The Variety of Carbon-Metal Bonds inside Cu-ZSM-5 Zeolites: A Density Functional Theory Study

Large-scale density functional theory calculations (DFT) found various types of binding of an unsaturated hydrocarbon (C2H2 and C2H4) to a ZSM-5 zeolite extraframework copper cation. We employed the DFT calculations based on the B3LYP functional to obtain local minima of an unsaturated hydrocarbon adsorbed on one or two copper cations embedded inside ZSM-5, and then compared their stabilization energies. The DFT results show that the stabilization energies are strongly dependent on the copper coordination environment as well as configurations of two copper cations. Consequently, the inner copper-carbon bonds are influenced substantially by a nanometer-scale cavity of ZSM-5.


Introduction
Interactions between a transition metal atom and a hydrocarbon have attracted many researchers [1][2][3][4][5][6][7][8][9], because the interactions may result in an activation of the hydrocarbon. The interactions weaken the C-H and C-C bonds of a hydrocarbon, and therefore facilitate the transformation of a hydrocarbon into a more valuable species. The activation of the C-H and C-C bonds is a key in catalytic reactions in heterogeneous and homogeneous systems. Thus we need to obtain detailed information on the activation processes for the purpose of constructing a promising catalyst. One of the well-known examples is that a transition metal atom binds coordinatively to an unsaturated hydrocarbon, such as alkenes and alkynes, called Dewar-Chatt-Duncanson models [10]. In these models,  and * orbitals of an unsaturated hydrocarbon are responsible for the interactions with a transition metal cation, because these orbitals match d orbitals in terms of orbital symmetry. Such orbital interactions can result in electron transfers between the two. If  orbitals of an unsaturated hydrocarbon are depopulated through the interactions with a transition metal atom, or its * orbitals are populated, the CC bonds of unsaturated hydrocarbons are activated.
Of course the electron transfers depend on types of transition metal atom as well as its coordination environment [10]. When a transition metal atom is embedded in a nanometer-scale cavity of a host, the interactions with a guest unsaturated hydrocarbon can be further affected by host confinement. The confinement effects on the inner bond formation have been well discussed in our recent theoretical studies [11][12][13][14][15][16]. In particular, we found various types of binding of a guest molecule into copper cations enclosed in the restricted environment of a ZSM-5 zeolite [14][15][16]. Thus it is intriguing to investigate whether the zeolite confinement can have an impact on its inner catalytic reactions. Along our previous studies, we have a special interest on how a guest molecule interacts with an extraframework copper cation of the ZSM-5 zeolite, because Cu-ZSM-5 exhibits unique catalytic behaviors [17]. With respect to chemical phenomena involving unsaturated hydrocarbons inside copper-containing zeolites, they can afford to catalyze the formation of diynes from alkyenes [18] and the partial oxidization of propylene into acrolein [19]. In these catalytic reactions, alkynes and alkenes are expected to coordinate to embedded copper cations. However, our knowledge how the zeolite confinement affects the inner copper-carbon bond formation is still lacking. The clarification will contribute to construct catalysts that can form selectively a desirable product.
In this direction, one of the promising tools is computer simulations based on quantum chemistry, in particular density functional theory (DFT) methods, because DFT results can provide atomic-scale view of the metal-carbon bond formation inside a zeolite cavity. Accordingly we employed DFT calculations to analyze how the restricted environment affects the inner coordination bonds. In this study, we focus on copper-carbon bonds formed inside a nanometer-sized cavity surrounded by a tenmembered ring of copper-exchanged ZSM-5 (Cu-ZSM-5) in Figure 1. In the present study, we will discuss two issues: (a) how an unsaturated hydrocarbon (acethylene or ethylene) interacts with an extraframework copper cation of ZSM-5, and (b) factors determining characters of copper-carbon bonds formed in the restricted environment of a ten-membered ring of ZSM-5.

