J. Chem. SOC., Faraday Trans. I, 1985, 81, 1513-1525 Ab Initio Molecular-orbital Study on the Adsorption of Ethylene and Oxygen Molecules over Vanadium Oxide Clusters BY HISAYOSHI KOBAYASHI* AND MASARU YAMAGUCHI Faculty of Living Science, Kyoto Prefectual University, Shimogamo, Kyoto 606, Japan AND TSUNEHIRO TANAKA AND SATOHIRO YOSHIDA Department of Hydrocarbon Chemistry and Division of Molecular Engineering, Kyoto University, Kyoto, Japan Received 14th May, 1984 The ab initio Hartree-Fock molecular-orbital method has been used to investigate the electronic structures of a VO,H, cluster as a model for silica-supported vanadium oxide catalysts and the interactions between the cluster and ethylene and/or oxygen molecules. Wavefunctions have been obtained for the singlet ground state and the lowest triplet state formed by irradiation of ultraviolet light.The V=O bond in the triplet state is longer by 0.3 A than that in the ground state. The ethylene molecule is adsorbed in a stable form on the cluster only in the triplet state. The interaction between the cluster and oxygen is repulsive for both the singlet and triplet states. However, the coadsorption of both molecules is found to be stable for the triplet state, These results are consistent with recent experimental data, and the mechanism of electronic interactions is discussed in detail using the molecular-orbital expansion technique. Photoassisted reactions over transition-metal oxides have attracted much attention as a possible process for solar-to-chemical energy conversion, and many reports have been published.' However, most studies have been concerned with the yield or distribution of products.Only a few papers attempt to clarify the mechanism of photoassisted reactions at the molecular The elementary reaction steps and, especially, the structure of intermediates in the photo-oxidation of hydrocarbons have scarcely been discussed, although a general scheme from alkanes to aldehydes or ketones through alcohols and olefins has been pr~posed.~ In a previous experimental study2 we examined the nature of active oxygen species and the intermediates in the photo-oxidation of propene over vanadium oxide supported on silica, and proposed a mechanism initiated by photoadsorption of propene and oxygen molecules to form the first intermediate.A detailed discussion of the electronic state of the excited catalyst and of the electronic process of interaction between the catalyst and reactants, however, has remained for further study. The active state of vanadium oxide is generally recognized as an electronic triplet state and was first proposed by Kazansky et al.5 Although some evidence supporting the proposal has been reported,2v6 it remains as merely a concept explaining the observed experimental data. In the present paper we try to provide a quantum-chemical explanation of the first step in the photo-oxidation by performing an exact molecular-orbital (MO) calculation. The electronic state of the catalysts, the structure of the intermediates and electronic aspects of the catalyst-molecule interactions are discussed in detail.15131514 M.O. STUDY OF VANADIUM OXIDE CLUSTERS model A model B i model D: model E model C model G Fig. 1. Models used in the calculation. Model A is the VO,H, free cluster. The lengths of the V-0 and 0-H bonds and the V-0-H angle are taken to be 1.85 and 0.96 8, and 125", respectively. The VO, group is assumed to have tetrahedral symmetry (the 0-V-0 angle is 109.3"). The length of the V=O double bond is optimized. This optimized value is employed without further optimization in the following models for molecular adsorption. Models B-E are for ethylene adsorption. In models B and C the C=C axis of ethylene and the V=O axis of the cluster are perpendicular and T-shaped. Model C is obtained from model B by rotating the ethylene molecule by 90" around the V=O axis.Only the distance between the free cluster and the ethylene molecule is varied. The geometry of the free ethylene molecule is used throughout the calculation. In models D-G the V=O bond is inclined to the opposite side of the adsorbing molecules. In model D the V=O and C-C bonds form a trapezoid whose height is taken to be 1.8 A. In models E and G the angle c between the C,, axis of the VO, group and