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International Journal of Polymer Science

Volume 2012 (2012), Article ID 391325, 14 pages

http://dx.doi.org/10.1155/2012/391325

## A Theoretical Study of the Insertion of Atoms and Ions into Titanosilsequioxane (Ti-POSS) in Comparison with POSS

Department of Chemistry and Chemical Biology, Graduate School of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu 376-8515, Japan

Received 9 June 2012; Revised 26 August 2012; Accepted 26 August 2012

Academic Editor: Kensuke Naka

Copyright © 2012 Yosuke Komagata et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The insertion reaction of various guest species, such as rare gases (He, Ne, and Ar), cations of group 1 (Li^{+}, Na^{+}, and K^{+}), and anions of group 17 (F^{−} and Cl^{−}) elements, into the Ti analogues of POSS (polyhedral oligomeric silsesquioxanes), Ti-POSS, [HTiO_{1.5}]_{n} (
and 10), has been investigated by ab initio molecular orbital and density functional methods. For each case, the properties of the exohedral and endohedral complexes and transition-state structure connecting them on the potential energy surface and energetics are discussed in comparison with the case of POSS. Furthermore, in order to understand the origin of the stability of these structures, the binding energy () and the energy barrier of the encapsulation are analyzed by an energy decomposition method. As a result, some similarities and differences between Ti-POSS and POSS were explored.

#### 1. Introduction

Polyhedral oligomeric silsesquioxanes (POSS), [RSiO_{1.5}]_{n} (), referred to as T_{n}, have been the focus of considerable experimental and theoretical interest because of their wide variety of practical uses for many years [1–4]. Among a huge number of investigations for these diverse polyhedral compounds, the approach to make use of their cavity for various purposes, such as a container of atomic or molecular species [5–19], medical supplies [20, 21], molecular sieves, or a reaction filed for H_{2} formation [22], is one of the extremely attractive research areas of the POSS chemistry. In addition to many interesting experimental observations, theoretical studies have been making considerable contributions in this area. For example, there are systematic and comprehensive studies for the encapsulation of various atomic or ionic species into T_{8} and T_{10} by Hossain et al. [9, 13, 15, 16]. Furthermore, incorporation of molecular species such as H_{2}, N_{2}, and O_{2} inside T_{n} () that also been investigated by our group [5, 18, 19]. These studies must give useful information for the future design of the molecular sieve or better drug delivery.

On the other hand, metal-substituted POSS (metallasilsesquioxanes) where the skeletal silicon atoms of POSS are all or partially replaced with various metals such as group 4 (Ti, Zr, and Hf) [23–29] or other heavier group 14 (Ge Sn) [29] elements are also fascinating research targets. The titanosilsequioxanes especially (Ti-T_{n}) have extensively been studied both by experimental and theoretical chemists because of their potential as useful materials such as promising catalysts. For the experimental works, the titanium-substituted T_{8} with the TiSi_{7}O_{12} core [24, 26] and even the Si/Ti-alternated T_{8} with the Ti_{4}Si_{4}O_{12} core [23, 25] have already been synthesized and their stability or catalytic activity investigated years ago. On the other hand, not for Ti-POSS but some theoretical studies on the structures and catalytic reactions of the model compounds of titanosilicate or titanium-containing zeolites are available [30, 31]. In the past several years, therefore, we have studied the structures and catalytic ability of the titanium analogues of POSS, [HTiO_{1.5}]_{n} and H_{8}Ti_{p}Si_{8-p}O_{12} [27]. Incidentally, the experimental result [23] for the structure of the Si/Ti-alternated T_{8} is in good agreement with our calculational result [27]. Our next target is their various intramolecular reactions. Therefore, in the present study, as a continuation of our theoretical approach for Ti-POSS and to deepen our understanding for POSS, the result of the investigation for the encapsulation of various atoms and ions into Ti-T_{8 }([HTiO_{1.5}]_{8}) is shown and discussed in comparison with the case of the Si analogue, T_{8 }([HSiO_{1.5}]_{8}).