Computational Section
In order to investigate interactions between an unsaturated hydrocarbon (acethylene or ethylene) and an extraframework copper cation of ZSM-5, we employed a hybrid Hartree-Fock/DFT method (B3LYP) [20][21][22][23][24], in the Gaussian 03 program package [25]. ZSM-5 zeolite consists of 5-and 6-membered rings (MRs) on channel walls, and 10-MRs in the straight and sinusoidal channels, as shown in Figure 1. Note that the 10-MRs are on the order of nanometers in terms of separation between diametrically-opposed Si atoms. In this study we adopt Si 3 O 4 H 8 and Si 92 O 151 H 66 clusters as models of aluminum-free ZSM-5 (silicalite) [26], as shown in the right-hand side of Figure 1. The Si 92 O 151 H 66 model, whose terminal Si atoms are bound by H atoms, corresponds to the red part of the ZSM-5 framework [26], and contains ZSM-5 ten-MRs explicitly. The B3LYP calculation shows that the model has purple ten-MR cavities whose diametrically-opposed Si atoms are ~9.4 Å apart [14,15]. The cavity sizes are essentially identical to those observed experimentally. Thus the model is realistic to represent a 10-MR cavity of ZSM-5.   Figure 1, we constructed a Cu n -ZSM-5 model (n = 1 or 2) where a copper cation is located in the vicinity of an aluminum atom substituted for a silicon atom within the purple ten-MR. To obtain optimized geometries for an unsaturated hydrocarbon adsorbed on a copper active center inside the ZSM-5 model, we used the 6-311G* basis set for the adsorbing molecule and the Cu + cations [27][28][29], and the 6-31G* basis set for substituted Al atom and the two O atoms bound to the substituted Al atom, and are usually coordinated by the cations [30][31][32], and the 3-21G basis set for other atoms in the zeolite framework [33][34][35]. After the optimizations for an unsaturated hydrocarbon adsorbed on Cu n -ZSM-5, we estimated their stabilization energy E stabilization , defined as E(adsorbent-Cu n -ZSM-5) -E(adsorbent) -E(Cu n -ZSM-5), where E(adsorbent-Cu n -ZSM-5) is the total energy of an optimized structure for an adsorbent bound to Cu n -ZSM-5, E(adsorbent) is that of an optimized structure for an adsorbent, and E(Cu n -ZSM-5) is that of an optimized structure for Cu n -ZSM-5. In the estimation, the E stabilization values were corrected for basis set superposition errors (BSSEs) by using the counterpoise method [36]. Within the B3LYP calculations, the optimized separations between a copper cation and a framework oxygen atom fall in the range of 1.89 to 2.55 Å, being consistent with the previous DFT results [37][38][39][40][41][42][43][44]. The ranges of the calculated Cu-O separations are in good agreement with those obtained from the XRD [45] and EXAFS [46][47][48] analyses (1.98~2.56 Å). Thus the theoretical method of our choice is appropriate for the present study.

ZSM-5 containing monocopper cation (Cu 1 -ZSM-5)
3.1.1. The small monocopper zeolite model First we investigate bindings of an unsaturated hydrocarbon into a monocopper cation bound to a small zeolite framework (AlSi 2 O 4 H 8 ) for obtaining a baseline for comparison. In the small zeolite model, the monocopper cation is coordinated by two framework oxygen atoms. Using the small zeolite model, we obtained optimized geometries for the binding of an unsaturated hydrocarbon into the monocopper cation, as shown in Figure 2.  The Cu-C bond lengths were optimized to be 1.925 and 1.967 Å in the acethylene and ethylene cases, respectively. The optimized structures lie 33 kcal/mol below their dissociation limits toward an unsaturated hydrocarbon and the small zeolite model. The E stabilization values are consistent with those reported in the previous theoretical studies [49][50][51][52]. The stabilization mainly comes from inphase interactions between the d xz (Cu) orbital of the extraframework monocopper and a * orbital of C 2 H 2 or C 2 H 4 , as shown in Figure 2. Due to the orbital interactions, the Cu(I) cation can donate electrons to the empty * orbital of an unstaturated hydrocarbon. Accordingly, their CC bonds are activated by the bindings: the optimized CC bond lengths in the acethylene (1.241 Å) and ethylene (1.388 Å) cases are longer than the unperturbed cases by 0.042 Å and 0.061 Å, respectively.