the line passing through the V atom and the middle of the C=C or 0=0 bond is fixed at 30". The distance between the C and V atoms is assumed to be 1.92 A in model E. Model F for oxygen adsorption is obtained from model E by replacing ethylene with oxygen. The standard values for 8 and c and the 0=0 and V-0, bond lengths are 45 and 30" and 1.44 and 1.87 8,, respectively, while other configurations are also examined.Model G is constructed from model F by adding an ethylene molecule. The angle q between the V=O axis and the line passing through the 0 atom and the middle of the C=C bond is varied. The VO-C,H, distance is fixed at the optimum value determined in models B and C.H. KOBAYASHI, M. YAMAGUCHI, T. TANAKA AND S. YOSHIDA 1515 MODELS A unit of vanadium oxide supported on silica is modeled by the VO,H, cluster, which hereafter is referred to as model A, as shown in fig. 1. Our e.s.r. and other data suggest that the active site in V205/Si02 is an isolated VO, unit rather than a V205 crystallite.' The VO, unit seems to be connected to the support, forming an 0-Si-0 linkage. Hydrogen atoms are used to saturate the valency of the oxygen atoms, which appears by a truncation of the cluster from the support. Although the cluster is improved by including silica units, the expansion of cluster size makes MO calculations on adsorption systems very difficult.The present truncation technique may not be the best, but we think it is better than a technique employing a highly charged cluster with an 0- anion instead of the OH group. Thus replacing the OSiO with the OH group is not an unreasonable approximation since we are mainly concerned with the reactivity of the V=O double bond. According to our recent experimental study, the propene molecule is thought to be adsorbed on the vanadium oxide through the C=C double bond.2 Since we are concerned with the initial modes of interaction between propene and the oxide, ethylene is used in place of propene in the present theoretical study to facilitate numerical calculations.Cluster-thylene interactions have been investigated by employing four adsorption models (models B-E), with model B the most extensively employed. In models B and C the C=C and V=O axes are perpendicular to each other, and ethylene forms an epoxide-type complex. In model D the C=C and V=O bonds constitute a trapezoid, i.e. a four-membered metallocycle. In model E ethylene is coordinated to the vanadium atom. In the latter two models, the V=O bond is inclined to the opposite side of the ethylene molecule in order to decrease steric repulsion. The oxygen molecule is assumed to be adsorbed on the vanadium atom in the side-on configuration shown in fig.1 (model F). This model is obtained from model E by replacing ethylene by an oxygen molecule. Model G shows the coadsorption state of ethylene and oxygen. METHOD OF CALCULATION The MO calculations were carried out at the Hartree-Fock (HF) level using the GAUSSIAN-80 program.8 For the triplet state the restricted HF (RHF) and unrestricted HF (UHF) methods were employed. Both methods give similar features for the free cluster, the ethylene-adsorbed cluster and the ethylene- and oxygen-adsorbed clusters with respect to the structure of stable configurations and the electron- and spin-density distributions. For oxygen adsorption a very large spin polarization occurs in the V=O group for the UHF calculation, but this is absent for the RHF calculation.Therefore we will discuss the electronic interactions mainly with reference to the RHF results, although the UHF results are also shown. The ( 1 2 ~ 6 ~ 4 4 Gaussian basis set for the vanadium atom reported by Roos et al. was contracted to [5~2pld],~ and a d orbital with the exponent 0.0885 was added to the set according to Hay.l0 In order to represent the 4p atomic orbitals (AO) a p orbital with the exponent 0.22 was added. Thus the basis set for V adopted in the present study is expressed as (12~7p54/[5~3p2d]. For the carbon and oxygen atoms and the hydrogen atom the 3-21G and 21G basis sets, respectively, were used?1516 0 - M.O. STUDY OF VANADIUM OXIDE CLUSTERS (C) .