10342
J. Phys. Chem. C 2007, 111, 10342-10346
Prediction of Gold Zigzag Nanotube-like Structure Based on Au32 Units: A Quantum Chemical Study Frederik Tielens* and Juan Andre´ s Departament Cie` ncies Experimentals, Box 224, UniVersitat Jaume I, E-12080 Castello´ , Spain ReceiVed: February 13, 2007; In Final Form: May 16, 2007
The present study using theoretical methods based on density functional theory (DFT) discloses the conceivable existence of polymers composed of Au32 (Ih) units corresponding to a conducting zigzag nanotube-like structure. The properties and reactivity of Au32 cage-hollow structures as well as their corresponding assembled polymers have been analyzed by means of DFT descriptors.
Introduction Recent intensive research interest in cluster-assembled materials is driven by their possible use as nanoscale building blocks in materials and devices. In particular, gold-containing nanoclusters1,2 have attracted great interest due to the fundamental importance and wide variety of technological applications3,4 in different areas such as optical, magnetic, or molecular electronics.3-5 Nanometer gold clusters tend to organize as two- and threedimensional, 2D and 3D, respectively, clusters. For neutral Au clusters the 2D-3D transition may occur at Au8,6 while the 3D geometry is favored over the 2D geometry at about 14-15 atoms7 for anionic clusters, which is more than twice the number of atoms in other metals. Recently, Fa and Dong pointed out that the calculations of vibrational spectra can be used to determine the 2D-3D crossover size of AuN (N < 16)8 systems. With the discovery of the W@Au12 icosahedral9,10 cluster, the Au20 tetrahedral11 cluster, and the gold nanotube,12-17 the idea emerged that a cagelike structure for gold could exist. In particular, the Au32 fullerene system (Ih) was first predicted from high-level quantum chemical calculations by Johansson et al.18 and confirmed by Gu et al.19 Its cagelike hollow structure was ascribed to the relativistic character of its electrons, to its icosahedral symmetry, and to a 4-fold degenerate HOMO, which prevents any Jahn-Teller distortion. In addition, the Au50 cagelike structure is more stable than its alternative space-filling isomeric form.20 Other Au cages showing different degrees of sophistication were found to be stable,17,20-22 but their amorphous space-filling structures are favored or have competing bonding energies.20,23 Why do some Au structures prefer a cagelike arrangement? This remains an open question. Different factors have been invoked to explain this behavior, such as the high spherical aromaticity,24 the larger values of HOMOLUMO gaps (1.5-2.0 eV),18 and the relativistic effects10,25 attributed to the stabilization of the 6s orbital and destabilization of the 5d one, favoring the hybridization of these orbitals.10 In comparison with other metals such as Cu and Ag, it has been shown19 that the particularly high stability of the cagelike Au32 structure is likely due to the relativistic effect. For Cu and Ag amorphous nonhollow clusters are found to be more energetically stable than their cagelike structure. * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +34 964 72 80 73. Fax: +34 964 72 80 69.
The physical and chemical properties of this new type of system are naturally worthy of being carefully studied. Actually, the optical properties26 of Au32 have been reported theoretically as have the transport properties.27 Very recently their interaction with CO, H2, and O2 has been investigated at the ab initio level showing a high chemical inertness.28 It has been stated that these gold fullerenes are expected to be chemically inert; however, the fact they do not react with each other has not been proven yet. In analogy with carbon nanotubes21 zigzag nanotubes based on Au32 units can be derived. In fact, polyicosahedral gold-containing systems have been synthesized by Zhang et al.,29,30 and the bonding nature of these systems has been discussed.30 Searching for self-assembly behavior of gold-containing polymers remains a fascinating experimental challenge, and theory is invited to disclose still unexplored features of this chemistry. With