Quantum-Mechanical Study of Small Au 2 Pd n (n = 1 4) Clusters

Transcription

1 Commun. Theor. Phys. (Beijing, China) 46 (2006) pp c International Academic Publishers Vol. 46, No. 1, July 15, 2006 Quantum-Mechanical Study of Small Au 2 Pd n (n = 1 4) Clusters GUO Jian-Jun, YANG Ji-Xian, and DIE Dong Institute of Applied Physics, Xihua University, Chengdu , China (Received October 19, 2005; Revised February 8, 2006) Abstract Gold-doped palladium clusters, Au 2Pd n (n = 1 4), are investigated using the density functional method B3LYP with relativistic effective core potentials (RECP) and LANL2DZ basis set. The possible geometrical configurations with their electronic states are determined, and the stability trend is investigated. Several low-lying isomers are determined, and many of them are in electronic configurations with a high-spin multiplicity. Our results indicate that the palladium-gold interaction is strong enough to modify the known pattern of bare palladium clusters, and the lower stability as the structures grow in size. The present calculations are useful to understanding the enhanced catalytic activity and selectivity gained by using gold-doped palladium catalyst. PACS numbers: w, q, ct Key words: Au-Pd clusters, geometrical configuration, density functional method 1 Introduction The study of physicochemical properties of bimetallic clusters is nowadays an important field of research in cluster science. [1 4] This is motivated by the fact that when doping pure metals or metal surfaces with metallic heteroatoms, the new system often exhibits more favorable properties for applications than the non-doped pure metals. [5,6] One of the industrial applications is heterogeneous catalysis: enhanced catalytic activity and selectivity is often gained by using doped bimetallic catalysts. [7] Due to the unique catalytic properties, small transition metal clusters have been widely studied in recent years. [8 10] The intermetallic compounds formed by transition metals continue to be an important object of investigation because of their wide range of applications. [11,12] Especially, extreme size sensitivity of catalytic activity of supported Pd clusters is worthy of particular attention. [13] Small bimetallic clusters containing the noble-metals (Cu, Ag, and Au) have been studied by several experimental and theoretical works [14 19] and these studies have included chemical reactivity, [20 22] photoelectron spectroscopy of negative ions, [23 26] and absorption spectroscopy of embedded clusters. [27] Palladium-doped gold clusters, Au n Pd (n = 1 4), were investigated using anion photoelectron spectroscopy by Koyasu et al., [11] and judging the geometric structure of Au n Pd is likely maintained by the substitution of an Au atom by a Pd atom. The geometric, electronic, and bonding properties of Au n Pd (n = 1 7) clusters were investigated by Yuan et al. [13] Au n Pd 2 (n = 1 4) were investigated by two Pd-atom substitutions on the Au n clusters using the density functional method in our previous works. [12] In this paper, we investigate the structural properties of small Au 2 Pd n (n = 1 4), clusters using quantum-mechanical calculations. Our main objective is to determine the stable geometrical structures with their electronic states of binary Au 2 Pd n clusters. This information will be useful to understand the physical and chemical properties of the Pd-Au system. Density functional calculations are used to investigate structures and stabilities of Au 2 Pd n (n = 1 4) clusters. Effective core potentials (ECP) including relativistic effects for the palladium and gold atoms (RECP) are introduced in order to describe the inner core electrons. We use this methodology to perform the cluster geometry optimizations and testing different spin multiplicities. In Sec. 2, we briefly describe our theoretical approach. Results for the geometries of the lowest-lying isomers of Au 2 Pd n (n = 1 4) clusters are given in Sec. 3, and the stability trend is investigated in Sec. 4. Section 5 contains a summary of our results. 2 Computational Methods For DFT calculations, we adopted Becke s threeparameter hybrid exchange functional [28] with the correlation functional by Lee et al. [29] (B3LYP) as it is implemented in the GAUSSIAN 98 program. [30] In present calculation, full electron calculation for Au 2 Pd n clusters is rather time-consuming, so it is better to use an RECP and the basis sets of Hay and Martin [31] including mass-velocity, Darwin and spin-orbit coupling correction. Under this approximation, the 4s 2 4p 6 4d 10 outermost valence electrons of the Pd atom and 5s 2 5p 6 5d 10 6s 1 outermost valence electrons of the Au atom are described through the corresponding LANL2DZ basis set. 3 Geometrical Configurations 3.1 Au n (n = 2, 3) and Pd n (n = 2, 3, 4) The calculated total energy E, equilibrium distance r e, vibrational frequency ω e, and dissociation energy D e for the Pd 2 and Au 2 clusters are reported in Table 1 together with the experimental values. [8,9] Our results for The project supported by the Foundation of the Education Department of Sichuan Province of China under Grant No. 2004A117

