanium as a Potential Addition for High-Capacity Hydrogen Storage Medium

Authors: Filippo Zuliani; Leonardo Bernasconi; Evert Jan Baerends
Journal: Journal of Nanotechnology
 (2012)

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## Abstract

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 fourH2 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 (~0.4 eV) to the value estimated for adsorption on Ti-SWNTs. We analyze in detail the orbital interactions responsible for the H2 binding.


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## Body

## 1. Introduction

Developing safe, cost-effective, and practical means of storing hydrogen is crucial for the advancement of hydrogen and fuel-cell technologies [1–3].  In this context, titanium-decorated organic compounds have received attention for their potential use as high-capacity hydrogen storage materials [4–9]. 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 σu 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 “an unusual combination of chemisorption and physisorption” [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 Section2. 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) [12–14]. 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, 1s–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 [17–19]. 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 [20–27] 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 C6v 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 C6v configuration. In this analysis, the  C6H6-Ti (C6v) 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 xy-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 (dz2) orbital, two 3e2 (dxy and Ti-3dx2-y2), and two 3e1* (dxz and dyz) orbitals, respectively. The important bonding interaction is between the benzene π orbitals of E1 symmetry and the Ti-3dxz,yz 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 π orbitals of E2 symmetry and the Ti-3dxy and Ti-3dx2-y2 orbitals, which are parallel to the benzene plane and little interaction of the 3dz2 with the much lower lying  C6H6-π orbital of A1 symmetry. The 3da1 (Ti-3dz2) 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.Figure 1
Orbital interaction diagram of the  C6H6Ti -C6v configuration.The fourd 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 “high-spin” 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-C2v configuration as ground state of the  C6H6-Ti compound, with the quintet-C6v (e2)2 (da1)1 (4s)1 and triplet-C6v (e2)3 (da1)1 (4s)0 configurations lying higher in energy by 0.372 and 0.242 eV, respectively. Previously, both triplet-C2v [20, 24, 26] and quintet-C6v [21–23, 25, 27, 28] states have been theoretically predicted as possible ground states. However, a quintet-C6v 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-C2v 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 C6v  C6H6  structure undergoes a deformation, characterized by a ruffling of the C6 ring (up or down displacement of the C atoms along the z-axis), Figure 1. Also, an elongation of all the C–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 C6v planar configuration may distort in two different ways towards a C2v configuration, one characterized by a displacement along the z-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 z-axis between the Ti and the displaced C atoms is reduced from the C6v value of 1.66 Å to 1.56 and 1.59 Å values of the [2 + 4] and [4 + 2] C2v configurations, respectively. Energies reported in Figure 2 are relative to the C6v structure with planar  C6H6.Figure 2
Energy diagram at DFT-OLYP level of the calculated  C6H6-Ti triplet configurations. The smooth line is a pure schematic guide between the three configurations. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.Figure3 shows the electronic structure of the  C6H6Ti  (C2v– [2 + 4]) complex. The Jahn-Teller distortion from the planar C6v to the [2 + 4] distorted C2v 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-3dz2 (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-3dx2-y2) and 3a2 (Ti-3dxy) MOs by admixing in a bonding fashion. The x-axis is perpendicular to the direction of the 2 C atoms of the [2 + 4] structure (and again the 2 C atoms of the [4 + 2] structure). The triplet C2v − [2 + 4] configuration is thus characterized by a doubly occupied 8a1-Ti-3dx2-y2 state and singly occupied 9a1-Ti-3dz2 and 3a2-Ti-3dxy states. In the alternative C2v − [4 + 2] Jahn-Teller configuration, the splitting of the e2 is reversed, the 3a2-Ti-3dxy state lies lower in energy, while the Ti-3dx2-y2 lies in higher position. Thus, the electron configuration in the distorted [4+2] geometry is characterized by a doubly occupied 3a2-Ti-3dxy state of the metal atom and a singly occupied Ti-3dx2-y2. However, in both configurations, the 3dz2 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.Figure 3
MO interaction diagram of the formation of  C6H6Ti  C2v − [2 + 4] from Ti and  C6H6. In parentheses the parentage of the levels from those of C6v  C6H6Ti (with planar  C6H6), see Figure 1. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.


