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J. Phys. Chem. C 2010, 114, 20–27
Structures and the Electronic Properties of Au19X Clusters (X ) Li, Na, K, Rb, Cs, Cu, and Ag) Tapan K. Ghanty,*,† Arup Banerjee,‡ and Aparna Chakrabarti§ Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400 085, India, Laser Physics Application DiVision, Raja Ramanna Centre for AdVanced Technology, Indore 452013, India, and Semiconductor Laser Section, Raja Ramanna Centre for AdVanced Technology, Indore 452013, India ReceiVed: July 7, 2009; ReVised Manuscript ReceiVed: NoVember 19, 2009
We employ an ab initio scalar relativistic density functional theory based method to calculate the ground state structures and the electronic properties for Au19X clusters, X being the alkali metal atoms, Li, Na, K, Rb, and Cs as well as the coinage metal atoms, Ag and Cu. The tetrahedral Au20 clusters have been doped exohedrally with these atoms at three different types of unique sites where the dopant atom substitutes one gold atom from (i) the vertex, (ii) the surface, and (iii) the edge sites. In addition to the structures based on tetrahedral Au20, we also consider cage-like structures for Au19X clusters with the dopant atom located at an endohedral position. We first optimize the geometries of these clusters and then we carry out vibrational analysis on these optimized structures of the substituted Au20 clusters in order to check the stability of the final optimized structures. Further, using the optimized geometries of these doped clusters, we calculate the binding energy, interaction energy of the dopant atom with the Au19 cluster, vertical ionization potential, vertical electron affinity, and HOMO-LUMO gaps of these doped clusters. For these systems, we also carry out the charge population analysis. We compare these properties of the doped clusters with those of the pure Au20 cluster to characterize the stability and chemical inertness of the doped clusters. Few cage like endohedrally doped Au19X clusters (X ) Li, Na, and Cu) are found to have binding energies comparable to those of the corresponding exohedrally doped clusters. For the larger atoms (X ) K, Rb, Cs, and Ag), all of the endohedrally doped cage-like structures have been found to be less stable than the corresponding exohedral structures. Nevertheless, exohedrally doped Au19X clusters with X located at one of the surfaces of tetrahedral structure correspond to the most stable isomer for all the dopants. We observe that the Li and Cu doped gold clusters, where the dopant atom is located at one of the surface sites of the Au20 cluster are more stable than the pure Au20 cluster. This leads to the possibility of finding highly reactive anions of these doped clusters. Geometric as well as energetic considerations indicate that it may be possible to characterize these species experimentally using photoelectron spectroscopy. I. Introduction Gold is one of the most unique elements in the periodic table with a wide range of applications in chemistry, physics, and material science including clusters and nanomaterials. Now it has been well recognized that mostly the relativistic effects dominate the chemistry of gold.1-3 In recent years gold clusters as well as gold clusters doped with impurity atoms of alkali metal or transition metal have attracted the attention of both theoreticians and experimentalists working in the field of cluster science.1-5 The intense activity on these systems is driven by both fundamental and practical interests. It is the discovery of catalytic effects5-9 in gold cluster toward oxidation of CO which has prompted large number of studies to understand and characterize the structure and properties of these clusters. Besides being used as catalysts, gold clusters are also finding applications in many other areas like material science,10 molecular electronics devices, and medical and biological diagnostics.11,12 * To whom correspondence should be addressed. E-mail: tapang@ barc.gov.in. † Bhabha Atomic Research Centre. ‡ Laser Physics Application Division, Raja Ramanna Centre for Advanced Technology. § Semiconductor Laser Section, Raja Ramanna Centre for Advanced Technology.
Along with pure gold clusters, bimetallic doped gold clusters have also been considered for the catalytic applications. With a suitable choice of metallic impurity atom doped in a pure gold cluster, it is possible to tune the geometric and electronic structures and consequently the chemical reactivity of these clusters in desirable fashion. For example, it has been found that, although Au4 is catalytically inert, doped Au3Sr is active.13 Ab initio scalar relativistic density functional theory (DFT)based calculations have revealed that the nature of chemical bonding and the activation of molecular oxygen by these nanoclusters lead to novel size-sensitive chemical reactivity of doped bimetallic clusters. Size-dependent structural evolution obtained from electron diffraction measurements combined with first-principles calculations revealed14 the changes in dimensionality and symmetry of gold clusters from planar species at n ) 11 and to threedimensional structures around n ) 13, to hollow cages for n ) 16 and 17, followed by the appearance of a tetrahedral structure at n ) 20, and the emergence of a highly symmetric tubelike structure at n ) 24. In the family of gold clusters, it is well established now that a magic number cluster containing 20 gold atoms (Au20) is a highly stable and chemically inert cluster possessing a tetrahedral pyramidal structure both by experimental studies (photoelectron spectroscopy15 and far-infrared
10.1021/jp906400t 2010 American Chemical Society Published on Web 12/15/2009
Au19X Clusters
Figure 1. Ground-state geometry of tetrahedral Au20 cluster with Td symmetry.