#### 2. Computational Methods

Geometry optimizations were performed for all of the molecules investigated here at the Hartree-Fock (HF) and a hybrid type of the HF and DFT theories, B3LYP [32] levels of theory. For the basis set, 6-311+G(d) [33–35] was finally chosen after the investigation of several kinds of basis sets. We have investigated the effect of six kinds of basis sets (6-31G(d), 6-311G(d), 6-31+G(d), 6-31G(d,p), 6-31+G(d,p), and 6-311+G(d)) for the geometries of exohedral and endohedral complexes between X (He and F^{−}) and Ti-T_{8} at the HF and B3LYP levels of theory. As a result, a set of p functions on hydrogen atoms is found to have small effect so it was not considered in this study. All optimized geometries were characterized as minima or transition states by normal frequency mode analyses. In addition, single point energy calculations on the optimized geometries were carried out at the second-order perturbation (MP2) [36] level of theory for a part of the system involving F^{−} to obtain more reliable energetics. Finally, the relative energies of the stationary points were corrected by considering the zero point energy (described as “+ZPC”).

Furthermore, in order to explore the origin of the stability of the stationary points on the potential energy surface of the encapsulation reactions in detail, we carried out a kind of energy decomposition for the binding energy () between the guest species and the host Ti-T_{n} cage. The is the energy accompanying the formation of complexes (exohedral and endohedral complexes, and the transition-state structures connecting them), and it is decomposed into two kinds of energy—(a) the deformation energy () of the host cage caused by the complexation, and (b) the interaction energy () between the guest species and the deformedhost cage:
The former always brings about the destabilization of the system, but even the latter is possible to contribute the destabilization (repulsion) as well as the stabilization. The “minus” value means stabilization, while “plus” does destabilization of the system relative to the referred one for the binding energy () and both energy components, and .

The is obtained as the energy difference between the deformed cage () and the optimized (empty) one (): On the other hand, the is defined as the energy difference between the complexes () and the sum of two energy components as shown as follows: As a result, the can be described as another formula as expected: All calculations were performed with the Gaussian 03 [37] and GAMESS [38, 39] electronic structure codes.

#### 3. Results and Discussion

##### 3.1. Ti-T_{8} versus Si-T_{8}

Before discussing the encapsulation reaction, it may be worth to compare some properties of the host molecule, Ti-T_{8}, (HTiO_{1.5})_{8}, with those of the Si analogue, T_{8}, (HSiO_{1.5})_{8}. Both molecules have highly symmetric O_{h} structure [27]. The geometric parameters, the averaged NBO [40]* *and the Mulliken net atomic charge of the skeletal atoms, and the energy levels of the frontier orbitals (the Kohn-Sham orbitals in the DFT results) of both molecules are shown in Table 1. As the table shows, all distances in Ti analogue are longer than those in T_{8}, suggesting Ti–T_{8} has the larger cavity compared to that of the Si analogue. It is convenient for the encapsulation of guest species as well as the extremely floppy titanoxane (Ti–O–Ti) bonds in the framework suggested by our previous study [27]. The two kinds of the bond angles, however, are very similar in both molecules.

In addition, the averaged net atomic charges in the table suggest that the Ti–O bond is less polarized compared to the Si–O, which is in agreement with our previous results for the siloxane and titanoxane compounds (H(OH)_{2}XOX(OH)_{2}H; X = Si and Ti) [29]. In the Si/Ti-mixed POSS, however, Ti atom is found to have larger positive charge than that of Si atoms [27]. As the present basis set involves the diffuse functions, absolute values of the Mulliken charge seem to be remarkably underestimated compared to those of the NBO charge.

On the other hand, the B3LYP level significantly underestimates the HOMO-LUMO gap compared to the corresponding value obtained at the HF level, as expected. According to the HF results, the HOMO is higher and LUMO is lower in Ti-T_{8} than in T_{8}, which makes the HOMO-LUMO energy gap of the T-T_{8} slightly smaller compared to that of T_{8}. Nevertheless, the figures of the orbitals, especially for HOMO, are very similar in the HF and B3LYP levels. As seen from Figure 1, the d orbitals on Ti atoms seem to play an important role for both frontier orbitals in Ti-T_{8} while the contribution of the p orbitals on oxygen atoms seems to be large in T_{8}.

