Density Functional Study of Cationic and Anionic Ag m Cu n (m + n 5) Clusters

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1 Commun. Theor. Phys. 57 (2012) Vol. 57, No. 3, March 15, 2012 Density Functional Study of Cationic and Anionic Ag m Cu n (m + n 5) Clusters ZHAO Shuang ( Ï), 1 LU Wei-Wei ( åå), 1 REN Yun-Lai ( ), 1 WANG Jian-Ji ( ), 1,2, and YIN Wei-Ping ( ) 1 1 School of Chemical Engineering, Henan University of Science and Technology, Luoyang , China 2 School of Chemical and Environmental Sciences, Henan Key Laboratory of Environmental Pollution Control, Henan Normal University, Xinxiang , China (Received August 29, 2011; revised manuscript received December 30, 2011) Abstract The structural and energetic properties of bimetallic Ag mcu n clusters (m + n 5) in the cationic and anionic charged states have been investigated by density functional theory with relativistic effective core potentails. The stable cationic pentamers have three-dimensional structures in contrast to anionic clusters assume planar structures. For the given cluster size the electron affinities decrease as the Cu content increases, while no clear trend can be found in adiabatic ionization potentials. The binding energy per atom also increases with the increasing Cu content and follows the order anion < cation. The most probable dissociation channels of the clusters considered are also discussed. PACS numbers: Wa Key words: bimetallic clusters, density functional theory, Ag, Cu 1 Introduction The nanoparticels and clusters of coinage-metals Cu, Ag, and Au have attracted considerable attentions due to their importance in basis research, as well as technological applications such as catalysis, electrochemistry and medical science. [1 6] In the last decades a number of studies of bimetallic coinage clusters have been performed because the mixed coinage metals often exhibit more especial properties than pure coinage clusters. [7 12] Among the candidate systems to be considered, the bimetallic Ag/Cu clusters have been the topic of some experimental and theoretical studies. [13 18] A recent experiment has suggested that counterelectrodes made of the mixed Ag/Cu nanoparticles had four times higher ionic migration resistance in comparison with counterelectrodes made only of Ag nanoparticles. [13] Jiang et al. performed density functional calculations on the charge distributions and stability of Cu n 1 Ag clusters with n = 2 8 in neutral and cationic states. [14] Their results reveal that all neutral and cationic Cu n 1 Ag clusters can be derived from a substitution of the peripheral position occupied by Cu atom with an Ag atom in the corresponding Cu n clusters. The geometries of the most stable Ag m Cu n neutrals up to five atoms have been theoretically determined by Papageorigiou et al. [17] It is found that planar structures are favored, triangular for trimers, rhombic for tetramers and trapezoidal for pentamers. Lou et al. investigated the interaction between the atomic hydrogen and neutral Ag n Cu m (n+ m 5) clusters using density functional methods and found that the hydrogen adsorption energies increase with the increasing Cu composition. [18] Compared with neutral clusters, it is much more straightforward to study the properties of ionic clusters in experimental. However, no systematic theoretical study of the charged Ag/Cu bimetallic clusters considering the effects of charge state and composition has been reported to our knowledge. Here, we present a theoretical study of the cationic and anionic Ag m Cu n clusters (m + n 5) by the first-principles method based on the density functional theory (DFT). The ground state structures and their isomers are predicted. The energy difference between a given isomer and the ground state is also given. The ionization potentials, electron affinities, binding energies, and the possible dissociation channels of the Ag m Cu n cations and anions are investigated and discussed. We find some interesting trends in the energetic properties with changing the composition of the bimetallic clusters. This paper is organized as follows. Section 2 gives a brief description of the computational details. Main results and discussions are presented in Sec. 3 and followed by a summary in Sec Computational Details The calculations are carried out using GAUSSIAN 03 package. [19] The Becke s three parameter hybrid exchange functional [20] with the correlation functional by Lee et al. [21] was employed for all the calculations in this study. The Los Alamos relativistic effective core potential (RECP) plus DZ basis set [22] augmented with the f polarization functions [23] were used for Ag (f exponent, 1.611) and Cu (f exponent, 3.525) atoms. To calibrate the accuracy of this approach, we calculated the spectroscopic parameters of the smallest Ag 2, Cu 2, and AgCu clusters. The B3LYP calculation results in Table 1 show Supported by the National Natural Science Foundation of China under Grant No and the Fund for Doctorates of Henan University of Science and Technology Corresponding author, jwang@henannu.edu.cn c 2011 Chinese Physical Society and IOP Publishing Ltd