2 156 GUO Jian-Jun, YANG Ji-Xian, and DIE Dong Vol. 46 the equilibrium distance and the vibrational frequency show good agreement with the experimental values, although changes in the D e values might be expected with the basis set. All recent Pd 2 electronic structure calculations established a triplet ground state and a singlet lowest excited state. [8] The present calculations show that the ground and first excited electronic state configurations for the Pd 2 molecule are 3 Σ + u and 1 Σ + g, respectively. For both clusters, Pd 3 and Au 3, the ground state configuration is an isosceles triangle with C 2v symmetry. The ground electronic state configuration of Pd 3 is 3 B 2, and it is 2 B 2 for Au 3. The present calculations for the Pd 4 cluster obtain a noncompact tetrahedron (a butterfly-like structure with Pd-Pd cross-bonding) ground state structure with C s symmetry in the 3 A electronic state, which could be a Jahn Teller deformation from the higher symmetrical T d structure. Our results are consistent with the previous theoretical ones reported in Refs. [8] and [9]. Satisfactory agreement indicate that our choice of density functional, effective core potential, and basis set used in current density functional calculations should be good to describing the small Pd-Au mixed clusters. Table 1 Total energy, equilibrium distance, vibrational frequency, and dissociation energy of the Au 2 and Pd 2 dimers calculated using B3LYP with the LANL2DZ basis set (experimental values [8,9] in bracket). Cluster State/group E (a.u.) r e (Å) ω e (cm 1 ) D e (ev) Pd 2 3 Σ + u /D h (2.48) (0.76) 1 Σ + g /D h Au 2 1 Σ + g /D h (2.47) 199 (191) 1.84 (2.29) 3 Σ + u /D h Au 2 Pd Figure 1 and Table 2 show the results of the isomers of Au 2 Pd obtained by one Pd atom substitutions on the Au 3 cluster. [9] The ground state (isomer I) with a triangular structure has C 2v symmetry, which shows a relaxed Au Au distance with respect to the Au 2 and Au 3 clusters equilibrium distance. This structural change already reflects the degree of distortion that one impurity atom can produce on the geometry of bare metal clusters. Isomer III of the Au 2 Pd cluster, the Au-Au bond has been broken, is in a triplet state of spin multiplicity. Linear structure comes next in energy, which could be a transition state. The linear form breaking the Au 2 bond is the least stable form. This result is consistent with the higher stability of Au 2 relative to the AuPd dimer. [11] Fig. 1 Optimized structures of Au 2Pd. The stable structures are shown with the Pd atoms depicted as darker spheres. Table 2 Properties of the Au 2Pd cluster: molecular state and point group, total energy, energy referred to isomer I, and vibrational frequency. Isomer State/group Total energy (a.u.) Referred to I (ev) Frequency (cm 1 ) I 1 A 1 /C 2v , 123, 177 II 1 Σ + /C 8v , 113, 172 III 3 B 2 /C 2v , 117, 168 III 1 Σ + g /D h , 77, Au 2 Pd 2 The trial geometries used in the geometry optimizations of the Pd 2 Au 2 cluster are rhombic, T (C 2v ), and tetrahedral geometries. In addition, we also consider a trapezoidal form obtained from the parallel approach of the Au 2 and Pd 2 dimers, and linear configurations. The calculated stable structures are shown in Fig. 2, and their properties are