##### 3.2. Insertion of Rare Gas Elements (He, Ne, and Ar)

In Scheme 1 displayed is the schematic process of the insertion of some rare gas elements and cations into Ti-T_{8}. As seen in the scheme, the guest species and Ti-T_{8} form exohedral complex (X(Ti-T_{8})) where the rare gas elements are above the center of a D_{4} ((HTiO)_{4}) face of the cage first. Then the species inserts into the host cage via the transition-state structure with keeping the same C_{4v} symmetry as the first complex. The resultant endohedral complex (X@(Ti-T_{8})) has the guest species in the center of the cage so the symmetry is as high as D_{4h} (O_{h}).

The B3LYP/6-311+G(d) geometries of these structures are depicted in Tables 2 and 3. For the exohedral complexes, as Table 2 shows, the attached species X is far from the cage (>3 Å). Also, for the endohedral complexes, the geometry of the host cage does not largely change by the inclusion of guest species except for the heaviest rare gas element in this study, Ar atom. On the other hand, for the transition-state structures (see Table 3), the geometry of the D_{4} face where the insertion takes place is remarkably expanded and the extent becomes large as the atomic radius of the guest element becomes large in the order He < Ne < Ar as expected. The other faces are not much affected as seen in the H_{2} insertion into POSS [18].

The energetics of the insertion reaction in Table 4 show that the energy barrier increases as the atomic radius of the guest element increases as expected from the geometrical change mentioned above. Apparently, the inclusion complex is less stable than the exohedral complex but that may be possible to exist because of the large release energy in all cases.

On the other hand, the binding energies () together with the result of energy decomposition are summarized in Table 5. For the rare gas elements, and the two energy components ( and ) of the exohedral complex are very small. Furthermore, the absolute values of the deformation energy () of the endohedral complex and the transition structure are much smaller than those of the interaction energy (). These results suggest that the encapsulation of the rare gas elements has just a small effect for the cage of Ti-T_{8} and the origin of the binding energy is mainly the repulsion with the cage and not the deformation of the cage.

The reaction mechanism and the structures of the stationary points are similar to those of the Si analogue by Park et al. [9].

##### 3.3. Insertion of Cations of Alkali Metal Elements (Li^{+}, Na^{+}, and K^{+})

The insertion reaction discussed next is that of the cations of three alkali metal (group 1) elements. Among these, the reaction of the Na^{+} and K^{+} resembles that of the rare gas elements and the structures of the stationary points are also similar. For the exohedral complexes, the distance between the cations and the cage is smaller than that of the rare gases as shown in Table 2. The same is true in the *r*(X-O), while the opposite (longer) is seen in the *r*(X-Ti), for the endohedral complexes. This may be explained from the electrostatic interaction between the plus charge of the guest cations and skeletal Ti^{δ+} and O^{δ−} atoms of the host. Such interaction especially in the endohedral complex of Na cation is considered to be significant as the symmetry of the structure of Na^{+}@Ti-T_{8} is reduced from D_{4h} to C_{2v}. This is in sharp contrast to the fact that the Si analogue keeps the highest symmetry in the endohedral complex, Na^{+}@T_{8} [9].

In contrast, the both complexes of Li^{+} are quite different with other cases as shown in Figure 2. There is another exohedral complex (exo-2) in addition to the normal C_{4v} structure (exo-1). As the figure shows, Li^{+} is attached on one of the skeletal oxygen atoms in “exo-2” while the cation interacts with all oxygen atoms of the D_{4} face in “exo-1” and the former is 0.6 kcal/mol less stable than the latter. Furthermore, two types of the endohedral complex (“endo-1” and “endo-2”) were located as in the case of the Si analogue [9]. The “endo-1” has the stretched cubic structure with the D_{4h} symmetry, while in “endo-2” the cage is remarkably deformed compared to “endo-1.” The large deformation of the cage in both structures is brought about by the strong interaction between Li^{+} and skeletal oxygens as indicated by the short Li–O distances of 2.181 and 2.081 Å in the planar or tetrahedral Li^{+}O_{4} moiety of “endo-1” and “endo-2,” respectively. As a result, the symmetry of “endo-2” is reduced to D_{2d}, and this is found to be more stable than “endo-1” by 2.2 kcal/mol at the B3LYP/6-311+G(d) +ZPC level. These are the same trend in the Li^{+}@T_{8 }[9].