The adsorbed acethylene and ethylene cannot retain liner D ∞h and planar D 2h structures, respectively. The geometrical distortions change their vabrational structures. In fact, we see in Tables 1 and 2 that calculated CC stretching vibrational frequencies in the adsorbed acethylene and ethylene are 1793.8 and 1529.4 cm -1 , respectively [53]. The values are smaller than those of free acethylene and ethylene (2001.4 and 1645.2 cm -1 , respectively). The significant decrease in the CC stretching vibrational frequencies is due to the CC bond activation. Furthermore, their bindings into the extraframework copper cation make CC stretching modes infrared (IR)-active, due to symmetry lowering. Note that CC stretching vibrational modes of free C 2 H 4 and C 2 H 2 span A g and  g + , respectively and thus the modes are IR-inactive [54,55]. Similar symmetry lowering can be seen in the symmetric CH stretching mode in the adsorbed C 2 H 2 , and thus a new IR peak appears around 3273 cm -1 after the C 2 H 2 binding into the monocopper cation [56][57][58].

Realistic Cu 1 -ZSM-5 model
In the previous section (3.1.1), we discussed how an unsaturated hydrocarbon binds into a twocoordinated copper cation by using the small zeolite model. Although we obtained a baseline of the Cu-C bindings, the information is not sufficient to fully understand inner Cu-C interactions in real Cu-ZSM-5 framework due to the variety of the copper coordination environment. The coordination environment should change d-splittings of an extraframework copper cation, and therefore the d-* interactions are influenced by the copper sites. As a result, the coordination environment should determine the attraction forces operating between the copper cation and an unsaturated hydrocarbon. ZSM-5 zeolite has 12 distinguishable tetrahedral(T)-sites in the orthogonal structure. Ref. [37] shows there is no significant difference between the relative energies of ZSM-5 where one Al atom replaces one Si atom in different T-sites. In addition, Nachtigall and Bell separately investigated CO adsorption into Cu-ZSM-5 with one substituted Al atom in different T-sites. Their extensive studies show that the interaction energies between CO and Cu-ZSM-5 as well as CO stretching frequencies change significantly, depending on Cu site types. Also they indicated that the location of the Al atom does not have influence on the binding energies. Judging from the interaction energies, binding sites for an extraframework cation inside ZSM-5 are categorized into three subgroups in Figure 3: one is a cation site near an intersection between a straight and a sinusoidal channels, denoted by I, and the others are cations located above a 5-membered and 6-membered rings of a wall along a straight channel, denoted by 5-MR and 6-MR, respectively. Along their theoretical findings, we considered the three binding sites for the Cu cation inside ZSM-5, where the substituted Al atom is located near the cation. Figure 3 shows that the copper coordination environment in the I configuration is similar to that in the small zeolite model: in the I configuration, the monocopper cation is bound to two framework oxygen atoms near the substituted Al atom. In contrast, the 5-MR and 6-MR configurations have the monocopper cations with a coordination number of 3 [16]. Due to the different copper coordination environment, their electronic configurations are different, as shown in Table 3. The coordination of a Cu(I) cation into ZSM-5 framework results in some degree of the 3d 10 →3d 9 4s 1 promotion [41]. In terms of the 3d 10 -3d 9 4s 1 promotion, there is a slight difference between the I and 5-MR (6-MR) configurations: the amount of the 4s electron in the I configuration (0.25e) is less significant than those in the 5-MR and 6-MR configurations (~0.4 e). Since we found the differences in the Cu coordination environments in the three configurations, it is interesting to investigate how the copper coordination environment affects the interactions with an unsaturated hydrocarbon. Table 3. Electronic configurations of Cu-ZSM-5 before and after the binding of an unsaturated hydrocarbon, based on natural atomic orbital analyses (NPA). Optimized structures for unsaturated hydrocarbons adsorbed on a Cu 1 -ZSM-5 model are shown in Figure 4. Table 4 tabulates key parameters for all optimized geometries. We can see in Figure 4 the same types of bindings of the unsaturated hydrocarbons into the copper cation ( 2 -fashion), irrespective of different copper coordination environment as well as types of unsaturated hydrocarbon considered. Similar binding fashions have been already reported in Refs. [49][50][51][52]. In the  2 -fashion of the C 2 H 2 (C 2 H 4 ) bindings, the