Theoretical study of oxidative methane addition to palladium clusters Victor M. Mamaev,* Igor P. Gloriozov, Vahan V. Simonyan, Andrew V. Prisyajnyuk and Yury A. Ustynyuk Department of Chemistry, M. V. Lomonosov Moscow State University, 119899 Moscow, Russian Federation. Fax: + 7 095 932 8846; e-mail: vmam@nmr.chem.msu.su The mechanism of oxidative addition of methane to palladium clusters has been analysed whithin the framework of the reaction- The mechanism of oxidative addition of methane to palladium clusters has been analysed whithin the framework of the reaction- path Hamiltonian approximation, and the higher catalytic activity of the cluster compared to a bare Pd atom has been elucidated. path Hamiltonian approximation, and the higher catalytic activity of the cluster compared to a bare Pd atom has been elucidated. Activation of C±H bonds in alkanes is an essential and important step in their catalytic functionalization. One of the most challenging problems in modern hydrocarbon chemistry is to find chemical processes which allow this conversion to be carried out under conditions as mild and selective as biochemical ones. 1 Oxidative addition (OA) of alkanes to either bare atoms or clusters of transition metals is one of the most promising methods of C±H bond activation. 2 Model reactions of this type have been studied by both theoretical and experimental methods. High level ab initio calculations have been performed for the structures corresponding to the most important stationary points on potential-energy surfaces (PES) for the simplest OA of methane to the first- and second-row transition metal bare atoms, 3±5 reaction (1). The results obtained opened up an opportunity to compare the catalytic activities of different transition metals. We have developed the first quantum dynamic model for reaction (1) (M = Pd) 6 within the framework of the reaction-path Hamiltonian (RPH) approximation. We have shown in ref. 6 that tunneling contributes mainly to the thermal rate constant at low temperatures. A kinetic study of both methane and ethane OA to a bare Pd atom and Pd n clusters in the gas phase has shown the simplest Pd 2 cluster to be much more active than the Pd atom. 7 Blomberg et al. 8 have performed a theoretical investigation of methane OA to the Pd 2 cluster within the ab initio framework using extended bases (augmented with the f-AOs on Pd) and electron correlation. They showed that an isolated Pd 2 cluster had a triplet term 7 kcal mol 71 lower in energy than the singlet one. In contrast, for the reactive system the triplet state proves to be less stable than the latter. According to ref. 8, a planar pseudo-square complex (PR3)HPd 2 Me corresponds to the global PES minimum. The corresponding precursor complex (PC3) and transition state (TS3) lie 8.8 and 12.9 kcal mol 71 higher in energy, respec- tively. The most interesting fact is that the saddle point (TS3) on the singlet PES is 0.8 kcal mol 71 lower in energy than the separated reactants. The cis-product and the trans-product (cis-PR2, trans-PR2) energies both calculated in the same bases proved 10.7 and 5.1 kcal mol 71 , respectively, higher than that of PR3. However, none of these structures was completely optimized, and an additional study is needed to conclude finally on the trajectory of the methane OA to the Pd 2 cluster. More recent calculations by Blomberg showed that due to a geometry optimization the energy of trans-PR2 fell below that of the PR3. 9 In general, the data from ref. 8 show good consistency with the experimental data in ref. 7. In this communication we report a detailed study of the mechanism of reactions (2) and (3) in the RPH approximation. The general approach developed in ref. 6, and the computer program for RPH construction written earlier 10 based on the semiempirical SCF CNDO/S 2 scheme 11 were employed in this study. The CNDO/S 2 formalism was developed specially to compute the PESs of reactions catalysed by transition metals. We showed earlier that for reaction (1) the CNDO/S 2 scheme reproduces quantitatively both the barrier heights and the PES stationary point structures acquired from ab initio high level calculations. 3±5 We assumed the Pd 2 cluster to be in the 1 P  g term. Preliminary test CNDO/S 2 calculations on the interatomic distance in the naked cluster have found an equilibrium at 2.91A. The frequency of Q Pd±Pd was found at 111 cm 71 . These results are consistent with ab initio data obtained with both relativistic and correlation corrections (R Pd±Pd =2.87A, o QPdPd = 121 cm 71 ). 12 Thus, the CNDO/S 2 scheme may well be used for our goals. We have computed, using the software in ref. 10, for both reaction (2) and (3): 7 the V 0 (s) potentials along the minimum energy path (MEP), i.e., reaction path (RP), leading from the reactants to the products via a transition state (TS), where s is the intrinsic reaction coordinate IRC expressed in terms of mass-weighted Cartesian coordinates [ A(amu) 1/2 ]; 7 vibration frequencies o i (s) of the modes orthogonal to the RP; 7 [B 1j (s)] functions of dynamic coupling between the motion along the RP and j-th orthogonal vibrational mode, which determine the RP curvature. We have obtained the structures and reactive energies of both cis-PR2 and trans-PR2 quite similar to those in ref. 8, while the energies of PR3 and TS3 are by ca. 10 kcal mol 71 higher than those in reaction (2) (see Figure 1). Here we will discuss the reaction (2) data in more detail. According to our results, the RP passes through the PES stationary points in the following order: precursor complex PC2, transition state TS2, intermediate pseudo-product cis- PR2, and the ultimate product trans-PR2. The structures of the stationary points are given in Figure 1, while Figure 2 displays their relative positions upon the RP. Note that the four structures are of C s symmetry. As with PC2 the two Pd atoms bind to the methane, so the PC2 minimum is three times deeper than that in reaction (1) (PC1, M = Pd; see Figure 1). In a special additional study we have found that in the course of approach of PC1, in the presence an extra bare Pd atom, either PC2 or PC3 may be formed, depending on which s v plane of the PC1 the Pd moves in. Rotation of the methane about axes perpendicular to the Pd±Pd bond in PC2 and PC3 does not change the energy of the molecular systems (MSs) by more than 1 kcal mol 71 . Therefore, the geometry of the MSs is determined by M + CH 4 M H 3 C H (1) Pd 2 + CH 4 (2) Pd Pd H 3 C H Pd Pd H CH 3 Pd 2 + CH 4 (3) 146 Mendeleev Commun. 1996