Figure 3 shows the potential energy surface of the insertion of Li^{+} into Ti-T_{8}. The exo-2 and endo-1 are not involved in the figure. It is noteworthy that Li^{+} seems to keep some interaction with several specific oxygens during the insertion process as the transition-state structure is not symmetric with respect to the center.

The energetics of the insertion reaction of these cations can be compared with those of rare gas elements in Table 4. The energy changes with regard to atomic number in both groups resemble each other. As the atom becomes heavy in each group, the energy barrier becomes high and the endohedral complex becomes less stable. However, the stability of the endohedral complex relative to the exohedral complex is smaller in the cations compared to the rare gas elements. For the case of Li^{+}, especially the release energy is too small (2.0 kcal/mol) for Li^{+}@Ti-T_{8} to exist stably. As a result, for the encapsulation of Li^{+} in Ti-T_{8}, only the exohedral complex is predicted to be existable. On the other hand, the endohedral complex of the other cations is kinetically existable but the energy barrier is too high for the exohedral complex to isomerize to the endohedral complex at least in the room temperature.

* ** *As Table 5 shows, the deformation energy () of the exohedral complex of the cations is much larger than that of the rare gas elements as expected from the significant geometrical changes mentioned above. The host cage is considerably destabilized as suggested by the large value of , but the stabilization by overwhelms the disadvantage so the complex becomes more stable than the isolated cation and cage eventually in all cases. The large plus values of (destabilization) and large minus values of (stabilization) in the cation complexes compared to those of the rare gases may be explained from the electrostatic interaction between the plus charge of the cations and the skeletal elements. For all stationary points of the cations, as ionic radius becomes small, becomes large (destabilized) and becomes small (largely minus, stabilized) except for of the transition-state structure of K^{+}. Here, it may be interesting to compare the of isoelectronic pairs, He/Li^{+}, Ne/Na^{+}, and Ar/K^{+}. The NBO analyses [40] show the plus charge of the free cations (formally 1) is significantly reduced by the complexation, such as Li^{+} (exo-1/exo-2 : 0.777/0.912, end-1/endo-2 : 0.509/0.495), Na^{+} (exo: 0.883, endo: 0.484), and K^{+} (exo: 0.943, endo: 0.558), suggesting the considerable electrostatic interaction with the host cage and this brings about the large stability of the complexes indicated by the largely minus .

For the endohedral complex of the cations, however, the destabilization caused by the significant geometrical changes mentioned above is more serious compared to the exohedral complexes, as indicated by the larger value of . The strong interaction between the cations and skeletal atoms may be the main reason for the large as suggested from the geometrical parameters in Table 2. As a result, is still minus for the Li^{+}@Ti-T_{8} while K^{+}@Ti-T_{8} gives remarkably plus value so severe steric repulsion between the guest with large ionic radius and host may be expected in the case of K^{+}. The value of Na^{+}@Ti-T_{8} is the intermediate between the cases of Li^{+} and K^{+}. Incidentally, of the transition-state structure for the Li^{+} case is minus, −11.7 (−10.3 with ZPC) kcal/mol, too. This minus value is caused by the largely minus as shown in Table 5. This stabilization may be explained from the unique structure (Figures 2 and 3) mentioned above and makes the TS of the insertion of Li^{+} lower compared to that of the other cations and the endohedral complex kinetically unstable.

##### 3.4. Insertion of Anions of Halogen Elements (F^{−} and Cl^{−})

Next guests are the minus ions of halogen (group 7). The structures of the complexes and reaction paths of the halogen anions investigated here (especially F^{−}) are significantly different with those of the rare gas or cationic elements in the preceding sections. Incidentally, there are many comprehensive studies for the encapsulation of F^{−} into POSS, and it is well known that the endohedral complex F^{−}@T_{8} has been observed experimentally [7, 8, 12].