2 No. 3 Communications in Theoretical Physics 453 good agreement with experimental values. All calculations were performed with (99, 590) pruned grid (ultrafine grid as defined in Gaussian 03). Vibrational frequency calculations were performed to guarantee the optimized structures locating the minima, not as transition structures. Table 1 Comparisons of the calculated bond lengths (R in Å), binding energies (E b in ev) and frequencies (in cm 1 ) of Ag 2, Cu 2 and AgCu dimer. R Eb Freq Species B3LYP exp B3LYP exp B3LYP exp Ag [28] [29] [28] AgCu [27] [27] [31] Cu [28] [30] [28] 3 Results and Discussions 3.1 Geometries The natural bond orbital (NBO) population analyses [24] indicates that the Ag and Cu atoms possess 0.02e and 0.02e in AgCu dimer, whereas the respective Ag and Cu atoms bare 0.52e and 0.48e in the cationic AgCu +, 0.53e and 0.47e in the anionic AgCu. For AgCu dimer, we found an Ag-Cu bond length of 2.57 Å, agrees well with previous theoretical result of 2.62 Å. [15] AgCu + has a bond length of 2.60 Å, exactly between the B3LYP results of Ag + 2 (2.80 Å) and Cu+ 2 (2.42 Å). For both Ag 2 Cu + and AgCu + 2 only one energy minimum was obtained, each has triangular structure (see Fig. 1). The calculated Ag-Cu-Ag angle is 64.8 and the Cu atom exhibits +0.27e NBO charge. In the singlet ground state of AgCu + 2 the Cu-Ag-Cu angle is 55.7 and the Ag atom possesses +0.39e. All stable anionic trimers have linear structures with the one in which Cu atoms occupying the middle positions more stable. The energy difference between the ground state and the next stable isomer is 0.18 and 0.19 ev for Ag 2 Cu and AgCu 2, respectively. Fig. 1 Structures and relative energies (in ev) for the stable cationic and anionic bimetallic trimers. Fig. 2 Structures and relative energies (in ev) for the stable cationic bimetallic tetramers.

3 454 Communications in Theoretical Physics Vol. 57 Fig. 3 Structures and relative energies (in ev) for the stable anionic bimetallic tetramers. Fig. 4 Structures and relative energies (in ev) for the stable cationic bimetallic pentamers.

4 No. 3 Communications in Theoretical Physics 455 For tetramers the rhombuses and Y-shaped structures can represent local minima of cations and anions, while the stable linear structures can only be found for anions. In the most stable structures of Ag 3 Cu + the Cu atom is located at the short diagonal of rhombus. The silver atoms tend to occupy outer positions while the Cu atoms tend to occupy interior positions and form a higher number of bonds. Such topologies are due to the smaller atomic radius of Cu than Ag so as to easily reduce geometrical resconstruction and have been interpreted in the previous study of neutral Ag/Cu clusters. [14,18] It is noticed that for cationic Ag 3 Cu + tetramer, the next stable rhombus and the lowest Y-shaped structure have almost equal energies according to B3LYP functional. For anionic Ag 3 Cu the B3LYP calculation indicated that the Y-shaped structure with Cu atom in the central is the most favorable. Next higher in energy is the linear structure with Cu atom being doubly coordinated to Ag atoms. However, the energy difference between the two structures is only 0.01 ev. The lowest energy structures of Ag 2 Cu + 2 and Ag 2Cu 2 tetramers both assume rhombic forms in which the two Cu atoms are located at the short diagonal, which favors short distances of Cu-Cu bonds. The similar rhombus topology has also been reported for Ag 2 Au 2 clusters [11] by Bonačić Koutecký et al. The Au atom occupies the outer position analogical to Ag atom in the charged Ag 2 Cu 2 clusters. In Ag 2 Cu 2 we can have three different rhombuses, four Y-shaped structures and four linear structures. The energy differences of the first four stable isomers are within 0.10 ev. The most stable tetramers with a single Ag atom are characterized by low coordination of Ag. For cationic AgCu + 3 clusters the Ag atom is located at the long diagonal of the rhombus. In the case of the anionic AgCu + 3 the rhombic structure with the Ag atom at the long diagonal is only 0.06 ev more stable than the Y-shaped structure with Ag atom connected to only one Cu atom. Fig. 5 Structures and relative energies (in ev) for the stable anionic bimetallic pentamers. As shown in Fig. 5, in most cases stable anionic pentamers assume planar trapezoidal structures with triangular subunits, which is similar to the case of neutral pentamers. [17 18] In all anionic pentamers the isomers in which one Cu atom keeps four-coordinated are more stable than the isomers in which the Cu atom is less coordinated. In contrast to anionic species, all the stable cationic pentamers prefer three-dimensional structures. The lowest energy form of Ag + 5 has D 2d symmetry, [25 26] and can be looked upon as two Ag 2 units cross-linked by a central