the development of first-principle approaches, it is possible today to design new materials with particular properties on the basis of theory. The main goal of this paper is to present the existence of a conducting nanotube formed by assembled nonmetallic Au32 fullerenes. Computational Details Theoretical methods and techniques based on density functional theory (DFT)31,32 have been employed to carry out this work. We have studied the formation of nanotube-like structures from assembled polymers composed of Au32 units by means of the VASP33,34 computer package. The hybrid RPBE (revised Perdew-Burke-Ermzerhof) functional35-37 has been chosen to perform the periodic DFT calculations. This functional is the best available in the VASP4.6 code for dispersion forces38 without parameters fitted to the experimental data. The energy values are the most reliable that DFT can provide for evaluating the large aurophilic contribution that stabilizes the Au-Au bonds. The accuracy of the method has been tested elsewhere.19 Only the valence electrons were treated explicitly, and their interactions with the ionic cores are described by the projector augmented-wave method (PAW),39,40 which allows the use of a low-energy cutoff for the plane-wave basis set of 230 eV, with scalar relativistic effects included. All the calculations for the Au32 (Ih) monomer cluster (see Figure 1) have been carried out by Becke’s three-parameter hybrid functional with the Parr-Wang 91 correlation functional B3PW9141 in combination with the LANL2DZ42-44 pseudopo-
10.1021/jp071246u CCC: $37.00 © 2007 American Chemical Society Published on Web 06/26/2007
Prediction of Gold Zigzag Nanotube-like Structure
J. Phys. Chem. C, Vol. 111, No. 28, 2007 10343
TABLE 1: Calculated Properties of Au32 (Ih) diameter/nm Au-Au distance/Å frontier orbital configuration HOMO-LUMO gap/eV degeneracy of HOMO/LUMO binding energy per atom/eV IPb/eV EAb/eV vib frequency/cm-1 high low NICS at the center of the cage/ppm a
ref 18
ref 19
0.9 (PBE0) 2.776-2.850 (PBE0) (t2u)6(gu)8(gg)0 1.7 (PW91) 4/4
0.9 2.778a (PW91) (t2u)6(gu)8(gg)0 1.56 (PW91) 4/4 -3.89 (PW91) 6.12 (PW91)
147 (PBE0) 37 (PBE0) -100 (PW91)
ref 20
this work
(t2u)6(gu)8(gg)0 1.527 (PBE) 4/4 2.269 (PBE)
0.9 (PBE) 2.795-2.866 (B3PW91) (t2u)6(gu)8(gg)0 2.33 (B3PW91), 1.57 (PBE) 4/4 2.125 (PBE) -2.19 (PBE) 7.19 (PBE)
0.9
-81 (PBE)
138 (PBE) 20 (PBE) -88 (B3PW91)
b
Average bond length. Energy difference between the optimized neutral Au32 and the structurally similar ionic system.
Figure 1. Au32 (Ih) icosahedral cluster.
tential describing 19 valence electrons adopted for the gold atom available in the Gaussian03 package.45 The electronic properties, such as electron density, Mulliken charges, molecular electrostatic potential46 (MEP), Fukui function47 (FF), and nuclear independent chemical shift (NICS), are calculated with the above-mentioned method. The periodic DFT geometry optimizations were carried out using one k-point for the Brillouin-zone integration and a unit cell with dimensions equal to 18 Å × 18 Å × 18 Å for the Au32 monomer, 18 Å × 18 Å × 12 Å for the polymer and nanotube, and 18 Å × 18 Å × 24 Å for the Au32 dimer. The optimization of the polymer has been performed by varying the cell dimensions and atom positions and fixing the volume of the unit cell; this strategy has been successfully used in our former studies.48,49 Results and Discussion The Au32 cage (Ih) consists of 12 5-fold and 20 6-fold Au atoms, and some calculated properties of this cluster are reported in Table 1. An analysis and comparison of the present results and previous theoretical studies point out that the geometry as well as the electronic structure do not change significantly with the level of theory used in the calculation, while the value of the band gap is very sensitive to the method used. It is known that the HOMO-LUMO gap is underestimated using pure DFT methods50 and is improved when hybrid methods are used. This underestimation is due to the description of the exchange energy
Figure 2. (A) Electrophilic Fukui function. (B) nucleophilic Fukui function. (C, D) MEP for Au32 (Ih). Color scale: negative to positive values from red to blue.