First, the properties of the complexes between the halogen anions and Ti cage are explained in detail. For F^{−}, as Figure 4 shows, various kinds of exohedral ((a)–(d)) and endohedral (e) complexes were located but we could not find the exohedral structure with the higher C_{4v} symmetry like the rare gas or cationic species. F^{−} tends to interact strongly with small number (1 or 2) of skeletal Ti atoms. Among these, (a) and (b) have the partial triangular bipyramidal structure so we call each of them as “axial” and “equatorial” complex, respectively (see Scheme 2). The similar exohedral complexes are observed in the Si analogue too, though the “equatorial” conformation is not an equilibrium structure [9]. F^{−} interacts with one Ti atom in (a) and (b) while it does with more than two Ti atoms in the others in Figure 4. Apparently in the diagonally bridged structures, “diagonal-bridge” (d), the Ti-T_{8} cage is considerably deformed as suggesting with the largest , so it is remarkably less stable than other isomers as seen in Table 6.

On the other hand, the structure of the endohedral complex “endo” (e) is quite interesting since F^{−} is notthe center of the cage but close to a specific skeletal Ti atom, which is completely different with the initial expectation. As a result, this complex also seems to have the partial triangular bipyramidal structure with F^{−} at the axial position in a corner of the cage. This is also different with the fact that the F^{−} is encapsulated in the center of the silicon analogue, T_{8} [9]. Nevertheless, Tossell has found that in the larger POSS such as T_{10} and T_{12} with the double-decker structure F^{−} is bound at the Si atom in a corner of the cage so the present result resembles that [12].

The distance between F^{−} and the Ti in (e) is 2.321 Å so it is rather longer than 1.814 Å in (a). As apparent from Table 6, the smallest deformation energy among the isomers suggests that this structure does not bring about such a severe energetic damage of the cage seen in the other structures. That is the reason why the endohedral complex (e) is most stable in spite of the smallest interaction energy among the five isomers. The relative stability was found to increase (−3.2 to −7.6 kcal/mol) at the more reliable MP2 level. In order to confirm whether the small space of T_{8} triggers such a unique structure, we have investigated the case of larger Ti-T_{10}. However, as Figure S1 (in Supporting Information available online at http://dx.doi.org/10.1155/2012/391325) shows, the similar endohedral (endo) complex was also located, and the F-Ti distance is ca. 0.1 Å shorter than that in “endo” (e) of Ti-T_{8}. Interestingly, in contrast, it is found that Ti-T_{6} with a smaller titanoxane cage (a prismatic shape) has a F^{−} in the center of the cage like in the case of F^{−}@T_{8} at the same B3LYP/6-311+G(d) level (see Figure S2). This means the cavity of Ti-T_{8} is large enough for a F^{−} moves rather freely compared with that of Ti-T_{6}. Therefore, the limited space of Ti-T_{8} is found not to be the reason for the strange behavior of F^{−} in the endohedral complex but the strong electrostatic interaction between F^{−} and Ti atom of Ti-T_{n} ( and 10) may be the plausible explanation. Furthermore, in consideration of the Tossell results for F^{−}@T_{n} ( and 12) [12], F^{−} seems to prefer to interact with a specific Ti or Si rather than with plural skeletal atoms at the same time if there is enough space to allow that in the cage.

On the other hand, the isomerization between “axial” and “equatorial” exohedral complexes of F^{−}(Ti-T_{8}) takes place via the transition structure also shown in Figure 4. The “equatorial” structure is less stable than “axial” by 3.6 (2.7 at the HF/6-311+G(d)+ZPC level) kcal/mol at the B3LYP/6-311+G(d)+ZPC level, while the extremely low energy barrier (0.3 kcal/mol at the HF level) needed for the isomerization to “axial” is further reduced to less than 0.1 kcal/mol at the B3LYP level. Therefore, for the exohedral complex of F^{−}(Ti-T_{8}), “axial” is the main structure but the interconversion of the two conformations is possible to take place very easily.

