Mendeleev Communications Electronic Version, Issue 6, 1997 (pp. 213–252) A theoretical study of the mechanism of oxidative dihydrogen addition to palladium clusters Victor M. Mamaev,* Igor P. Gloriozov, Vahan V. Simonyan, Elena V. Zernova, Andrew V. Prisyajnyuk and Yurii 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 dihydrogen oxidative addition to the simplest palladium cluster has been analysed within the framework of the reaction-path Hamiltonian approximation; a planar dihydride complex has been found to form without the potential energy barrier and intramolecular degenerate exchange of the protons in the complex has been investigated. The catalytic hydrogenation of unsaturated compounds is one of the most important chemical processes currently used in chemical synthesis and in industry. Its first step involves activation of the dihydrogen molecule.Under the conditions of heterogeneous catalysis the activation is carried out as dissociative dihydrogen chemisorption on the transition metal surface leading to formation of M–H bonds.1 Under the conditions of homogeneous catalysis, in solution oxidative addition (OA) of the dihydrogen occurs to a transition metal atom within its complex and the oxidation number of the atom increases by two.2 The OA of dihydrogen to transition metal atoms and small clusters also occurs in the gas phase,3 according to mass spectrometry and ICR data.Both experimental and theoretical investigations of OA of dihydrogen to transition metal complexes and clusters as well as the dissociative chemisorption on the metal surfaces are of great interest in the development of theoretical models that might govern the creation of new, efficient catalytic systems.4 Palladium metal and its compounds are known to be very active hydrogenation catalysts,5 hence a study of them is especially important.According to the kinetic data,6 among small Pdn (n = 1–5) clusters the simplest Pd2 cluster shows the highest activity in the dihydrogen OA in the gas phase. The structures of the intermediates, transition states and products of the H2 OA to bare palladium atom, reaction (1), were calculated by ab initio quantum chemical techniques including both correlation and relativistic effects,7 as well as spin–orbit coupling.8 The geometries and energy values of the precursor complex, transition state and the reaction product (i.e., PdH2 dihydride) are given in refs. 7 and 8. We have developed the first dynamic model of reaction (1) within the framework of the reaction-path Hamiltonian approximation (RPH).9 Nakatsuji et al.considered the Pd2 + H2 reaction as the simplest model process simulating the interaction of H2 with the Pd metal surface.10 They did not intend to study the entire potential energy surface (PES), but restricted themselves to a study of a tentative model trajectory for reactant approach. Both the molecules were presupposed to be lying in the same plane, while the Pd–Pd distance was fixed at 2.75 Å.The authors showed that the mutually parallel lateral orientation appeared to be the most favourable for the reactants approaching each other. They approach along the c1–c2 line (where c1 and c2 are the mass centres of the Pd2 and H2 fragments). The calculations of the cross-sections of the PESs were made using the MC SCF formalism. A minimum on the PES was found to be as deep as 15 kcal mol–1 (here and below all energies are given with respect to the energy of the separated reactants, SR) for the structure with parameters: R(Pd–H) = 1.78 Å, r(c1–c2) = 1.5 Å, and r(H–H) = 0.85 Å.This value of r(H–H) is slightly higher than in an intact H2 molecule where r(H–H) = 0.74 Å. The authors suggest that this structure is a model of the product of physical dihydrogen adsorption by the palladium metal surface.They showed that the PES in the vicinity of this minimum is essentially flat and within the r(c1–c2) range 1.4–1.6 Å the energy is almost independent of r(H–H). Cross-sections of the PES for further scission of the H–H bond had been calculated at fixed r(c1–c2) values and r(c1–c2) = 1.5 Å appeared to be the optimum value.A second minimum on the model PES was found (E = –17.2 kcal mol–1) at r(H–H) ~ 2.1 Å, and a potential-energy barrier as high as 3.4 kcal mol–1 was shown to separate the two minima. This second minimum is related to the structure with R(Pd–H) = 