in the DFT functionals. In pure DFT functionals no HF exchange is considered, while in hybrid methods some part of the exchange is included. The FF values are more positive and more spread over the molecule’s surface; therefore, the nucleophilic character is dominant (see Figure 2A,B), and the most suitable site for a nucleophilic attack is the 5-fold-coordinated Au atoms. The MEP of the Au32 cage shows positive values in the region of the 5-fold-coordinated Au atom (see Figure 2C,D), more precisely outside the cage. All negative values are found inside the cage (red area in Figure 2D). The shape of the cage provokes the compacting of the electrons along the convex side (i.e., inside). On a flat one-layer (111) gold surface the electron density is equal on both sides; however, when the surface is bent, the electron density of the convex side starts to compact. This phenomenon results in a forced polarization of the atoms so that the negatively charged gold atoms have an electrondense side pointed to the center of the cage. In addition, the NICS value is very high in the center of the cage (higher than in the carbon fullerenes), in agreement with the results reported by Johansson et al.18 From a reactivity viewpoint, Pearson’s HSAB principle51,52 states that an electron-rich system having a high softness (i.e., low hardness) is expected to react with a soft reaction partner. However, in this special case, since the outside is electron-poor,
10344 J. Phys. Chem. C, Vol. 111, No. 28, 2007
Tielens and Andre´s
Figure 3. HOMO (A) and LUMO (B) of the Au32 unit (coordination indicated by 5 or 6).
the opposite trend is observed. Indeed, the 5-fold-coordinated Au atoms, having the highest MEP values (see Figure 2C,D), are nucleophilic sites at the outside of the cage, so the hardhard interactions predict a reaction via the 5-fold-coordinated Au atoms. The HOMO density (see Figure 3A) is centered along the atoms forming the equator of the Au32 sphere. The poles have almost zero HOMO density. The HOMO in the neighborhood of the 6-fold Au atoms has a distorted d orbital shape with a considerable s orbital contribution. This orbital is oriented along the Au (6-fold)-Au (5-fold) bonds. The HOMO in the neighborhood of the 5-fold Au atoms points out of the spherical cluster and is consequently more suited for eventual implication in reactive processes. The LUMO density (see Figure 3B) is mainly concentrated along the Au (5-fold)-Au (6-fold) bonds and on the 5-fold Au atoms covering the sphere’s surface. After consideration of only one isolated cage, the Au32 cluster is repeated as a single unit in one direction (Au32)N, and combinations between two Au32 units, forming an infinite ((Au32)2)N polymer, have been analyzed. This procedure enables us to increase the optimization flexibility of the polymer and construct extra link combinations. Since there are two types of Au atoms in the Au32 (Ih) fullerene, namely, the 5- and 6-foldcoordinated atoms, we can construct three different combinations of linkages between pairs of Au atoms: 5-5, 6-6, and 5-6 structures. The possibility to link two 5-fold Au atoms from one cage to one 5-fold atom from another cage was found to be possible as well (5-5,5 structure). One can also construct links between two different Au atoms of each cage, which turns out to be only one due to steric hindrance: (5,5-5,5), i.e., two 5-fold-coordinated Au atoms from one cage linked to two 5-foldcoordinated Au atoms from another cage. The results for the binding energies of the different interconnections for the (Au32)N polymer constructed showed clearly that the 5,5-5,5 linkage (four Au-Au bonds) is the most stable structure (see Figure 4A). This result is in line with the predictions of the FF and MEP, confirming that the hard-hard interactions are dominant in this system (5-fold Au atoms have higher nucleophilic FF values than the 6-fold Au atoms). Another point supporting the hardness of the Au32 (Ih) unit is that, from all different cagelike structures known, only the Au32 cation maintains a cagelike structure,23 which suggests a better distribution of its positive charge (electron-poor regions), which is the typical behavior of a hard system. In parallel soft systems which redistribute their electron-rich zones (negative charge), it should be noted that if no double bonds between the units are considered, the 6-6 link gives the most stable structure. This structure corresponds to an interaction between two soft sites (less positive charged sites). Harmonic-frequency calculations were performed on the optimized geometries. The vibrational frequencies revealed that
Figure 4. Geometry of the most stable Au32-polymer intermediate (a), showing the most electropositive (dark blue) and most positive nucleophilic Fukui function (light blue) areas. This structure progresses after full geometric optimization to a stable zigzag nanostructure (b).