In contrast with the F^{−} case, the situation of the encapsulation of Cl^{−} into Ti-T_{8} cage is quite simple. The “axial” is a unique exohedral complex and the endohedral complex has a Cl^{−} at the center of the cage with the D_{4h} symmetry like those of the rare gases and K^{+} as shown in Figure 5. As seen from Table 4, the endohedral complex is less stable only by 7.7 kcal/mol than the exohedral complex. This is in sharp contrast with the fact that the endohedral complex is largely less stable than the exohedral complex in the isoelectronic Ar and K^{+} as shown in Table 4. This is explained from the small (17.3 kcal/mol) and large absolute value of the (−67.5 kcal/mol) of the endohedral complex of Cl^{−}@Ti-T_{8} (see Table 5). As a result, the endohedral complex is not so unstable compared to the other cases.

Incidentally, the deformation energy () of the complexes of F^{−} and Ti-T_{8} is larger than that of the complexes of Cl^{−} and Ti-T_{8} probably because of the larger geometrical changes. This is the same trend in the relation between Li^{+} and the heavier cations (Na^{+} and K^{+}). That is, as the element of the group is lighter (smaller), it is able to interact with specific skeletal atoms in the cage, which brings about the larger deformation of the host cage.

On the other hand, the NBO charge of Cl^{−} in the endohedral complex Cl^{−}@Ti-T_{8} is −0.427 while that of F^{−} in F^{−}@Ti-T_{8} is −0.688. This result suggests that the larger amount of minus charges is transferred from Cl^{−} to the cage compared to the case of F^{−} and the considerable electrostatic interaction between Cl^{−} and the cage because of the large ionic radius even at the center of the cage.

The last topic of this section is the reaction mechanisms of the encapsulation of the halogen anions into Ti-T_{8}. The potential energy surface of F^{−} and Cl^{−} is displayed in Figures 6 and 7, respectively. In both cases, the formation reaction of the exohedral complex (axial) is largely exothermic in energy. However, the following process is one-step reaction for Cl^{−} while two-step reaction for F^{−} because the “neighbor-bridge” structure exists between the exohedral and endohedral complexes for the latter as displayed in Figure 6. The “neighbor-bridge” complex has a diamond-shaped Ti_{2}O_{2} part in the strained structure. From the complex to the second TS (TS-2), the F^{−} falls down into the cage with pushing out the oxygen of the flexible titanoxane (Ti–O–Ti) bond to outside of the cage. As a result, the rhombus Ti_{2}O_{2} structure is broken down and the energy needed for the motion brings about the second energy barrier of the reaction. All stationary points are lower than the reactants in energy. Therefore, the encapsulation of F^{−} into Ti-T_{8} is predicted to take place rather easily. In fact, the absolute value of the (−102.1 kcal/mol) of the endohedral complex of F^{−} and Ti-T_{8} is largest among all species investigated in this study. In the silicon analogue, F^{−}@T_{8} has already been observed experimentally so the Ti analogue may also be observed in near future.

For the encapsulation of Cl^{−}, the anion inserts from the center of the D_{4} face as indicated from the TS structure in Figure 7. For the silicon analogue, Cl^{−}@T_{8}, the siloxane bond seems to be partially broken in the transition-state structure of the insertion and it could not keep the highly symmetric structure probably because of the smaller size of the cage [9]. As Figure 7 shows, the transition state “TS” for the insertion of Cl^{−} into Ti-T_{8} is higher than the reactants in energy, which is different with the F^{−} case but rather resembles to the rare gas elements and Na^{+} and K^{+} except for the fact that the endohedral complex is lower than the reactants.

##### 3.5. Comparison with POSS

Finally, we compare the present results for the insertion reactions with those of the Si analogues (T_{8}) in order to clarify the characteristics of the Ti compounds. As already mentioned frequently, the same reaction of T_{8} has been investigated comprehensively by Park et al. [9] and the results are referred to in the preceding sections. Therefore, we just mention here the comparison of energetics of the reaction of Ti-T_{8} and T_{8} at the same level of theory in Table 7.

The trend of the binding energy (), relative energies of the complexes, and the transition structures on the potential energy surface are similar for both compounds. The of the exohedral complex of all elements except for Ar is minus, suggesting that these complexes are easily formed energetically. In addition, as the element becomes heavy, the relative stability of the transition state and endohedral complex becomes small probably because of their steric repulsion. Furthermore, the steric repulsion may explain that their relative energies are always larger in T_{8} than in Ti-T_{8} as the size of the cage of the former is smaller. Only one exception is the endohedral complex of F^{−}@T_{8}. The remarkable stability may be the reason why the complex has been observed experimentally. Also, the endohedral complex (endo) of F^{−}@Ti-T_{8} is more stable than the exohedral (axial) complex though the relative stability is smaller than the Si analogue.