5 456 Communications in Theoretical Physics Vol. 57 silver atom. It is noted that the most stable Ag 4 Cu +, Ag 3 Cu + 2, Ag 2Cu + 3, and AgCu+ 4 can be viewed as the replace of Ag with Cu atoms in the Ag 2 unit of the D 2d structure, with copper the central atom in all cases. For AgCu + 4 Jiang et al. characterized a trigonal bipyramid with a peripheral position occupied by an Ag atom to be the global minimum, [14] however, with present study this structure is the least stable isomer. 3.2 Adiabatic Ionization Potentials and Electron Affinities Table 2 The calculated adiabatic ionization potentials (AIPs) and electron affinities (EAs) in ev of bimetallic Ag/Cu clusters. Species AIP EA AgCu Ag 2 Cu AgCu Ag 3 Cu Ag 2 Cu AgCu Ag 4 Cu Ag 3 Cu Ag 2 Cu AgCu From the data of Table 2 it is observed that the adiabatic ionization potentials (AIPs) of the bimetallic clusters with even number of electrons are higher than their neighboring clusters with odd number of electrons, while quite the reverse for electron affinities (EAs), which reflects the higher stability of the clusters with closed electron shells. For the given cluster size the EAs decrease as the Cu content increases. This indicates that the substitution of Cu with Ag atoms in anionic cluster makes the anions easier to lose electrons. In contrast to EAs, there is no clear trend in AIPs. When increase the number of Cu atoms from 1 to 2, the AIPs decrease in trimers, while increase in tetramers and pentamers. The adding of the third Cu atom in tetramers has almost no changes on the value of AIPs. For pentamers the AIPs show a maximum at 60% Cu composition. 3.3 Binding Energies For the charged clusters, the binding energy corresponds to the way in which the charge is carried away by the Ag atom is defined by E b (Ag ± ) = [(m 1)E Ag + E Ag ± + ne Cu E Agm Cu ± ]/m + n, while the binding energy corresponds to the way in which the charge is car- n ried away by the Cu atom is defined by E b (Cu ± ) = [(n 1)E Cu + E Cu ± + me Ag E Agm Cu ± ]/m + n. The n calculated binding energy per atom of the charged clusters versus the number of Cu atoms is displayed in Fig. 6. As shown in Table 1, experimentally, the E b of Cu 2 is larger than that of Ag 2, and the E b of AgCu dimer is in between that of Ag 2 and Cu 2 clusters. Thus we may expect that E b of the charged bimetallic Ag/Cu cluster tends to increase with increasing number of Cu atoms. Indeed, as shown in Fig. 6, the binding energies of the bimetallic clusters increase with increasing number of Cu atoms for the given cluster size, irrespective of the charge state. It is also observed that with the same cluster size and same composition, the binding energy per atom of anion is smaller than that of the cation. Furthermore, the binding energy involves of the charged Cu ion is larger than the binding energy involves of the charged Ag ion for both anions and cations, which is due to the larger ionization potential and smaller electron affinity of Cu than Ag. Fig. 6 Binding energy per atom (E b (Cu + ) of cation ( ), E b (Ag + ) of cation ( ), E b (Cu ) of anion ( ), E b (Ag ) of anion ( ), vs. the number of Cu atoms (m) for trimers (a), tetramers (b), and pentamers (c). 3.4 Dissociation Channels The most probable dissociation channels and the corresponding dissociation energies (D e ) of the most stable clusters calculated by B3LYP functional are shown in Table 3. We define the dissociation energy (D e ) as D e = E(Ag a Cu ± b ) + E(Ag m acu n b ) E(Ag m Cu ± n ), a m, b n. The most favorable dissociation channel corresponds to the minimum dissociation energy. A general odd-even behavior of the dissociation energies implies that the bimetallic clusters with even number of electrons are usually more stable with respect to bond dissociations in comparison with their neighbors with odd number of