vibrational spectroscopy16) and ab initio DFT-based calculations.15-17 Also see the review paper on the properties of the magic gold cluster Au20 by Kryachko and Remacle.18 The calculated excitation energy for the lowest triplet state is 1.77 eV, and it is found to be in close agreement with the experimentally determined value of 1.777 eV.15 This large energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), which is even greater than that of C60, suggests that the Au20 cluster should be a very stable and inert molecule. The tetrahedral structure of the Au20 cluster (as shown in Figure 1) can be viewed as a relaxed small piece of bulk gold with face-centered cubic (FCC) lattice. In fact, the Au20 cluster has been used as a model of the bulk surface to investigate the interaction of pyridine molecules with the gold surface.19 It is well-known that free neutral clusters with large HOMO-LUMO gaps are very active as anions due to their small electron affinity. This consideration has led to the study of the catalytic activity of an anion of Au20 toward CO oxidation as a function of charge transfer state.20 These authors have found that as compared to the neutral cluster Au20, which is moderately active, its anion is extremely active due to the presence of weakly bound unpaired electrons in it. The high stability and symmetric structure of Au20 have also prompted further studies devoted to the linear and nonlinear (second-order) optical properties of this cluster.21 It has been shown that the Au20 cluster possesses a large second-order nonlinearity coefficient (βxyz), and it is the charge transfer from the edged gold atoms to the vertex ones that plays a crucial role in nonlinear optical response.21 At this point we note that in spite of Au20 possessing some unique properties not much has been reported in the literature on the characteristics of doped Au20 cluster. For the sake of completeness, we should mention here that several studies involving modification of the structural and electronic properties of neutral and ionic gold clusters (other than Au20) doped with alkali or transition metal atoms have been reported in the literature.11,13,22-31 It then becomes natural to ask the question how the high stability and chemical inertness associated with Au20 are altered when it is doped with a metallic atom. In this paper we make an attempt to answer this question by performing a systematic investigation of electronic properties of doped neutral gold clusters Au19X (for alkali metal doping X ) Li, Na, K, Rb, and Cs and for coinage metal doping X ) Cu and Ag). In the tetrahedral structure of the Au20 cluster, 20 gold atoms can be grouped into three categories, namely four equivalent vertex atoms AuV (Au1-4 as shown in Figure 1), four equivalent face-centered or surface atoms AuS (Au17-20 as shown in Figure 1), and twelve equivalent atoms lying on the edges AuE (Au5-16 as shown in Figure 1). For our purpose we replace a single gold atom from one of these three groups by an alkali
J. Phys. Chem. C, Vol. 114, No. 1, 2010 21 atom (Li, Na, K, Rb, and Cs) or a coinage metal atom (Ag or Cu). In particular, we replace one of the gold atom located at either the 4th (vertex) or 16th (edge) or 20th (surface) site in the tetrahedral Au20 (see Figure 1) by one of the abovementioned alkali or coinage metal atom. We denote these doped clusters by Au19X(V), Au19X(E), and Au19X(S) corresponding to the replacement of vertex, edge, and surface gold atom, respectively, by the dopant atom X (X ) Li, Na, K, Rb, Cs, Ag, and Cu). Apart from exohedrally doped structures obatined by replacing the symmetry unique atoms from the tetrahedral Au20 cluster, we also consider several cage-like stuctures of doped Au19X clusters in which dopant atom is situated in an endohedral position to make our serach for the geometry of these clusters more extensive. Results pertaining to these structures are discussed in section III. Using optimized stuctures of these doped clusters, we carry out ab initio scalar relativistic DFT-based calculations of binding energy (BE) per atom, HOMO-LUMO gap (∆EHL), ionization potential (IP), and electron affinity (EA) to characterize their stability and chemical inertness with respect to pure Au20 cluster. In the next section, we briefly outline the computational methods employed to calculate various quantities mentioned above. Results of our calculations are presented and discussed in section III. The main results of the paper are summarized in section IV. II. Computational Methods In the present paper, all of the calculations on doped gold cluster Au19X have been performed by using Amsterdam Density Functional (ADF2006) program package.32 In order to account for the relativistic effect which is quite significant for high Z atoms like Au, Rb, Cs, Ag, and Cu, we perform all of the calculations within the scalar relativistic method based on zero-order regular approximation (ZORA).33 For each doped cluster Au19X, we first optimize the geometry by using the Perdew-Wang 1991 (PW91)34 exchange-correlation (XC) functional within a generalized gradient approximation (GGA). We use the triple-ζ Slater type orbital (STO) basis set added with two polarization functions (TZ2P of ADF basis set library) at the frozen core approximation level. The