### 3.2. H2 Dissociative Adsorption on C6H6-Ti

Taking the triplet C2v– [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].Figure4 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 z-axis and the  H2  bond axis perpendicular to the z-axis and in the direction of the two equivalent C atoms of the [2 + 4] configuration, which is the x-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 1.72 Å. At variance with the barrierless dissociative adsorption of  H2  on the (8,0) Ti-SWNT studied in Reference [10], a finite barrier (0.17 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 ~2 Å.Figure 4
Total energies of the  C6H6Ti[2 + 4]-H2  complex for different constrained Ti-H2  distances, measured from Ti to the center of mass of H2. H2 approaches perpendicular to the z-axis, lying along the x-axis (in the direction of the 2 C atoms of the [2 + 4] structure). The triplet and singlet states (dashed and straight line, resp.) are compared. Vertical lines indicate the equilibrium distance of 1.12 Å (straight line) and the transition point at 1.72 Å (dashed line). All energies are relative to the value of the triplet curve at large distance we indicated as zero.The  H2  lowest unoccupied orbital (LUMO) 1σu has B1 symmetry in C2v, so it cannot mix with the de2 orbitals (8a1 and 3a2 in Figure 3) or with the 3dz2 or 4s (both A1), but it mixes very strongly with the e1*-derived Ti-3dxz (the 6b1 of the  C6H6Ti  fragment). This orbital is a typical frontier orbital which is hybridized with the 4px and thereby acquires a large amplitude towards the incoming  H2. The strong interaction of 1σu and 3dxz 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 9a1α and next 3a2α of  C6H6Ti[2 + 4] of Figure 3. This is a typical example of a bond-breaking reaction, where the initially empty strongly H–H-antibonding orbital becomes occupied. The stabilization of the 1σu which makes the mixing with 3dxz 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 0.17 eV.Table 1
C6H6TiH2 MOs energies (eV). Orbital labels refer to Figure 5.
d(Ti-H2) (Å)
2.2 (↑/↓)
1.72 (↑↓)
1.17 (↑↓)
C6H6TiH2-6b1
−2.71/−1.55
−3.85
−5.64
C6H6TiH2-8a1
−11.50/−11.28
−6.53
−5.94Table 2
C6H6TiH2 MOs composition (%). Orbital labels refer to Figure 5.
d(Ti-H2) (Å)
2.2 (↑/↓)
1.72 (↑↓)
1.17 (↑↓)
C6H6TiH2-6b1
1σu
22/44
48
59
6b1-3dxz
55/42
41
33
C6H6TiH2-8a1
1σg
89/91
74
67
101-4s
3/3
8
12
9a1-3dz2
1/1
8
8a1-3dx2-y2
15Figure 5
MO diagram for the  C6H6Ti-H2  dissociative interaction. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.The interaction of H2 with a transition metal is often weak, because occupied metal orbitals have Pauli repulsion with the occupied 1σg orbital of H2, preventing H2 from coming so close that the interaction of a metal d orbital with the H2  1σu orbital can become strong. Typically another occupied metal d orbital then interacts only weakly with the high-lying H21σu, 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 1σg mixes (allowed by symmetry) with the 4s and the 3dz2 states (9a1 and 10a1 of the  C6H6Ti  fragment) but not with the 3dx2-y2 (8a1), see Table 2. The antibonding combination of 3dz2 and 1σg, 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 1σu with 3dxz 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) 1σg orbital with the Ti-3dz2, resulting in the orbital 8a1, which remains fully occupied (with the original two electrons of 1σg). This orbital is further stabilized by favorable mixing with the Ti 4s (10a1) and the Ti-3dx2-y2 (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-1σg(H2) bonding orbital 8a1 and out of the four Ti electrons two go into the Ti-1σu(H2) bonding orbital 6b1 (H–H bond breaking), while the two remaining ones reside in the largely nonbonding Ti-3dx2-y2 (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 1.72 Å between the Ti atom and the incoming  H2  molecule.Figure5 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  C2v − [2 + 4] complex described before and the hydrogen molecule with the H–H distance lengthened to the dissociated value (2.61 Å). At such a long H–H distance the 1σg (A1 symmetry in C2v) and 1σu (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  C2v − [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 Å, respectively, with a lengthened 0.84 Å bond for the second nondissociated molecule and a H–H distance of 3.22 Å for the dissociated one. The H–H distance in a free  H2  molecule is 0.74 Å. 