1.53 Å that corresponds exactly to the R(Pd–H) distance in a free PdH molecule.11 The structure was considered to be a model of the dihydrogen chemisorbed by the palladium surface.Blomberg et al.12 investigated a different trajectory of H2 OA to the Pd2 cluster using the modified coupled-pair functional procedure and extended atomic basis sets. They suggested the H2 and Pd2 to approach in perpendicular planes while C2v symmetry was conserved. This trajectory seemed to lead to a different product without a potential-energy barrier.The product looks like a planar rhombus with bridging hydrogens, and its energy is –35.1 kcal mol–1. They computed only the energies of structures which were presupposed to correspond to the stationary points of the PES, while their geometry parameters were taken from the corresponding structures of the Pd2 + CH4 reaction. Castillo et al.13 studied these and other trajectories.They investigated four possible directions of the H2 OA to each of three lowest electronic states of the Pd2 cluster using the MC SCF formalism. Potential curves as functions of r(c1–c2) were calculated with the R(Pd–Pd) distance kept frozen at 2.75 Å (this value had been taken as the experimental distance between the atoms in the crystal lattice of metallic palladium). In particular, as in ref. 12, the deepest minimum (–65 kcal mol–1, cf. –35.1 kcal mol–1 in ref. 12) for the 1S+g term of Pd2 was found for the product obtained at the mutually perpendicular Pd + H H Pd H H (1) Pd H c1 c2 H Pd Pd H c1 c2 H Pd Pd Pd H HMendeleev Communications Electronic Version, Issue 6, 1997 (pp. 213–252) orientation of the approaching reactants, i.e.r(H–H) = 1.8 Å. The structure corresponding to the chemisorption complex from ref. 10 was the lowest of those from the planar approach if the four atoms were placed into the same plane, in agreement with ref. 10. Its energy is –37 kcal mol–1, r(H–H) = 1.16 Å, R(Pd–H) = 1.54 Å. The results cited above show the PES of the Pd2 + H2 to be of a complicated shape with several local minima, as well as possessing a relatively flat plateau.All calculations in refs. 10, 12 and 13 were carried out with fixed R(Pd–Pd) and the geometry optimisation was incomplete. In order to obtain more detailed information on the PESs and dynamical behaviour of the molecular system (MS), we have studied the mechanism of the Pd2 + H2 reaction in terms of the RPH approximation.14 The PESs were calculated using the CNDO/S2 semiempirical technique developed specially to treat systems containing transition metals.15 CNDO/S2 was parametrised on the base of either experimental data or ab initio high-level calculations and proved to be a very suitable tool for study of methane and ethane OA to Pd atom and Pd2 cluster.9,16–18 As a result of construction of the RPHs two trajectories (A and B) were discovered (Figure 1) and a connection between them was made.We have computed using the software in ref. 19 for both paths A and B: – the V0(s) potentials along the minimum-energy path (MEP), i.e. reaction path (RP), where s is the intrinsic reaction coordinate (IRC); – vibrational frequencies wi(s) of the modes orthogonal to the RP; – [B1j(s)] functions of dynamic coupling between the motion along the RP and jth orthogonal vibrational mode, which determine the RP curvature.We have found the following stationary points on the PES (Figure 1): 1. Bifurcation point (BP). The MS is of C2v symmetry. We referred it to as ‘BP’ since there are two different vectors leading to the different products (i.e., to the minima of the PES) of the OA, namely to either PR1 or PR2. EBP = –20.4 kcal mol–1, and r(H–H) = 0.89 Å, which is consistent with those of the adsorption complex in ref. 10. However, the Hessian matrix for BP has a negative eigenvalue w2 RP (wRP = 113i cm–1) corresponding to rotation of the H2 and Pd2 fragments about the c1–c2 axis. This rotation transfers the MS from trajectory A to B. 2. Transition state (TS) of C2 symmetry.ETS = –15.5 kcal mol–1, wRP = 271i cm–1. The vector corresponding to the negative Hessian eigenvalue is of the type. 3. Vicinal product (PR1) of C2 symmetry. EPR1 = –16.6 kcal mol–1. 