-? I 1.44 1.54 1.64 1.74 1.44 1.54 1.64 1.74 1.64 RESULTS AND DISCUSSION FREE CLUSTER The stable structures of the free cluster were calculated in both the ground (singlet) and the lowest triplet states by optimizing the V=O bond length, Both the RHF and UHF methods give a lower total energy for the triplet state when the V=O bond is elongated.An absolute comparison in energy between states with different spin multiplicities requires correlated wavefunctions beyond the HF level. In this work we examine the stable structure of clusters for the ground and triplet states individually without comparing the total energy between the two states. Fig. 2 shows the relative energy of the cluster as a function of the bond length. A value of 1.54 A was obtained for the singlet states. This agrees with the V=O bond length in the V,O, crystal.12 For the triplet state the value was calculated to be 1.84 A by means of both the RHF and UHF methods.Thus the bond length is elongated by 0.3 A. These optimal V=O bond lengths are used in later calculations for the chemisorbed clusters without further optimization. In the VOgH3 cluster the lowest twenty-nine orbitals are occupied in the singlet state as shown in fig. 3. The lowest thirteen MO (41-413) are composed of the core A 0 (the 1s to 3p A 0 of V and the 1s A 0 of 0). 419-417 are ascribed to the four 2s A 0 of 0 and 41a-420 the three 0-H bonds. 421 constitutes the V=O a-like bond,? and t The VO,H, cluster has C, symmetry. However, it is convenient to consider the VO bond as being composed of one a and two n bonds. So we refer these bonds as the ‘a-like’ and ‘n-like’ bonds.H.KOBAYASHI, M. YAMAGUCHI, T. TANAKA AND S. YOSHIDA 1517 -12 -13 b ' -14 - 15 - 1 6 -17 * 31 V = O ( f i c ] 30 LUMO O ( n ) 29 O ( n ) 28 27 26 v-0 - v- 0 25 24 23 v=o ( N v=o (fi) 21 v=o (6) - 22 Fig. 3. The energy and nature of the higher-lying MO for the VO,H, cluster. v=o (W v-0 m") SOMO 0 0 1.84 I I 1,54 I V V ground state triplet state Fig. 4. Orbital patterns for the n- and n*-like MO in the VO,H, cluster.1518 a M.O. STUDY OF VANADIUM OXIDE CLUSTERS 100 r 80 60 LO 20 ' ,y-7 , 0, '. 20 0 1.5 2.0 2.5 3.0 d&A d&A Fig. 5. Adsorption energy of ethylene on the VO,H, cluster. (a) Ground state, d = 1.54 A; (b) triplet state (RHF), d = 1.84 A; 0, model B; 0, model C; (c) triplet state (UHF). 422 and 423 the V=O n-like bonds.The higher-lying six MO (424-429) constitute the three V-0 single bonds and the three OZp lone-pair orbitals. Thus the n-like MO localizing in the V=O region are not the highest occupied MO (HOMO), while the lowest unoccupied MO (LUMO) is the corresponding n*-like MO. The orbital patterns for these two MO are shown in fig. 4(a). The triplet-state wavefunction was constructed by one-electron excitation from the bonding n-like MO to the antibonding n*-like MO, which spreads in the same plane as the n-like MO. The two SOMO are also shown in fig. 4(b). The V=O bond population decreases from 0.39 for the singlet state to 0.26 in the RHF result for the triplet state, which clearly shows a weakening of the bond. ADSORPTION OF ETHYLENE The interactions between ethylene and the free cluster were examined in both the singlet and triplet states.The changes in the total energy are shown in fig. 5 for models B and C. The distance between the oxygen atom in V=O and the carbon atoms in ethylene, do+, was varied. In the singlet state the energy increases monotonically as the molecule approaches the cluster. However, a stable intermediate is expected around 1.6 A of do.+ in the triplet state, although a potential barrier of ca. 40 kcal mol-l should be overcome.? Models B and C are compared with each other at the optimal do-c distance. The difference in energy is very small, as expected from the quasi-C,, symmetry of the free cluster. (The V04 species is of exactly C3, symmetry.) In order to understand the difference in reactivity for ethylene between the singlet and triplet states, the mode of electronic interactions has been analysed using the MO t 1 cal = 4.184 J.H.KOBAYASHI, M. YAMAGUCHI, T. TANAKA AND S. YOSHIDA 1519 C- C + n f 4 7 Fig. 6. Antibonding-orbital mixing between the n MO of ethylene and the MO localized in the V=O bond for the singlet state. expansion technique. The MO of the chemisorbed system (here V04H,-C,H4) are represented by a linear combination of the MO of the component subsystems (here VO,H, an+ C2H4). In the singlet state the n MO of ethylene mixes with the 2s A 