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 0.98 Å and 1.77 Å along the z-axis and the xy-plane, respectively. The adsorbed  H2  bond length was calculated to be 0.78 Å. The first configuration is energetically favored by 0.38 eV over the second.Adsorption patterns of two  H2  molecules addition: (a)  C6H6Ti  H2-H2, (b)  C6H6Ti -2H2. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.
(a)
(b)Table3 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 0.20 eV per  H2  molecule, respectively.Table 3
Compositions of the MOs involved in the H2 donation/backdonation bonding mechanism for the adsorption of two H2 molecules on the C6H6Ti complex.
C6H6TiH2-H2
C6H6Ti-2H2
6a1
3b1
83%  H2-1σg
91%  H2-1σg (x2)
7%  C6H6TiH2-10a1
6%  C6H6Ti-6b1
6b1
6a1
87%  C6H6TiH2-6b1
85%  H2-1σg (x2)
10%  H2-1σu
4%  C6H6Ti-6a1
3b2
88%  C6H6Ti-3a2
10%  H2-1σu (x2)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 1σg with 8a1). Strong mixing of the high-lying  H2  1σu with a suitable occupied metal fragment orbital is therefore blocked, and significant stabilizing mixing between the 1σg and the empty 10a1-3dz2 and the 11a1-4s is also prevented. Charge donation from the  C6H6Ti  complex to the 1σu of the second  H2  molecule is thus avoided, (which could take place in the first dissociative  H2  addition and caused the H–H bond breaking). The empty 10a1 and 11a1 orbitals, with large 3dz2 and 4s character, do act to some extent as acceptor orbitals (cf. the 7% 10a1 mixing with the 1σg in Table 3), but bond breaking would require the antibonding 1σu 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 1σg 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 1σu gets filled through its strong interaction with the exposed Ti-3dxz. 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 1σg's. In addition, bond breaking requires occupation of the 1σu orbitals. In the depicted configuration the 1σu 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-3dxz, a lower lying  C6H6-e1 and the Ti-3dxy/C-pz 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 0.32 eV lower than Ti + 4H2. In the very symmetric Ti + 4H2  configuration, all the four molecules stay intact, with an average H–H bond distance and bond energy of 0.82 Å and 0.23 eV, respectively.The two most stable four-H2  addition patterns: (a) TiH2  + 3H2  and (b) Ti + 4H2. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.
(a)
(b)Table4 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 Ti–C–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 0.83 eV to 0.37 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 0.10 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 0.54 eV for the SWNT support to 0.23 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 “almost converged” 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 Eg:
(1)λ<ℏ22mEg,
where λ is the so called localization length [30], defined by a unitary operator based on a Berry phase in place of the position operator, and m is the electron mass. Qualitatively, (1) can be read as “the larger the gap, the more localized the electrons are”. 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.Table 4
Comparison  of SWNT and C6H6 supports for H2 adsorption on Ti.
Support
C6H6
SWNT [10]
preferred configuration
TiH2  + 3H2
Ti + 4H2
adsorption energy per  H2 molecule
0.23 eV
0.54 eV
first dissociative  H2 addition energy
0.37 eV
0.83 eV
Ti + 4H2: H–H distance
0.82 Å
0.84 Å