4. Product of D2h symmetry (i.e., planar rhombic product PR2). EPR2 = –34.1 kcal mol–1. As the MS moves along the IRC from the SR toward PR2, the potential energy falls monotonously, and C2V symmetry is conserved.We have found a plateau on the PES where the norm of the energy gradient is least. The plateau contains an inflection point (IP, wRP ® 0) that must be distinguished because it lies between two other inflection points and the two RPs (A) and (B) converge smoothly at this point. EIP = –22.9 kcal mol–1. The whole mechanism of the reaction may be represented by three processes.Plots of the energy and the vibrational frequencies vs. the IRC for the three stages are shown in Figures 2–4. The first step is the formation of a BP structure from the SR (Figure 2) along the A trajectory. In the region between SR and BP (s –3) the vector corresponding to the IRC depends mainly on the variation in r(Pd–H). The modes other than stretching ones Q(Pd–Pd) (w » 120 cm–1) and q(H–H) (w » 4400 cm–1) are negligible.In the vicinity of BP six non-zero modes arise owing to the interaction between Pd2 and H2. w4 ~ 1000 cm–1 corresponds to the IRC (that is the approach of the H2 and Pd2 fragments). w5 ~ 1500 cm–1 is related to the q–(Pd–H) mode. w6 ~ 2660 cm–1 is related to the q(H–H) mode, while w3 ~ 200 cm–1 corresponds to the b-(Pd–Pd–H) mode.w2 ~ 140 cm–1 is related to the vector containing mainly the variation in R(Pd–Pd). The frequency w1 = 113i cm–1 is related to the mode. The second step, i.e., formation of PR1 from BP via TS Figure 2 The potential (thick line) and the frequencies of the normal vibrations (thin lines) along the MEP of Pd2 + H2 leading from the SR to BP. 4500 4000 3500 3000 2500 2000 1500 1000 500 0 –500 0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22 –4.5 –4.0 –3.5 –3.0 –2.5 SR BP IRC, Å×u1/2 w/cm–1 E/kcal mol–1 w6 w5 w4 w3 w2 w1 wH–H wPd–Pd 0.76 Å 2.91 Å 1.76 Å 40° 1.55 Å 2.34 Å 0.89 Å 2.63 Å 1.73 Å 0.97 Å 2.76 Å 1.71 Å 2.71 Å 99° 1.54 Å 2.31 Å 0.76 Å 2.91 Å E = 0 TS; E = –15.5 BP; E = –20.4 PR1; E = –16.6 IP; E = –22.9 PR2; E = –34.1 E = 0 Figure 1 Structures and energies of the PES stationary points and scheme of H2 OA to Pd2.The energies are expressed in kcal mol–1 and measured with respect to the energy of the SR. A B B cPdH PdH Figure 3 The potential (thick line) and the frequencies of the normal vibrations (thin lines) along the MEP of Pd2 + H2 leading from BP to PR1. The dashed line corresponds to the IRC. IRC, Å×u1/2 w/cm–1 E/kcal mol–1 w6 w5 w4 w3 w2 w1 BP TS PR1 2500 2000 1500 1000 500 0 –500 w6 w5 w4 w3 w2 w1 –15 –16 –17 –18 –19 –20 –21 –2.5 –2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0 1.5 cPdH PdHMendeleev Communications Electronic Version, Issue 6, 1997 (pp. 213–252) (Figure 3) is related to the changes in all the vectors and frequencies. Near BP the RP vector is of Q(Pd–Pd) shape. In the region between TS and BP the RP vector transforms to the mode with w2 = 270i cm–1 at TS, whereas the vector of shape at BP turns into the Q(Pd–Pd) mode with w1 = 270i cm–1. The vector with w4 frequency (i.e., the RP of the previous trajectory) becomes the b+(Pd–Pd–H) mode.In going from BP to TS the q(H–H) vector gradually turns into the q+(Pd–H) mode. Thus, in the TS–BP region the frequencies of both stretching vibrations w6[q+(Pd–H)], and w5[q–(Pd–H)] (ca. 2300 cm–1), as well as the frequencies of both the bending ones w4[b+(Pd–Pd–H)], and w3[b–(Pd–Pd–H)] (ca. 500 cm–1) become closer to one another. The other trajectory (B) is a composition of PR2 from SR via IP (Figure 4). In going from SR to IP six non-zero vibrational frequencies appear. w3–w6 correspond to four vibrations of complex shape and A1, A2, B1, B2 symmetry, respectively.The totally symmetric q(H–H) mode takes A1 symmetry and becomes the q+(Pd–H) mode. Near PR2 w6(A1) » 1700 cm–1, w5(B2)»1550 cm–1, w4(A2)»1520 cm–1, and w3(B1)»1130 cm–1. w2 of Q(Pd–Pd) mode increases to 200 cm–1 near PR2. In going from SR to IP the displacements in a(Pd–Pd–H) internals contribute mainly to the RP vector.In the vicinity of IP w1 » 500i cm–1. In the region s 0 the RP vector is represented by the mode. On the whole RP (B) C2v symmetry is conserved. In addition, we have investigated the process of permutation of the bridging hydrogens in PR2 (PR2 ® IP ® BP ® IP ® PR2). The MEP corresponding to the permutation is depicted in Figure 5. When the vibrational problem for this potential was solved, the PR2 was revealed to be of a non-classical structure.The half-width of the Boltzmann