6 No. 3 Communications in Theoretical Physics 457 electrons. For cationic Ag m Cu + n, the energetically lowest dissociation channel corresponds to the loss of an Ag + ion for dimer and trimer while the loss of a single Ag atom for tetramer. For cationic pentamers the ejection of Ag 2 dimer is the most preferred except for AgCu + 4 whereby the ejection of the bimetallic AgCu dimer is the most preferred. Coming to anionic Ag m Cu n, the preferred decay channel is to eject an Ag ion for dimer and trimer while a single Ag atom for tetramer. For anionic pentamers, the ejection product changes from Ag 2 dimer for Ag 4 Cu to bimetallic AgCu dimer for Ag 3 Cu 2 to Cu 2 dimer for Ag 2 Cu 3 and AgCu 4, showing an increasing tendency of ejecting Cu-containing products as the number of Cu atoms increases. In general, for the given cluster size the dissociation energies of bimetallic clusters increase as the number of Cu atoms increases, indicating that the dissociation becomes more and more difficult with the increasing Cu composition. Table 3 The most probable dissociation channels and the corresponding dissociation energies of the most stable Ag/Cu clusters in cationic and anionic states (D e in ev). Dissociation channel D e Dissociation channel D e AgCu + Cu + Ag AgCu Cu + Ag 1.51 Ag 2 Cu + AgCu + Ag Ag 2 Cu AgCu + Ag 1.85 AgCu + 2 Cu 2 +Ag AgCu 2 Cu 2 + Ag 1.72 Ag 3 Cu + Ag 2 Cu + +Ag 1.05 Ag 3 Cu Ag 2 Cu +Ag 1.07 Ag 2 Cu 2 + AgCu + 2 +Ag 1.15 Ag 2 Cu 2 AgCu 2 +Ag 1.25 AgCu + 3 Cu + 3 +Ag 1.11 AgCu 3 Cu 3 +Ag 1.39 Ag 4 Cu + Ag 2 Cu + +Ag Ag 4 Cu Ag 2 Cu +Ag Ag 3 Cu 2 + AgCu + 2 +Ag Ag 3 Cu 2 Ag 2 Cu + AgCu 1.5 Ag 2 Cu 3 + Cu + 3 +Ag Ag 2 Cu 3 Ag 2 Cu +Cu AgCu + 4 Cu + 3 +AgCu 1.72 AgCu 4 AgCu 2 + Cu Summary A theoretical study was carried out on the cationic and anionic Ag m Cu n (m + n 5) clusters using B3LYP functional. Most of the tetrameric clusters in the ground states are rhombus shaped, with the exception of Ag 3 Cu, which has a Y-shaped structure with the Cu atom in the center. The stable anionic pentamers prefer planar trapezoidal structures while the stable cationic pentamers all prefer three-dimensional structures. For the given cluster size, one can observe the following trends of the energetic properties: (i) The EAs decrease with the increasing Cu content, which indicates that the replacement of Ag with Cu leads the anions easier to lose electrons; (ii) The dissociation of the bimetallic clusters becomes more and more difficult with the increasing dissociation energy as the number of Cu atoms increase; (iii) The binding energy per atom also increases with increasing Cu content and follows the order anion < cation with the same composition. The odd-even alternation patterns observed for the AIPs, EAs and dissociation energies reflect the stability of the clusters upon the valence electron configurations. References [1] K. Shimizu, H. Kawabata, H. Maeshima, A. Satsuma, and T. Hattori, J. Phys. Chem. B 104 (2000) [2] F. Solymosi and T. Bánági, J. Catal. 156 (1995) 75. [3] S. Sumiya, H. He, A. Abe, N. Takezawa, and K. Yoshida, J. Chem. Soc. Faraday Trans. 94 (1998) [4] S. Kameoka, T. Chafik, Y. Ukisu, and T. Miyadera, Catal. Lett. 55 (1998) 211. [5] M. Valden, X. Lai, and D.W. Goodman, Science 281 (1998) [6] D. Fischer, W. Andreoni, A. Curioni, H. Grönbeck, S. Burkart, and G. Ganteför, Chem. Phys. Lett. 361 (2002) 389. [7] Y.C. Choi, H.M. Lee, W.Y. Kim, S.K. Kwon, T. Nautiyal, Da-Yong, Cheng, K. Vishwanathan, and K.S. Kim, Phys. Rev. Lett. 98 (2007) [8] X. Liu, A. Wang, X. Wang, C.Y. Mou, and T. Zhang, Chem. Commun. 27 (2008) [9] Y. Negishi, Y. Nakamura, A. Nakajima, and K. Kaya, J. Chem. Phys. 115 (2001) [10] H.M. Lee, M. Ge, B.R. Sahu, P. Tarakeshwar, and K.S. Kim, J. Phys. Chem. B 107 (2003) [11] V. Bonačić-Koutecký, J. Burad, R. Mitrić, M. Ge, G. Zampella, and P. Fantucci, J. Chem. Phys. 117 (2002) [12] H.Q. Wang, X.Y. Kuang, and H.F. Li, Phys. Chem. Chem. Phys. 12 (2010) [13] Y. Morisada, T. Nagaoka, M. Fukusumi, Y. Kashiwagi, M. Yamamoto, and M. Nakamoto, J. Electron. Mater. 39 (2010) [14] Z.Y. Jiang, K.H. Lee, S.T. Li, and S.Y. Chu, Phys. Rev. B 73 (2006) [15] H. Partridge, C.W. Bauslicher Jr., and S.R. Langhoff, Chem. Phys. Lett. 175 (1990) 531.

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