frozen cores considered for various atoms are 1s-4f for Au, 1s for Na, 1s-2p for K, 1s-3d for Rb, 1s-4d for Cs, 1s-3p for Cu, and 1s-4p for Ag. For the Li atom we use an all electron TZ2P basis set. The geometry optimization calculation carried out in this paper is based on a quasi-Newton approach and the Hessian is updated in the optimization process by employing Broyden-FletcherGoldfarb-Shanno (BFGS) methods35 until the convergence criteria of 10-4 a.u. for Cartesian gradient and 10-6 a.u. for energy are met. We also carry out vibrational analysis on the optimized structures of substituted Au19X clusters in order to check the stability of these clusters, and all of them turn out to be stable with no imaginary vibrational frequency. III. Results and Discussion In order to investigate the electronic properties of substituted gold clusters, first we need to have the correct geometric structures of these systems. To this end, we make use of the tetrahedral geometry of the Au20 cluster and generate from it the starting geometries of Au19X for structure optimization by replacing a single gold atom from one of the three distinct group of atoms in the tetrahedral structure of Au20 (as mentioned in the Introduction) by an alkali atom (Li, Na, K, Rb, or Cs) or a coinage metal atom (Ag or Cu). As mentioned before we designate these three resulting systems as Au19X(V), Au19X(E),
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Ghanty et al.
TABLE 1: Comparison of the Theoretical and Experimental BE per Atom (in eV), ∆EHL (in eV), IP (in eV), and Vibrational Frequency ωf (in cm-1) for the Au20 Cluster reference
BE
∆EHL
IP
present (PW91) 2.37 1.786 7.188 2.93 7.398 theory (B3LYP)18 theory (PW91)17 2.58 1.433 expt.15 1.77 (1.81)a expt.36 7.82 expt.16 a
ωf lowest and highest 28, 138 26, 161
148
PW91 calculated value is given within the parenthesis.
and Au19X(S) which are obtained by replacing a gold atom located at a vertex, at an edge, and at a surface of the Au20 cluster, respectively (see Figure 1). These structures are then optimized by employing a DFT based geometry optimization scheme with PW91 XC functional and TZ2P basis set. Here it is important to mention that the global minimum structure of the Au19 cluster has been found to be a truncated pyramid in which one of the vertex atoms is missing.16 Therefore it is natural to consider the structure of Au19X (with X being a monovalent metal atom) as distorted tetrahedral. Also, it is supported by the fact that the negative ion of Au20 possesses a tetrahedral structure.15,18 Moreover, the shape of a neutral cluster with 20 valence electrons is most likely to be a highly symmetric one as it is a magic number cluster. This has motivated us to consider the above-mentioned three possible substituted exohedral structures of doped gold cluster Au19X. We note here that the tetrahedral sturcture of Au20 has also been shown to distort on adsorption of a molecule on an Au20 cluster.19 Besides these three exohedrally doped stuctures, we also consider more than 10 cage-like endohedral stuctures of doped gold cluster Au19X for each dopant atom and carry out DFT-based geometry optimization calculations. Before proceeding with the discussions of the results for the various properties of Au19X clusters, we first check the accuracy of DFT based method (specially the basis set and the XC functional) adopted in this paper by performing calculations for the Au20 cluster against the already published theoretical and experimental data.15-18,36 A compilation of the published theoretical and experimental data for BE, IP, ∆EHL, and vibration frequency ωf of an Au20 cluster along with the corresponding results obtained by us is presented in Table 1. The comparison of results in Table 1 indicates a satisfactory agreement between our results with the theoretical and experimental data already available in the literature. Thus we believe that our choice of basis set and the XC functional for the purpose of calculation of the properties of Au19X clusters should yield reasonably accurate results. In the following we first discuss the results for the properties of three exohedrally doped Au19X clusters and then present the results for some lowenergy endohedral cage-like structures of Au19X clusters. The optimized structures of Au19X clusters based on tetrahedral geometry of Au20 obtained by our calculations are displayed in Figure 2a-c. We note here that the optimized structures of clusters of types Au19X(V) and Au19X(S) possess C3V symmetry, whereas clusters of Au19X(E) type have Cs symmetry. To verify whether the optimized geometries obtained by us (shown in Figure 1) are stable or not, we calculate the harmonic vibrational frequencies for all of these structures. The absence of imaginary frequencies is used to confirm the stability of a structure. In our calculation we observe no imaginary frequencies for any of the structures shown in Figure 2. It can also be seen from Figure 2 that among alkali metals the Li atom causes minimum deformation from the tetrahedral structure of
Figure 2. Optimized geometries of doped Au19X(i) clusters, with i ) V, S, and E denoting the locations of the dopant atoms: (a) Au19Li(i), Au19Na(i), and Au19K(i); (b) Au19Rb(i) and Au19Cs(i); and (c) Au19Cu(i) and Au19Ag(i).