0 of the V=O oxygen ( 4 1 7 ) and the V=O a-like MO (421). These three MO are all occupied in the respective component systems. In the chemisorption system all three orbitals constructed by mixing the bonding and antibonding modes are occupied.In this case the overall interactions bring about destabilization because of exchange repulsion among the occupied MO. The antibonding combination constructed from the 4 1 7 , 421 and n MO is shown in fig. 6 . This destabilization causes a monotonic increase in total energy. The orbital interactions for the triplet state are complicated, as shown in fig. 7. The upper part of fig. 7 shows the two SOMO, the V=O a-like MO for the V04H, cluster and the n MO of ethylene. The bonding combination of the V=O a-like bond and the ethylene IC MO is stabilized by the cluster-ethylene interaction. The corresponding antibonding combination, however, is destabilized and raised to the energy nearest to those of the SOMO even at a long cluster-ethylene distance (do-c = 2.6 A).Simultaneously, the two SOMO of the cluster are rehybridized to form two non-bonding orbitals localized on the 0 2p and V 3d AO, respectively. As a result of these changes in orbital energy the 0 2p orbital is doubly occupied in the VO,H,-C2H4 system and further stabilized by the back-donated charge transfer to the n* MO of ethylene. The new antibonding SOMO, composed of the V=O CT and ethylene n MO, is further destabilized by the approach of ethylene, and changes smoothly to an orbital localized within the V=O region. These replacements of the MO are characteristic of ethylene adsorption in the triplet state, and not only avoid electronic repulsion but also weaken both the V=O and C=C bonds. In fact the V=O bond population decreases from 0.26 for the free cluster to 0.10 for the chemisorbed state, and the C=C bond population decreases from 0.54 for a free molecule to 0.20 for the chemisorbed state.Thus the rearrangement of MO occurs in the triplet state which can not completely be described by the HF wavefunctions. However, this rearrangement also occurs in1520 M.O. STUDY OF VANADIUM OXIDE CLUSTERS SOMO SOM 0 0 SOMO Y V S O M O Fig. 7. Modes of orbital mixing between ethylene and the cluster in the triplet state. long-range interactions, and the potential barrier shown in fig. 5 is not an artifact caused by the HF wavefunetions. In order to examine other possibilities in the coordination of ethylene to the cluster, calculations have been carried out for models D and E.The results show that the interactions are repulsive even in the triplet state. The adsorption energies are calculated to be - 122(RHF) and - 106(UHF) kcal mol-l for model D, and - 118(RHF) and -95(UHF) kcal mol-1 for model E. These models are examined by single-point calculations where the distance between ethylene and the cluster is notH. KOBAYASHI, M. YAMAGUCHI, T. TANAKA AND S. YOSHIDA Table 1. Adsorption energy (AE) of the oxygen molecule on a VO,H, cluster 0 55 1.21 2.0 - 74.6 15 30 1 .44a 1 .87a - 70.9 45 30 1.44 1.87 - 35.4 45 30 1.22 1.83 - 50.3 45 30 1.33 1.85 - 36.5 45 30 1.60 1.90 -61.6 1521 a These values for the 0-0 and V-0 bond lengths are taken from ref. (15). In units of kcal mo1-I. Fig. 8. Two SOMO for the VO,H,-0, system. varied.However, we may conclude that the configurations represented by models D and E are not realistic, judging from the large negative values of the adsorption energy. According to the GVB calculations for chromyl chloride by Rappe and Goddard,13 the metallocycle is stable if the metal atom possesses more than two 0x0 bonds. Since the present VO,H, cluster possesses only one 0x0 (V=O) bond, the unfavourable interaction for model D is also consistent with their conclusion. ADSORPTION OF OXYGEN MOLECULE Adsorption of oxygen molecule is investigated using model F. The two angles (6' and r) and the 0-0 bond length (do-o) are varied. Table 1 shows the results of RHF calculations for the interactions between the cluster and the oxygen molecule. The interactions are found to be repulsive for all configurations.This repulsion is decreased by the inclination of the V=O bond to the opposite side of the oxygen molecule and the stretching of the 0-0 bond. The least unstable configuration is calculated to be 0 = 45", 5 = 30" and do-o = 