3 No. 1 Quantum-Mechanical Study of Small Au 2 Pd n (n = 1 4) Clusters 157 reported in Table 3. The most stable form is a butterfly-like structure (isomer I). Isomer II in the 3 A 2 electronic state corresponds to the first excited state configuration, which is also a butterfly-like structure with Pd-Pd cross-bonding. No planar structures can be found by geometry optimization. However, there is only one linear structure for C v symmetry in the 1 Σ + electronic state, which could be a transition state. Fig. 2 Optimized structures of Au 2Pd 2. The stable structures are shown with the Pd atoms depicted as darker spheres. Table 3 Properties of the Au 2Pd 2 cluster: molecular state and point group, total energy, energy referred to isomer I, and vibrational frequency. Isomer State/group Total energy (a.u.) referred to I (ev) Frequency (cm 1 ) I 1 A 1 /C 2v , 84, 96, 130, 183 II 3 A 2 /C 2v , 81, 108, 120, 193, 205 III 1 Σ + /C v , 48, 73, 154, 191 Comparing the energy difference between the singlet- and triplet-spin configurations of Au 2 Pd 2 with the energy difference of the singlet- and triplet-spin states of the C 2v structure in the Au 2 Pd cluster (isomers I and III in Table 2), it results that the inclusion of the second Pd atom in the tetramer, lowers the singlet-triplet gap, by 0.8 ev. 3.4 Au 2 Pd 3 Fig. 3 Optimized structures of Au 2Pd 3. The stable structures are shown with the Pd atoms depicted as darker spheres. Table 4 Properties of the Au 2Pd 3 cluster: molecular state and point group, total energy, energy referred to isomer I, and vibrational frequency. Isomer State/group Total energy (a.u.) referred to I (ev) Frequency (cm 1 ) I 1 A /C s , 45, 77, 99, 100, 123, 163, 171 II 3 A 1 /C 2v , 11, 30, 72, 77, 113, 143, 151, 187 III 5 A /C s , 51, 75, 92, 103, 110, 121, 135, 178 IV 5 A /C s , 16, 54, 79, 90, 126, 139, 151, 183 The stable forms of the Au 2 Pd 3 cluster obtained from our calculations are depicted in Fig. 3, and their properties are reported in Table 4. The isomer of lowest energy is a triangular bipyramid form (C s ) in the 1 A electronic state. This geometry was the first excited state configuration for the Pd 5 cluster. [8] Isomers II with the planar structure comes next in energy, also as a stable isomer in the Pd 5 cluster optimizations. The first 2D 3D transition occurs at

4 158 GUO Jian-Jun, YANG Ji-Xian, and DIE Dong Vol. 46 isomer III with an energy change of 0.09 ev. Isomer IV might be obtained from the substitution of two Au atoms in the trapezoidal (W form) structure of the Pd 5 cluster. [8] 3.5 Au 2 Pd 4 Figure 4 and Table 5 show the isomers and properties of the Au 2 Pd 4 cluster. The square bipyramid structure (C 4v ) with breaking Pd-Pd bond in the 1 A 1 electronic state is the most stable isomer as it also occurred in the Pd 6 cluster optimizations. [8] Isomers I and II include geometries of different spin multiplicities, all related to the square Pd 4 subunit. For isomer II, the Pd-Au bonds have been broken and might be described as perturbations to the square Pd 4 cluster by the addition of two Au atoms. Planar structures of Au 2 Pd 4, isomers III, IV, V, and VI, might be obtained from the substitution of two Au atoms in the triangular structure of the Pd 6 cluster. [8] In fact, isomer III has the same geometrical structure as IV, but corresponds to a different spin multiplicity. Isomer VI in the 1 A 1 electronic state with a triangular structure and C 2v symmetry has energy 0.25 ev higher relative to the same form in a quintet state of spin multiplicity (isomer V). The planar structures show the higher stability with the two Au atoms at the outermost positions. Fig. 4 Optimized structures of Au 2Pd 4. The stable structures are shown with the Pd atoms depicted as darker spheres. Table 5 Properties of the Au 2Pd 4 cluster: molecular state and point group, total energy, energy referred to isomer I, and vibrational frequency. Isomer State/group Total energy (a.u.) referred to I (ev) Frequency (cm 1 ) I 1 A 1 /C 4v , 62, 93, 100, 104, 139, 145 II 3 B 2 /C 4v , 72, 73, 78, 80, 125, 134 III 3 A /C s , 29, 43, 75, 76, 84, 86, 116, 143, 157 IV 1 A /C s , 31, 42, 78, 79, 90, 117, 166, 183 V 5 A 1 /C 2v , 30, 32, 62, 78, 82, 89, 127, 130, 136, 188, 192 VI 1 A 1 /C 2v , 18, 34, 42, 67, 73, 83, 118, 146, Stability Trend The energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) is an important quality to characterize the clusters stability. A large energy gap corresponds to higher