optimized Cu-C and CC bond lengths are ~1.94 (~1.97) Å and ~1.24 (~1.38) Å, respectively. The CC bonds in the adsorbed unsaturated hydrocarbons are lengthened relative to the free unsaturated hydrocarbons, indicating that the Cu-C bond formation results in the CC bond activation. Interestingly the Cu-C bondings in the  2 -fashion are completely identical to those of the small model. Note that the copper coordination environments in the three configurations are also same after the bindings, in contrast to those before the bindings. Reflecting the same Cu coordination environments, the three models have similar electron configurations of the Cu(I) cation in Table 3. In addition, the amounts of electron transferring (~0.2e) upon the bindings are similar among the three configurations. However, we see slight difference between the I and 5-MR (6-MR) configurations in terms of how the electrons transfer between an unsaturated hydrocarbon and Cu-ZSM-5. In the I configuration, the 4s electron densities increase, whereas the 3d electron densities decrease. Since the two Cu-O bond lengths remain almost unchanged during the binding (Figures 3 and 4), the electron transfer is responsible for the Cu-C bond formation. On the other hand, we can see that both 3d and 4s orbitals are depopulated upon the bindings in the 5-MR and 6-MR configurations. Compared with the I configuration, the electron transfers in these configurations originate from not only the formation of the two Cu-O bonds but also significant changes in the copper coordination environments. In fact we see in Figures 3 and 4 that the Cu coordination number changes from 3 to 2, upon the bindings of an unsaturated hydrocarbon into an extraframework copper at 5-MR or 6-MR configuration. In contract, such changes in the Cu coordination number are not seen in the I configuration. Despite the same binding types in the three configurations, the stabilization energies depend on their copper coordination environment: the calculated E stabilization values in the I configuration (-34.4 (C 2 H 2 ) and -32.4 (C 2 H 4 ) kcal/mol) are more pronounced than those in the 5-MR configuration (-14.6 (C 2 H 2 ) and -14.3 (C 2 H 4 ) kcal/mol) and the 6-MR configuration (-14.4 (C 2 H 2 ) and -14.7 (C 2 H 4 ) kcal/mol). The stabilization energies in the I configuration are almost the same as those in the small zeolite models, whereas those in the 5-MR and 6-MR configurations are different. The different E stabilization values are also associated with the changes in the copper coordination environments upon the bindings. Here we consider quantitatively why the copper coordination environment plays an essential role in determining the stabilization energies. In general, an extraframework cation shifts from its original position by approaching of an adsorbent to the cation. The cation shifts destabilize a zeolite structure itself. The destabilization by the cation shifts counteracts direct attractive interactions between an extraframework cation and an adsorbent. Thus the balance between the destabilization by the cation shifts and the stabilization by the direct interactions determines a stable conformation of an adsorbent inside a zeolite. The importance of the balance has been already discussed by Nachtigall and coworkers [59,60]. We can see dependences of the destabilization on the copper coordination environment in Table 4 Table 4 indicates strong site-dependencies of the E(deform) values. In fact the E(deform) values in the I configuration (2.6 (C 2 H 2 ) and 2.3 (C 2 H 4 ) kcal/mol) are negligible relative to those in the 5-MR configuration (20.4 (C 2 H 2 ) and 17.8 (C 2 H 4 ) kcal/mol) and the 6-MR configuration (22.5 (C 2 H 2 ) and 20.3 (C 2 H 4 ) kcal/mol). The site-dependent E(deform) values are reasonable, because decreasing the copper coordination number in the 5-MR and 6-MR configurations loses attractive Cu-O interactions at some extent. Taking the different E(deform) values into account, we can understand that bindings of an unsaturated hydrocarbon to the monocopper cation in the I configurations are energetically favorable over those in the 5-MR and 6-MR configurations. Note that the deformation energies are more significant than those in the interaction with NO molecule (the E(deform) values are 1 and 8 kcal/mol for intersection and channel wall sites, respectively [41]). The larger E(deform) values suggest that the  2 -bindings require larger displacement of copper cations rather than the  1 -bindings. In this situation we demonstrated from DFT calculations that the copper coordination environment is a key factor determining the bindings of an unsaturated hydrocarbon into an extraframework monocopper cation of ZSM-5.