1.44 A. These structural parameters are used in model G for the coadsorption of ethylene and oxygen. The two SOMO for the VO,H,-O, system are the 0 2p non-bonding orbital of the V=O bond and the n* MO of the oxygen molecule, as shown in fig. 8. As in the case of ethlene adsorption, exchange among the doubly occupied, singly occupied and vacant MO occurs as the oxygen molecule approaches. Another n* MO of the oxygen molecule is doubly occupied by donative charge transfer mainly from the V 3d,, AO, as shown in fig.9. Thus the adsorbed oxygen is formally written as O,, although the charge on the oxygen molecule is considerably less than - 1 due to a relaxation of electron density. In the UHF calculation very large spin polarization occurs for the V=O bond region, and a large negative (p) spin density appears on the V atom with a still larger1522 M.O. STUDY OF VANADIUM OXIDE CLUSTERS Fig. 9. Donative charge transfer from the V 3d A 0 to the x* MO of oxygen. Table 2. Adsorption energy (AE) of ethylene and oxygen on a VO,H, cluster 45 30 180 20.2 17.5 45 30 150 25.0 21.5 45 30 120 -28.4 - 30.4 a In units of kcal mol-l. positive value on the 0 atom. The eigenvalue of s2 is ca. 3 (for RHF results it is 2). Therefore we do not refer to the UHF results for this system. ADSORPTION OF ETHYLENE AND OXYGEN MOLECULES The calculations for the VO,H,-C,H,-O, system are carried out using model G, where the angle 7 (see fig.1) is varied to find a stable configuration. Table 2 shows that stabilization is obtained in the range 150 < q / O < 180. A slightly larger adsorp- tion energy is obtained for q = 150" than for q = 180". This result suggests that the interactions between the ethylene and oxygen molecules are attractive although their magnitude is small. The SOMO are the V 3d non-bonding orbital and the n* MO of the oxygen molecule. The orbital interactions between ethylene and the cluster and between oxygen and the cluster are qualitatively the same as those for the case of single-molecule adsorption. However, the individual interactions are strengthened by coadsorption ; the mechanism is discussed in the next section.GENERAL DISCUSSION We have examined the interactions for the individual chemisorption systems. The systems are compared with one another in order to elucidate the difference between single-molecule adsorption and coadsorption. Table 3 shows the charges estimated from Mulliken population analysis1, within the atom(s) and molecule before and after adsorption. Comparing the charge on the V and 0 atoms in the VO,H, cluster for the singlet and triplet states, we cannot confirm that the triplet state is the one-electron-transferred state from the 0 atom to the V atom. The excitation of one electron from the n-like MO to the n*-like MO certainly contributes to electron transfer to the V atom.However, reverse electron transfer occurs in the V=O a-like MO and almost completely compensates for the electron deficiency in the 0 atom. On adsorption, ethylene becomes positively charged. The electron density withdrawnH. KOBAYASHI, M. YAMAGUCHI, T. TANAKA AND S. YOSHIDA 1523 Table 3. Charges on the atom(s) and molecule before and after adsorption V 0 C2H4 0, 3(0-H) - 0.9 1 V0,H3 (singlet) +1.29 -0.38 - - 0.97 VO4H3 +1.34 -0.37 - V04H,-C2H4 +1.19 -0.66 +0.82 - - 1.35 V04H3-C2H4a + 1.20 -0.62 +0.77 - - 1.35 V04H3-02a + 1.45 -0.33 - -0.31 -0.81 V04H3-C2H4-02a +1.43 -0.66 +0.79 -0.48 -1.08 - - a V=O bond is inclined. Table 4. Changes in the MO population for the n MO of ethylene and the n* MO of ethylene and oxygen C2H4 0 2 AP(n) AP(n*) AP(n* + z * ) ~ V04H3-C,H4 (singlet) - 0.760 0.195 - -1.120 0.339 - 0.600 V04H3-C2H442 - 1 .1 4 4 0.359 0.737 - - V04H3-C2H4 V04H342 a Since the two n* MO are singly occupied before adsorption and singlet oxygen is taken as the reference state after adsorption, the tabulated value is the sum of the two n* MO populations subtracted by 2. from ethylene accumulates not only at the V=O bond region but also on the oxygen atoms represented by the OH group. Thus even local electron transfer influences the electron distribution of the whole cluster, otherwise the electron density would be accumulated within narrow regions. A comparison between the fourth and fifth rows of table 3 shows that electron transfer from the