these polymer systems were not an energy minimum (presence of imaginary frequencies). These structures were only used to investigate the stability of the different links between two Au32 units. Subsequently, the most stable structure was further optimized until only positive vibrational frequencies were obtained (see Figure 4B). The other structures (energetically less favorable) were not investigated further. It should be stressed, however, that there is no reason that these structures would not optimize all to the same stable structure, or more generally to another type of polymer, tube or wire. Nevertheless, the study was limited to only one structure, i.e., the most stable one. It turns out that the most stable cage polymer (i.e., 5,5-5,5) is unstable and undergoes structural deformation. A first observation that should be emphasized is that the cage structure of the Au32 cluster does not collapse. This is in line with the results of Gu et al.,19 who predicted the possibility of formation of larger cages, being possible precursors of nanotubes. This possibility can be based on the fact that, as the number of Au atoms increases, the energy difference between compact and cagelike structures does not vanish. Then, a stable infinitely large cage or nanotube-like structure can be predicted. In fact, after a full geometrical optimization, the final structure consists of an array of typical stable Au triangles, which are encountered in other gold systems, especially in geodesic structures (see Figure 4). The distance between Au neighbors ranges from 2.70 to 2.96 Å. The mean value is 2.799 Å. The bulk distance calculated at the same level of calculation is 2.913 Å (experimental value 2.884 Å). The values obtained for the (5,3) nanotube range from 2.77 to 2.91 Å.53 The Au-Au distances show contractions up to 2.70 Å, which is more than 7% shorter than the bulk value. This shortening can be attributed to aurophilic interactions due to the relativistic dispersion effect. The extra stabilization of the bond length shortening, due to
Prediction of Gold Zigzag Nanotube-like Structure
J. Phys. Chem. C, Vol. 111, No. 28, 2007 10345 We hope that our results will stimulate the experimentalist to validate our theoretical prediction. Acknowledgment. F.T. thanks the Generalitat Valenciana and Fundacio BANCAJA-UJI for financial support to carry out a stay at the University Jaume I as an invited researcher. J.A. acknowledges continuous finacial support by DGI (Project BQU2003-04168-C03-03) and Projects GRUPOS04/28 and ACOMP06/122 (Generalitat Valenciana). The Servei d’Informatica (Universitat Jaume I) is also acknowledged for use of its computer facilities. References and Notes
Figure 5. DOS for both the Au32 (Ih) cluster and the obtained zigzag nanotube.
the relativistic effects, is also based on the stability of all gold cage structures. The binding energy per atom or cohesive energy, Eb, for the Au32 (Ih) cage is calculated as the difference between the total energy of a single Au atom, ET(A), and the total energy per atom of the fully relaxed cage having N atoms in the unit cell, ET(structure)/N. For the Au32 (Ih) fullerene we found Eb ) 2.13 eV (BPE0 functional), i.e., 0.5 eV lower than in the former calculation using the PW91 funtional19 (2.618 eV). For the (5,3) tube a binding energy per atom of 1.78 eV was found experimentally by Oshima et al.12 and 2.58 eV15 using ab initio methods. The zigzag nanotube-like structure has a binding energy per atom, Eb, of 2.27 eV, in agreement with the stabilization trend predicted by Gu et al.19 The exothermic energy indicates a stable structure corresponding to a total minimum on the Born-Oppenheimer surface. The value of the binding energy shows that the zigzag tube is of comparable stability compared with the fullerene and the (5,3) nanotube. On the same level of calculation using the PBE functional, we find the zigzag nanotube (2.33 eV) to be more stable than the fullerene (2.13 eV) and comparable in stability to the (5,3) nanotube. The highest vibrational frequency of the zigzag nanotube, 174 cm-1, is less soft than that of the fullerene (see Table 1). The electronic structure is investigated through the calculation of the density of states (DOS). A 3 × 3 × 1 k-point grid was used for the integration of the Brillouin zone, and the partial occupancies are set for each wave function using the tetrahedron method with Blo¨chl corrections.54 The band gap (HOMOLUMO difference) for the Au32 monomer is 1.57 eV, which is in agreement with other calculations, ∼1.5 eV.18,19 However, a comparison of both DOSs (see Figure 5), the Au32 monomer versus nanotube, shows the band gap disappears during the polymerization reaction and conducting behavior is found for the zigzag nanotube. Conclusion The results of our calculations first disclose that Au32 cages are predicted to assemble and a thermodynamical stable conductive gold zigzag nanotube-like structure is obtained. The reactivity controlled by hard-hard interactions has been explained by means of DFT descriptors. The binding energy per atom of the nanotube-like structure is increased versus that of the fullerene system and is comparable with that of the (5,3) nanotube. These compounds can represent a major advance in this field, and it should be possible, in the longer term, to use the present results to more clearly delineate any relationships between the nanotube growth mechanism and the catalytic activity and selectivity of gold zigzag nanotube-like structures.
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