ZSM-5 containing dicopper active center (Cu 2 -ZSM-5)
In this section we will focus on an unsaturated hydrocarbon bound to a dicopper active center embedded in ZSM-5. In this situation, configurations of the two copper cations within a ZSM-5 cavity may be responsible for the unsaturated hydrocarbon bindings, in addition to their copper coordination environment. Experimentally the presence of Cu pairs in ZSM-5 was demonstrated by using extended X-ray absorption fine structure (EXAFS) [61][62][63] spectroscopy and X-ray power diffraction [45] studies. To fully understand behaviors of an unsaturated hydrocarbon inside a ZSM-5 cavity, it is indispensable to clarify how configurations of the two copper cations inside ZSM-5 affect the properties of adsorbed unsaturated hydrocarbons.  As shown in Figure 5 and Table 5 the optimized C 2 H 2and C 2 H 4 -dicopper complexes lie, respectively, 34.0 and 21.4 kcal/mol below the structures with the S Cu•••Cu values of ~6 Å. These DFT results clearly show that the interactions of acethylene with the dicopper active center are more significant than the ethylene case. The differences between the acethylene and ethylene additions are unique in the dicopper cases, which cannot be seen in the monocopper cases. Moreover, we can see some discrepancy in the optimized structures between the acathylene and ethylene cases: the optimized C 2 H 2 -Cu 2 -zeolite contains a - 2 :  2 Cu 2 C 2 core with a butterfly form, whereas the C 2 H 4 -Cu 2 -zeolite contains a planar - 2 :  2 core. Reflecting the structural differences, the C 2 H 2 -Cu 2 -zeolite has a smaller S Cu•••Cu value than that in C 2 H 4 -Cu 2 -zeolite. Whether the Cu 2 C 2 core has a planar or a butterfly structure can be confirmed by their IR spectra, especially their CC stretching vibrational modes (Tables 6 and 7). We see in Tables 6 and 7 that CC stretching vibrational frequencies were calculated to be 1557.1 and 1469.4 cm -1 in C 2 H 2 and C 2 H 4 adsorbed on the dicopper active center, respectively. Lower CC stretching frequencies than those in the monocopper model are ascribed to more significant CC bond activation by the dicopper active center: the optimized CC bond lengths in the acethylene and ethylene additions are 1.297 and 1.449 Å, respectively (see Table 5). More importantly, the CC stretching vibrational mode in the acethylene addition is IR-active, whereas that in the ethylene addition is IR-inactive due to the planarity of its Cu 2 C 2 core. The calculated IR data will help to determine how an unsaturated hydrocarbon binds into a dicopper active center embedded inside ZSM-5. Table 6. Calculated vibrational frequencies (cm -1 ) of CC and CH stretching modes of C 2 H 2 before and after the binding into the small dicopper zeolite model.

Realistic Cu 2 -ZSM-5 model
In section 3.2.1, we used the small dicopper zeolite model, and found differences between the dicopper and monocopper cations in terms of the interactions with an unsaturated hydrocarbon. Next we turn to dicopper active centers located in a 10-MR cavity of the realistic ZSM-5 model Al 2 Si 90 O 151 H 60 . Since copper cations usually sit near the Al substituted positions, the locations of the double Si  Al substitution within the ZSM-5 framework control the configurations of a dicopper active center. Here we consider four locations of the double substitution in Figure 6: the 2NN, 3NN,  4NN, and 5NN configurations contain the Al pairs being, respectively second, third, fourth, and fifth nearest-neighbors with respect to tetrahedral sites contained in the 10-MR. Using the different configurations of the Al pair, their initial geometries were constructed by placing each Cu apart by ~2.0 Å from two oxygen atoms bound to a substituted Al atom. After the B3LYP optimization, four configurations of the dicopper center inside ZSM-5 were obtained, as shown in Figure 6 2NN and 3NN configurations are close to those obtained by EXAFS analyses (2.47-3.13 Å). In the optimized Cu 2 -ZSM-5 structures, each Cu cation coordinates into two or three framework oxygen atoms. The Cu•••Cu separations are out of the range of a suitable span between the two copper cations into which an unsaturated hydrocarbon preferentially binds in a - 2 :  2 -fashion ( Figure 5). Note that the formation of Cu pairs in the 3NN and 2NN configurations is consistent with the Spuhler's findings [38] by means of a combined quantum mechanics/interatomic potential function technique(QM-pot).