5 No. 1 Quantum-Mechanical Study of Small Au 2 Pd n (n = 1 4) Clusters 159 stability. It is well known that DFT typically underestimates the HOMO LUMO gap. However, it still makes sense to examine the tendency of HOMO LUMO gap among Au 2 Pd n clusters. The calculated energy level distributions of the most stable clusters are presented in Fig. 5, and the HOMO LUMO gaps (HLG) are shown in Fig. 6. A large gap of 2.19 ev is found in the lowest form of the Au 2 Pd cluster and much smaller gap of 1.19 ev in the ground state of Au 2 Pd 4. A gap of 1.72 ev has been found in Au 2 Pd 2, which has 0.5 ev higher relative to that of Au 2 Pd 3. The curve indicates that the lower stability as the structures grow in size. Fig. 5 Energy level distributions for the ground states of Au 2Pd n clusters for n = 1 4. The unoccupied molecular orbital levels are depicted as broken line. Fig. 6 The HOMO LUMO gaps of the ground states of Au 2Pd n clusters for n = Summary The low-lying isomers of the Au 2 Pd n (n = 1 4) clusters have been investigated in this work using the density functional method B3LYP with relativistic effective core potentials (RECP) and LANL2DZ basis set. Some of the Au 2 Pd n structures and spin multiplicities were investigated for the first time. Our results show that the palladium gold interaction is strong enough to modify the known pattern of bare palladium clusters, and the lower stability as the structures grow in size. Several low-lying isomers were determined, and many of them in electronic configurations with a high spin multiplicity. The present calculations are useful to understanding the enhanced catalytic activity and selectivity gained by using gold-doped palladium catalyst. The work in this direction is currently under progress. References [1] G.M. Koretsky, K.P. Kerns, G.C. Nieman, M.B. Knickelbein, and S.J. Riley, J. Phys. Chem. A 103 (1999) [2] T.G. Taylor, K.F. Willey, M.B. Bishop, and M.A. Duncan, J. Phys. Chem. 94 (1990) [3] U. Heiz, A. Vayloyan, E. Schumacher, C. Yeretzian, M. Stener, P. Gisdakis, and N. Roesch, J. Chem. Phys. 105 (1996) [4] O.C. Thomas, W.J. Zheng, T.P. Lippa, S.J. Xu, S.A. Lyapustina, and K.H. Bowen Jr., J. Chem. Phys. 114 (2001) [5] D.M. Zehner and D.M. Goodman, Physical and Chemical Properties of Thin Metal Overlayers and Alloy Surfaces, Vol. 83, Material Research Society, Wiley, New York (1987). [6] J.A. Rodriguez, Surf. Sci. Rep. 24 (1996) 223. [7] J.H. Sinfelt, Bimetallic Catalysis: Discoveries Concepts and Applications, Wiley, New York (1983). [8] I. Efremenko and M. Sheintuch, Surf. Sci. 414 (1998) 148. [9] G. Bravo-Pérez, I.L. Garzón, and O. Novaro, Chem. Phys. Lett. 313 (1999) 655. [10] G. Bravo-Pérez, I.L. Garzón, and O. Novaro, J. Mol. Struct. (Theochem) 619 (2002) 79. [11] K. Koyasu, M. Mitsui, A. Nakajima, and K. Kaya, Chem. Phys. Lett. 358 (2002) 224. [12] J.J. Guo, J.X. Yang, and D. Die, Physica B 367 (2005) 158. [13] D.W. Yuan, Y. Wang, and Z. Zeng, J. Chem. Phys. 122 (2005) [14] K. Balasubramanian, J. Chem. Phys. 86 (1987) [15] V. Bonacic-Koutecky, L. Cespiva, P. Fantucci, J. Pittner, and J. Koutecky, J. Chem. Phys. 100 (1994) 490. [16] R. Mitric, M. Hartmann, B. Stanca, V. Bonacic- Koutecky, and P. Fantucci, J. Phys. Chem. A 105 (2001) [17] V. Kello and A.J. Sadlej, J. Phys. Chem. 103 (1995) [18] C.W. Bauschlicher Jr., S.R. Langhoff, and H. Partridge, J. Chem. Phys. 91 (1989) [19] H. Hakkinen and U. Landman, Phys. Rev. B 62 (2000) R2287.

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