## 3.1. Orbital Interactions and Bonding in C6H6-Ti

The structure of the  C6H6-Ti complex has been theoretically [20–27] 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 C6v 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 C6v configuration. In this analysis, the  C6H6-Ti (C6v) 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 xy-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 (dz2) orbital, two 3e2 (dxy and Ti-3dx2-y2), and two 3e1* (dxz and dyz) orbitals, respectively. The important bonding interaction is between the benzene π orbitals of E1 symmetry and the Ti-3dxz,yz 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 π orbitals of E2 symmetry and the Ti-3dxy and Ti-3dx2-y2 orbitals, which are parallel to the benzene plane and little interaction of the 3dz2 with the much lower lying  C6H6-π orbital of A1 symmetry. The 3da1 (Ti-3dz2) 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.Figure 1
Orbital interaction diagram of the  C6H6Ti -C6v configuration.The fourd 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 “high-spin” 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-C2v configuration as ground state of the  C6H6-Ti compound, with the quintet-C6v (e2)2 (da1)1 (4s)1 and triplet-C6v (e2)3 (da1)1 (4s)0 configurations lying higher in energy by 0.372 and 0.242 eV, respectively. Previously, both triplet-C2v [20, 24, 26] and quintet-C6v [21–23, 25, 27, 28] states have been theoretically predicted as possible ground states. However, a quintet-C6v 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-C2v 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 C6v  C6H6  structure undergoes a deformation, characterized by a ruffling of the C6 ring (up or down displacement of the C atoms along the z-axis), Figure 1. Also, an elongation of all the C–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 C6v planar configuration may distort in two different ways towards a C2v configuration, one characterized by a displacement along the z-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 z-axis between the Ti and the displaced C atoms is reduced from the C6v value of 1.66 Å to 1.56 and 1.59 Å values of the [2 + 4] and [4 + 2] C2v configurations, respectively. Energies reported in Figure 2 are relative to the C6v structure with planar  C6H6.Figure 2
Energy diagram at DFT-OLYP level of the calculated  C6H6-Ti triplet configurations. The smooth line is a pure schematic guide between the three configurations. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.Figure3 shows the electronic structure of the  C6H6Ti  (C2v– [2 + 4]) complex. The Jahn-Teller distortion from the planar C6v to the [2 + 4] distorted C2v 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-3dz2 (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-3dx2-y2) and 3a2 (Ti-3dxy) MOs by admixing in a bonding fashion. The x-axis is perpendicular to the direction of the 2 C atoms of the [2 + 4] structure (and again the 2 C atoms of the [4 + 2] structure). The triplet C2v − [2 + 4] configuration is thus characterized by a doubly occupied 8a1-Ti-3dx2-y2 state and singly occupied 9a1-Ti-3dz2 and 3a2-Ti-3dxy states. In the alternative C2v − [4 + 2] Jahn-Teller configuration, the splitting of the e2 is reversed, the 3a2-Ti-3dxy state lies lower in energy, while the Ti-3dx2-y2 lies in higher position. Thus, the electron configuration in the distorted [4+2] geometry is characterized by a doubly occupied 3a2-Ti-3dxy state of the metal atom and a singly occupied Ti-3dx2-y2. However, in both configurations, the 3dz2 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.Figure 3
MO interaction diagram of the formation of  C6H6Ti  C2v − [2 + 4] from Ti and  C6H6. In parentheses the parentage of the levels from those of C6v  C6H6Ti (with planar  C6H6), see Figure 1. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.