C,H, group is weakened by the inclination of the V=O axis.For the adsorption of molecular oxygen the third and sixth rows of table 3 should be compared with each other. The electron density transferred to the oxygen molecule comes from the V atom and also from the OH oxygen atoms. For the coadsorption of oxygen and ethylene the negative charge on the oxygen molecule is larger than that for the adsorption of oxygen only, i.e. charge transfer to the oxygen molecule is enhanced. The charges in the V and 0 atoms of the V=O bond are similar to those for the case of single-molecule adsorption by oxygen and ethylene, respectively. However, the charge on the 0-H group lies between the values for the two single-molecule adsorptions. These results suggest that the OH oxygen atoms work as an electron reservoir although they are not reactive to the adsorbing molecules.In order to obtain information on different aspects of the cluster-adsorbate interactions, the MO populations for important orbitals of the adsorbates are calculated. Table 4 shows the changes in population for the n and n* MO of the ethylene and oxygen molecules in the chemisorbed states. In the VO,H,-C,H, system1524 M.O. STUDY OF VANADIUM OXIDE CLUSTERS both the decrease and increase in the populations for the n and n* MO are enhanced in the triplet state, which suggests that the C=C bond of ethylene is more weakened in the triplet state. The decrease in the n MO population is larger than the increase in the II* MO population. In the case of oxygen adsorption the increase in the n* MO population of oxygen is ascribed to donative charge transfer mainly from the V 3 4 , AO.The accumulated electron density in the n* MO certainly works to weaken the 0-0 bond. On the coadsorption of both molecules the enhanced decrease in the n MO population in ethylene and enhanced increase in the n* MO population in ethylene and oxygen again suggest that coadsorption mutually strengthens the individual molecule-cluster interactions, which is favourable for the decomposition of adsorbed molecules and the reaction between them. CONCLUSION The present paper reports the electronic structures of vanadium oxide catalyst modelled by the VO,H, cluster and the interactions between the cluster and adsorbed molecules, i.e. ethylene and oxygen, from the viewpoint of quantum chemistry. The following results have been obtained by a series of ab initio MO calculations.(1) The optimal V=O bond length for VO,H, in the triplet state is longer by 0.3 A than that in the ground state. A population analysis also shows that the bond is weakened in the triplet state. (2) The triplet wavefunction is constructed by one-electron excitation from the V=O n-like MO to the n*-like MO. The V=O bond in the triplet state is not recognized as the one-electron-transferred state from 0 to V owing to a redistribution of electron density over the whole cluster. (3) Ethylene is adsorbed on the cluster in the triplet state but not in the ground state. Electronic repulsion between the II MO of ethylene and the occupied MO localized in the V=O bond region prevents stable adsorption in the ground state.In the triplet state the repulsion is considerably diminished by a rearrangement of the MO. (4) The interaction between the oxygen molecule and the cluster is repulsive even for the triplet state. The two 7t* MO of oxygen are singly and doubly occupied. Thus the adsorbed oxygen possesses anionic character but the charge on the oxygen is much less than - 1 because of relaxation of the electron density. (5) The adsorption of both ethylene and oxygen leads to a return to attractive interactions. The electron density is transferred from ethylene to oxygen through the cluster, which enhances the individual ethylene-luster and oxygensluster interactions and is considered to make the whole system stable. Information drawn from the present theoretical study may shed light on fundamental problems in heterogeneous catalysis using metal oxides, and particularly in pho t ocatal y sis.We thank the Data Processing Centre of Kyoto University for generous use of the FACOM M-200/382 computer and the Computer Centre of the Institute for Molecular Science for permission to use the HITAC M-200H computer. 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