Au20 while the maximum deformation is caused by the Cs atom. This is consistent with the fact that the atomic radius of alkali atoms increases as one moves from Li (1.52 Å) to Cs (2.65 Å) down the group [Na (1.54 Å), K (2.27 Å), and Rb (2.48 Å)], and they are all larger than the atomic radius of the Au atom which is 1.44 Å.37 As the atomic radius of Li is comparable to that of Au, no appreciable deformation of the tetrahedral stucture is observed in the three exohedrally doped structures of Au19Li clusters. However, from Na atom onward, the difference in the atomic radii between alkali atom and the gold atom increases resulting in higher deformation of the tetrahedral stucture as we go down the group with the highest deformation being observed for the largest alkali atom Cs. On the other hand, for doping with coinage metal atoms, the tetrahedral structure undergoes significantly less distortions as these atoms belong to the same group as gold atom and atomic radii of Cu and Ag are quite close to that of the Au atom. However, the atomic radius of the Cu atom (1.28 Å) being smaller in size as compared to that of the Ag atom (1.44 Å), it is expected that insertion of the Cu atom will produce less distortion in the tetrahedral
Au19X Clusters
J. Phys. Chem. C, Vol. 114, No. 1, 2010 23
TABLE 2: Principal Values of the Tensor Rij for Optimized Doped Au19X Clusters system
Rxx
Ryy
Rzz
Au20 Au19Li(V) Au19Li(E) Au19Li(S) Au19Na(V) Au19Na(E) Au19Na(S) Au19K(V) Au19K(E) Au19K(S) Au19Rb(V) Au19Rb(E) Au19Rb(S) Au19Cs(V) Au19Cs(E) Au19Cs(S) Au19Cu(V) Au19Cu(E) Au19Cu(S) Au19Ag(V) Au19Ag(E) Au19Ag(S)
81.44 80.87 81.51 80.51 80.77 84.45 80.90 80.88 87.06 80.80 80.75 89.27 80.47 80.76 91.02 80.33 81.11 80.84 81.18 81.09 82.58 81.71
81.44 80.87 81.35 80.51 80.77 83.66 80.90 80.88 85.93 80.80 80.75 86.32 80.47 80.76 86.75 80.33 81.11 79.80 81.18 81.09 81.95 81.71
81.44 83.99 80.72 80.35 87.67 80.58 85.10 91.90 80.59 89.86 94.86 80.51 92.74 97.27 80.51 94.88 81.10 81.22 80.75 83.73 80.97 81.39
structure of Au20 as compared to the case of the Ag atom. These observations are clearly elucidated in Figure 2. Furthermore, in order to quantify the degree of deformation produced in the tetrahedral structure of Au20 due to doping, we calculate principal values of the quadrupolar tensor Rij ) ΣIxixj.38 Here xi ) {x, y, z} denotes the coordinates of the ith ion and the summation is performed over all of the ions of the system. The principal values of this tensor Rxx, Ryy, and Rzz define the dimensions Rx, Ry, and Rz of the ionic charge distribution in the cluster along the principal axes x, y, and z through the relations Rx ) Rxx/N, Ry ) Ryy/N, and Rz ) Rzz/N, where N is the total number of atoms present in the cluster. The results for the principal tensors Rxx, Ryy, and Rzz obtained from the optimized structures of Au19X clusters (as shown in Figure 2) are listed in Table 2. Note that for the tetrahedral structure of Au20, Rxx ) Ryy ) Rzz characterizing a spherically symmetric structure. In general the cluster shape can be characterized by the oblate (Rxx ) Ryy > Rzz), prolate (Rxx ) Ryy < Rzz), or triaxial (Rxx * Ryy * Rzz) deformation. From Table 2 we observe that for the alkali doped clusters (except Li atom) Au19X(V) and Au19X(S) show prolate deformation. The principal tensor along the z direction increases as we scan from the Li atom to the Cs atom. For the case of Au19Li(V), we find a prolate deformation in the structure, whereas the structure of Au19Li(S) remains almost tetrahedral. Similarly, in case of Au19Cu(V) and Au19Cu(S), we find both structures to be very close to tetrahedral geometry. The structural forms of Au19Ag(V) and Au19Ag(S) show similar deformations as those of Au19Li(V) and Au19Li(S). In contrast to the deformations of Au19X(V) and Au19X(S), all of the doped clusters Au19X(E) show triaxial deformation giving rise to low symmetry structures. It can also be seen from Table 2 that the triaxial deformation is a maximum for substitution of a Cs atom and a minimum for that of a Cu atom. To further study the structures of exohedrally doped gold clusters Au19X, we next examine the bond distances of dopant atom X with the nearest Au atoms. A list of these bond lengths is compiled in Table 3. In this table the entry in the square bracket in the first column denotes the position of the nearest neighbhour with which the bond distance has been enumerated. For comparison we also present the corresponding bond lengths between two Au atoms in Au20 clusters. Table 3 clearly reveals that among the alkali atom doped clusters only Li-Au bond distances reduce slightly