Taking varying Cu•••Cu separations by locations of the double Si  Al substitution into account, we discuss how an unsaturated hydrocarbon binds into a dicopper active center. Figure 7 shows the optimized structures for an unsaturated hydrocarbon adsorbed on a dicopper active center embedded in a ZSM-5 model, whose key parameters are listed in Table 8. We can see in Figure 7 and Table 8 two types of binding of C 2 H 2 into a dicopper active center. In the 2NN configuration, C 2 H 2 binds into the dicopper active center in a - 1 :  1 fashion, whereas the 3NN, 4NN, and 5NN configurations have a - 2 :  2 Cu 2 C 2 core. In the 3NN, 4NN, and 5NN     In the above discussion, we found that whether the two copper cations smoothly shift determines a preferable C 2 H 2 binding fashion in a ZSM-5 cavity. Although the importance of the copper shifts can be also seen in the monocopper case, the E(deform) values in the dicopper cases (Table 8) are more pronounced than those in the monocopper cases. In addition, we found from Table 8 3NN and 2NN configurations. Therefore, the dependent E(deform) values are understandable. Reflecting the E(deform) values, the stabilization in the 4NN and 5NN configurations is less significant than that in the 3NN configuration, because the destabilization by the cation shifts diminishes the attraction by the direct interactions. Thus the variety of the Cu-C bonding characters is unique in the restricted environment of ZSM-5.  4NN and 5NN configurations are similar to that obtained in the small zeolite model: in both cases, the Cu and C atoms virtually lie in a plane. The Cu•••Cu separations in the 4NN and 5NN configurations (3.730 and 3.787 Å, respectively) are essentially identical to the equilibrium separation between C 2 H 4 and the small zeolite model (3.735 Å in Figure 5), and thus the similarity in the binding fashion is reasonable. In contrast, the optimized S Cu•••Cu values in the 2NN and 3NN configurations are 1.482 and 0.512 Å smaller than the equilibrium separation in the small dicopper zeolite model. Accordingly these configurations cannot adopt a - 2 : 2 binding fashion. Note that the - 1 : 2 binding fashion (3NN) is an intermediate between the - 1 : 1 (2NN) and - 2 : 2 (4NN and 5NN) fashions. How C 2 H 4 binds into a dicopper active center inside ZSM-5 is also followed by the balance rule. As shown in Table 8, destabilization of the Cu 2 -ZSM-5 by the C 2 H 4 binding is similar to that by the C 2 H 2 binding form a viewpoint of energetics. However, direct interactions by the C 2 H 4 binding are 11.0 kcal/mol weaker than those by the C 2 H 2 binding (see Table 5). Compared with the C 2 H 2 bindings, the importance of the destabilization by the cation shifts to determine a preferable C 2 H 4 binding fashion is more effective rather than the direct attractive C 2 H 4 -dicopper interactions.

Conclusions
We found from large-scale DFT calculations that characters of copper-carbon bonds formed inside ZSM-5 change significantly, depending on its copper coordination environment. Actually attractive interactions of an unsaturated hydrocarbon with a two-coordinated extraframework copper cation are significant relative those with a higher-coordinated copper cation. The dependences of the interactions are related with shifts of a copper cation accompanied by the bindings: the shift of a cation with a higher coordination number costs energy a lot. Thus site-preferences of two-coordinated copper cations as the unsaturated-hydrocarbon binding site are reasonable. When an unsaturated hydrocarbon binds into an embedded dicopper active center, configurations of the two copper cations are important to determine the bindings, in addition to its coordination environment. Because of the different interactions between an unsaturated hydrocarbon and a mono-or dicopper copper active center, various binding fashions ( 2 , - 1 : 1 , - 1 : 2 , and - 2 : 2 fashions) are expected in Cu-ZSM-5. The variety of characters of the copper-carbon bonds is unique in the restricted environment of a zeolite.