## 3.2. H2 Dissociative Adsorption on C6H6-Ti

Taking the triplet C2v– [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].Figure4 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 z-axis and the  H2  bond axis perpendicular to the z-axis and in the direction of the two equivalent C atoms of the [2 + 4] configuration, which is the x-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 1.72 Å. At variance with the barrierless dissociative adsorption of  H2  on the (8,0) Ti-SWNT studied in Reference [10], a finite barrier (0.17 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 ~2 Å.Figure 4
Total energies of the  C6H6Ti[2 + 4]-H2  complex for different constrained Ti-H2  distances, measured from Ti to the center of mass of H2. H2 approaches perpendicular to the z-axis, lying along the x-axis (in the direction of the 2 C atoms of the [2 + 4] structure). The triplet and singlet states (dashed and straight line, resp.) are compared. Vertical lines indicate the equilibrium distance of 1.12 Å (straight line) and the transition point at 1.72 Å (dashed line). All energies are relative to the value of the triplet curve at large distance we indicated as zero.The  H2  lowest unoccupied orbital (LUMO) 1σu has B1 symmetry in C2v, so it cannot mix with the de2 orbitals (8a1 and 3a2 in Figure 3) or with the 3dz2 or 4s (both A1), but it mixes very strongly with the e1*-derived Ti-3dxz (the 6b1 of the  C6H6Ti  fragment). This orbital is a typical frontier orbital which is hybridized with the 4px and thereby acquires a large amplitude towards the incoming  H2. The strong interaction of 1σu and 3dxz 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 9a1α and next 3a2α of  C6H6Ti[2 + 4] of Figure 3. This is a typical example of a bond-breaking reaction, where the initially empty strongly H–H-antibonding orbital becomes occupied. The stabilization of the 1σu which makes the mixing with 3dxz 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 0.17 eV.Table 1
C6H6TiH2 MOs energies (eV). Orbital labels refer to Figure 5.
d(Ti-H2) (Å)
2.2 (↑/↓)
1.72 (↑↓)
1.17 (↑↓)
C6H6TiH2-6b1
−2.71/−1.55
−3.85
−5.64
C6H6TiH2-8a1
−11.50/−11.28
−6.53
−5.94Table 2
C6H6TiH2 MOs composition (%). Orbital labels refer to Figure 5.
d(Ti-H2) (Å)
2.2 (↑/↓)
1.72 (↑↓)
1.17 (↑↓)
C6H6TiH2-6b1
1σu
22/44
48
59
6b1-3dxz
55/42
41
33
C6H6TiH2-8a1
1σg
89/91
74
67
101-4s
3/3
8
12
9a1-3dz2
1/1
8
8a1-3dx2-y2
15Figure 5
MO diagram for the  C6H6Ti-H2  dissociative interaction. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.The interaction of H2 with a transition metal is often weak, because occupied metal orbitals have Pauli repulsion with the occupied 1σg orbital of H2, preventing H2 from coming so close that the interaction of a metal d orbital with the H2  1σu orbital can become strong. Typically another occupied metal d orbital then interacts only weakly with the high-lying H21σu, 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 1σg mixes (allowed by symmetry) with the 4s and the 3dz2 states (9a1 and 10a1 of the  C6H6Ti  fragment) but not with the 3dx2-y2 (8a1), see Table 2. The antibonding combination of 3dz2 and 1σg, 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 1σu with 3dxz 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) 1σg orbital with the Ti-3dz2, resulting in the orbital 8a1, which remains fully occupied (with the original two electrons of 1σg). This orbital is further stabilized by favorable mixing with the Ti 4s (10a1) and the Ti-3dx2-y2 (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-1σg(H2) bonding orbital 8a1 and out of the four Ti electrons two go into the Ti-1σu(H2) bonding orbital 6b1 (H–H bond breaking), while the two remaining ones reside in the largely nonbonding Ti-3dx2-y2 (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 1.72 Å between the Ti atom and the incoming  H2  molecule.Figure5 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  C2v − [2 + 4] complex described before and the hydrogen molecule with the H–H distance lengthened to the dissociated value (2.61 Å). At such a long H–H distance the 1σg (A1 symmetry in C2v) and 1σu (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  C2v − [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 Å, respectively, with a lengthened 0.84 Å bond for the second nondissociated molecule and a H–H distance of 3.22 Å for the dissociated one. The H–H distance in a free  H2  molecule is 0.74 Å. 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 0.98 Å and 1.77 Å along the z-axis and the xy-plane, respectively. The adsorbed  H2  bond length was calculated to be 0.78 Å. The first configuration is energetically favored by 0.38 eV over the second.Adsorption patterns of two  H2  molecules addition: (a)  C6H6Ti  H2-H2, (b)  C6H6Ti -2H2. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.