Furthermore, we should note that the considerably small release energy of the endohedral complex between Li^{+} and Ti-T_{8}, Li^{+}@Ti-T_{8}. This is the same trend as the corresponding silicon complex. As already noted, therefore, the inclusion complex of Li^{+} and Ti-T_{8} may be hardly observed experimentally.

#### 4. Concluding Remarks

In the present work, the insertion reaction of various guest species such as rare gas, cations of the group 1, and anions of the group 17 elements, into the Ti analogue of T_{8}, Ti-T_{8}, has been investigated in comparison with the case of the Si analogue.

For rare gas elements, the mechanism of the insertion is the same as that of the Si analogue, T_{8}; (1) formation of the exohedral complex where the atom is above the center of a D_{4} ((HTiO)_{4}) face, (2) interaction from the center of a D_{4} in the transition-state structure, and (3) formation of the endohedral complex with the atom in the center of the cage. The interaction with the host is rather small for all cases, and the energy for the encapsulation (energy barrier for the isomerization of exohedral to endohedral complexes) becomes large as the element becomes heavy.

On the other hand, for the cations of the group 1 elements, the reaction mechanism between Li^{+} and the heavier elements (Na^{+} and K^{+}) is different. The latter group is rather similar to the rare gas elements in the geometries of the complexes and transition state, but Li^{+} is found to interact with specific skeletal oxygen atoms and form two types of structures in both complexes as a result. Binding energy of all the complexes between Li^{+} and Ti-T_{8} is largely minus, suggesting that the complex of the cation and Ti-T_{8} is energetically more stable than the corresponding complex between rare gas elements and Ti-T_{8}. Furthermore, Li^{+} interacts with the skeletal oxygen strongly in the exohedral complexes and the transition state for the encapsulation, which seems to make important contribution for their stability. As a result, the final product of the reaction, an endohedral complex, Li^{+}@Ti-T_{8}, is found to be kinetically unstable so only the exohedral complex may be existable.

Finally, for the anionic species of the group 17 elements, the behavior of F^{−} is considerably unique. Several kinds of complexes are located for the reaction between F^{−} and Ti-T_{8}, while two types (exohedral and endohedral) of complexes are located for the case of Cl^{−}. It may be worth to note that especially the position of a F^{−} is not the center of the cage in the endohedral complex but it takes the quasitriangular bipyramidal conformation at a corner of the cage. This is in sharp contrast with the fact that F^{−} is in the center of the cage in the corresponding complex of the Si analogue, F^{−}@T_{8}. The same thing was also seen in the endohedral complex of F^{−}@Ti-T_{10}, while F^{−} was found to be the center of the cage in smaller Ti-T_{6}. Therefore, the larger room of the Ti-T_{8} and Ti-T_{10} compared to the corresponding Si cages as well as the strong electrostatic interaction between F^{−} and Ti atom may allow the unique structure. Furthermore, this prediction can explain the observation in F^{−}@Si-T_{10} and F^{−}@Si-T_{12} where F^{−} is bound at the corner of the cage [11, 12].

In summary, for the present encapsulation reaction of Ti-T_{8}, we found quite a few similar properties with those of the silicon analogue, T_{8}, in spite of the considerable difference in the nature of the skeletal bond and size of the cage. This means the reaction is mainly affected by the size of the host cage and not the skeletal elements. However, for the reaction of Ti-POSS, the strong interaction between the ionic species and a part of the skeletal atoms is still expected to play an important role. As an extension of the present study, therefore, an investigation of the intra-molecular catalytic reaction inside Ti-POSS is now in progress.

The discussion for the cage effect in the F^{−}@Ti-T_{n} ( and 10) (Figures S1–S3 and Tables S1 and S2), see the supplementary material available online at http://dx.doi.org/10.1155/2012/391325.

#### Acknowledgment

This work was partly supported by the “Element Innovation” Project by Ministry of Education, Culture, Sports, Science and Technology in Japan.

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