as compared to the corresponding Au-Au distances in Au20 cluster. The reduction in Li-Au bond distances is observed for doping at all three unique locations, viz., vertex, edge, and surface. For other alkali atoms (Na, K, Rb, and Cs), all bond lengths with nearest gold atoms are higher than the corresponding Au-Au bond lengths, and they also increase as one moves from Na atom to Cs atom. We note from Table 3 that like the Li atom, substitution of a gold atom by a Cu atom at all three locations results in a reduction of the bond lengths. On the other hand, for the Ag atom, bond lengths increase slightly as compared to the corresponding Au-Au bond lengths. Having discussed the results for the geometrical structures of exohedral Au19X and their degree of deformations with respect to the tetrahedral structure of the parent Au20 cluster, we now focus our attention on the electronic structure of these doped clusters. To this end we first perform Mulliken charge population analysis on all of the structures shown in Figure 2, and the results of this analysis are presented in Tables 4-6. For comparison we also present the charge population on an Au atom located at the same positions where the dopant atom X has been inserted in an Au20 cluster. It can be seen that all of the alkali atoms loose electrons to become positively charged species irrespective of their doping locations. This is in contrast to the charge on the Au atom located at vertex and edge of an Au20 cluster. The absolute value of the positive charge on the dopant atoms correctly correlates with the difference in the electronegativity between X and Au as it increases when we move from the Li atom to the Cs atom. In contrast to the alkali atom case, Cu atoms at all of the locations become negatively charged. The absolute value of the negative charge is a maximum for Cu(S) and a minimum for Cu(V). For Ag atom doped clusters, the charges on Ag(E) and Ag(S) are slightly negative, whereas on Ag(V) it is slightly positive. For all three substitution sites, viz., surface, vertex, and edge, the dopant atoms change the atomic charge considerably with reference to the pure Au20 cluster. For the surface doping, charge distribution on the vertex atoms undergoes a maximum change. Similarly, the change in the charge is a maximum at the nearest edge atoms for the case of impurities substituted at a vertex location. Also doping at any edge site changes the charge distribution of all other atoms. The thermodynamic stability of a cluster can be characterized by its BE. In order to discuss the stability of the doped Au19X clusters, we calculate the binding energy and the interaction energy (IE) of the dopant atom with the Au19 cluster. The BE of a doped cluster is calculated by employing
BE ) E(Au19X) - 19E(Au) - E(X)
(1)
while the IE of the dopant atom is obtained via
IE ) E(Au19X) - E(Au19) - E(X)
(2)
with E(Au19X), E(Au19), E(Au), and E(X) denoting the energies of Au19X and Au19 clusters and Au and X atoms, respectively. The results for the BE per atom and IE are given in the second and third columns respectively, of Table 7 along with the corresponding results for the tetrahedral Au20 cluster. From Table 7, we observe that for gold clusters doped with Li and Cu atoms (located at edge and surface positions) the BE per atom is higher than the corresponding value for Au20. In particular the BE per atom of Au19Li(S) is the highest among all of the systems considered in this paper. We also observe that for all other alkali atoms and also for the Ag atom BE is lower than the magic Au20 cluster. It is important to note that for all of the systems we find that BE[Au19X(V)]