(a)
(b)Table3 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 0.20 eV per  H2  molecule, respectively.Table 3
Compositions of the MOs involved in the H2 donation/backdonation bonding mechanism for the adsorption of two H2 molecules on the C6H6Ti complex.
C6H6TiH2-H2
C6H6Ti-2H2
6a1
3b1
83%  H2-1σg
91%  H2-1σg (x2)
7%  C6H6TiH2-10a1
6%  C6H6Ti-6b1
6b1
6a1
87%  C6H6TiH2-6b1
85%  H2-1σg (x2)
10%  H2-1σu
4%  C6H6Ti-6a1
3b2
88%  C6H6Ti-3a2
10%  H2-1σu (x2)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 1σg with 8a1). Strong mixing of the high-lying  H2  1σu with a suitable occupied metal fragment orbital is therefore blocked, and significant stabilizing mixing between the 1σg and the empty 10a1-3dz2 and the 11a1-4s is also prevented. Charge donation from the  C6H6Ti  complex to the 1σu of the second  H2  molecule is thus avoided, (which could take place in the first dissociative  H2  addition and caused the H–H bond breaking). The empty 10a1 and 11a1 orbitals, with large 3dz2 and 4s character, do act to some extent as acceptor orbitals (cf. the 7% 10a1 mixing with the 1σg in Table 3), but bond breaking would require the antibonding 1σu 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 1σg 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 1σu gets filled through its strong interaction with the exposed Ti-3dxz. 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 1σg's. In addition, bond breaking requires occupation of the 1σu orbitals. In the depicted configuration the 1σu 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-3dxz, a lower lying  C6H6-e1 and the Ti-3dxy/C-pz 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 0.32 eV lower than Ti + 4H2. In the very symmetric Ti + 4H2  configuration, all the four molecules stay intact, with an average H–H bond distance and bond energy of 0.82 Å and 0.23 eV, respectively.The two most stable four-H2  addition patterns: (a) TiH2  + 3H2  and (b) Ti + 4H2. Hydrogen, carbon, and titanium atoms are shown in white, dark grey, and light grey, respectively.
(a)
(b)Table4 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 Ti–C–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 0.83 eV to 0.37 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 0.10 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 0.54 eV for the SWNT support to 0.23 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 “almost converged” 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 Eg:
(1)λ<ℏ22mEg,
where λ is the so called localization length [30], defined by a unitary operator based on a Berry phase in place of the position operator, and m is the electron mass. Qualitatively, (1) can be read as “the larger the gap, the more localized the electrons are”. 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.Table 4
Comparison  of SWNT and C6H6 supports for H2 adsorption on Ti.
Support
C6H6
SWNT [10]
preferred configuration
TiH2  + 3H2
Ti + 4H2
adsorption energy per  H2 molecule
0.23 eV
0.54 eV
first dissociative  H2 addition energy
0.37 eV
0.83 eV
Ti + 4H2: H–H distance
0.82 Å
0.84 Å


## 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 0.17 eV. The Ti-H2-binding energy was estimated to be ~0.4 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 1σg orbital will have Pauli repulsion with occupied metal orbitals. This prevents  H2  from coming close and interacting strongly by way of its high-lying 1σu, which could lead to breaking of the H–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 “prepares” the Ti 3d orbitals for the interaction with  H2. Notably, the Pauli repulsion, which is embodied in the antibonding interaction of the occupied 1σg of  H2  with an occupied mostly 3dz2 orbital, is relieved by the loss of the two electrons from the rising antibonding combination of the 1σg and 3dz2. These electrons are transferred to an in-phase (bonding) combination of the (originally empty) Ti 3dxz and  H2  1σu 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.



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*Source: 831872-2012-07-09.xml*