distribution function (BDF) versus q(H–Pd–Pd–H) is ca. 70° at T = 298 K. The use of the PES for SR ® IP ® PR2 ® IP ® SR for the vibrational problem gives similar results. In order to estimate the dynamic effects in the reaction of H2 OA to Pd2 we have computed the dependence of the energy of the MS against two internals: r(c1–c2) and the dihedral angle g between the Pd–c1–c2 and H–c1–c2 planes.All internals other than r(c1–c2) and g were optimized in the course of calculation of the PES. It appeared that when r(c1–c2) 1.5 Å the rotation about the c1–c2 axis had little affect on the energy of the MS (the energy changed little more than 0.4 kcal mol–1), which was evidence for free rotation of the H2 over the Pd2.Additionally, the PES of the RR2 ® IP ® BP ® IP ® PR2 was analysed with fixed R(Pd–Pd) in the range 2.3–2.9 Å depending on r(c1–c2) while r(H–H) was optimized. The results of the solution of the vibrational problem show that the half-width of the BDF for PR2 is governed by the R(Pd–Pd) bond length at T = 298 K.At R(Pd–Pd) = 2.7 Å the half-width of the BDF is equal to 0.8 Å. If R(Pd–Pd) shortens by ca. 0.2 Å the half-width of the BDF increases to 1.4 Å, and the H–H bond remains broken, since within such a range of the half-width of the BDF r(H–H) is close to 2 Å. Probably, variation of the ligand environment in dimer complexes of Pd(0), and Pd(I), leading to change in the Pd–Pd bond length, may well be an important factor governing the half-width of the BDF in the products of the H2 OA to such complexes and open up an opportunity to create efficient catalytic systems based on these complexes. References 1 G.C. Bond, Catalysis by Metals, Academic Press, New York, 1962. 2 A. E. Shilov, The Activation of Saturated Hydrocarbons by Transition Metal Complexes, Riedel, Dordrecht, 1984. 3 Small Particles and Inorganic Clusters; eds. N. Joht and E. Recknagel, Springer–Verlag, Berlin, 1991. 4 F. A. Lewis, The Palladium–Hydrogen System, Academic Press, New York, 1967. 5 N. Koga and K. Morokuma, Chem. Rev., 1991, 91, 823. 6 P. Fayet, D. M. Kaldor and J. Cox, J. Chem. Phys., 1990, 92, 254. 7 (a) J. J. Low and W. A. Goddard III, J. Am. Chem. Soc., 1984, 106, 8321; (b) J.J. Low and W. A. Goddard III, J. Am. Chem. Soc., 1986, 108, 609. 8 K. Balasubramaniam, J. Chem. Phys., 1988, 88, 6955. 9 V. M. Mamaev, I. P. Gloriozov, V. A. Khmara, V. V. Orlov and Yu. A. Ustynyuk, Dokl. Ross. Akad. Nauk, 1991, 338, 65 [Dokl. Chem. (Engl. Transl.), 1991, 338, 171]. 10 H. Nakatsuji, M. Hada and T. Yonezawa, J. Am. Chem. Soc., 1987, 109, 1902. 11 K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold, New York, 1979. 12 M. R. A. Blomberg, P. E. M. Siegbahn and M. Svensson, J. Phys. Chem., 1992, 96, 5783. 13 S. Castillo, A. Cruz, V. Bertin, E. Poulain, J. S. Arellano and G. del Angel, Int. J. Quantum Chem., 1997, 62, 29. 14 W. H. Miller, J. Phys.Chem., 1983, 87, 3811. 15 M. J. Filatov, O. A. Gritsenko and G. M. Zhidomirov, J. Mol. Catal., 1989, 54, 462. 16 V. M. Mamaev, I. P. Gloriozov, S. Ya. Ishchenko, V. V. Simonyan, E. M. Myshakin, A. V. Prisyajnyuk and Yu. A. Ustynyuk, J. Chem. Soc., Faraday Trans., 1995, 91, 3779. 17 V. M. Mamaev, I. P. Gloriozov, V. V. Simonyan, A. V. Prisyajnyuk and Yu. A. Ustynyuk, Mendeleev Commun., 1996, 146. 18 V. M. Mamaev, I. P. Gloriozov, A. V. Prisyajnyuk and Yu. A. Ustynyuk, Mendeleev Commun., 1996, 203. 19 V. V. Rusanov, I. P. Gloriozov and V. M. Mamaev, Zh. Strukt. Khim., 1993, 34, 170 (Russ. J. Struct. Chem., 1993, 34, 326). Figure 4 The potential (thick line) and the frequencies of the normal vibrations (thin lines) along the MEP of Pd2 + H2 leading from the SR to PR2. The dashed line corresponds to the IRC. IRC, Å×u1/2 w/cm–1 E/kcal mol–1 4000 3000 2000 1000 0 –1000 5 0 –5 –10 –15 –20 –25 –30 –35 –40 0 1 2 3 4 5 6 7 8 SR IP PR2 cPdH PdH cHH PdPd Figure 5 The solution of the 1D vibrational problem (thin line) with the potential of BP ® IP ® PR2 ® IP ® BP pseudo-rotation (thick line). There is also the cumulative wave function with allowance for the Boltzmann distribution at T = 298 K. IRC, Å×u1/2 E/kcal mol–1 14 12 10 8 6 4 2 0 –2 –4 –3 –2 –1 0 1 2 3 4 BP IP V(s) BP IP PR2 n = 4 The wave functions n = 3 n = 2 n = 1 n = 0 cPdH PdH Pd Pd H H Received: Moscow, 13th March 1997 Cambridge, 23rd April 1997; Com. 7/02259J
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