INTRODUCTION
One of the main goals of researchers working on Nanoscience and Nanotechnology is the design and the fabrication of nanostructured materials with novel and perhaps unexpected properties.1-1-1 These systems are defined as materials constructed from structural elements (clusters, crystallites, or molecules) with dimensions in the range of 1-100 nm. The case of gold-based nano-structured materials has been especially relevant because of the potential applications in nanoelectronics[2] and in biological diagnostics.1-3-1 An important contribution in this area was the self-assembly of two- and three-dimensional superlattices of nanometer-diameter gold particles linked to each other by organic interconnects.1-4-6-1 Thiol-pas-sivated gold nanoclusters, assembled in closed-packed arrays, showed interesting electronic transport properties, such as single-electron tunneling at room temperature, and are expected to be useful for the development of nanoscale electronics.[5,6] It was also shown that although the self-organization of nanoparticles is a powerful route to grow these materials, imperfections in the superlattice can result from incorrect chemical recognition between the consti-tuents.[2] This can be a serious limitation in making nanostructured materials for electronic applications, where long-range order is important. On the other hand, biological systems are able to solve complex recognition problems. In particular, DNA transmits well-defined chemical information through the pairing properties of nucleotide bases. A major advance in controlling the self-assembly of metal particles was achieved by using oligonucleotides to organize colloidal gold nanoclusters into superlattices, allowing for the controlled growth of hybrid DNA-gold nanostructured materials.1-7,8-1
Although the main mechanisms to synthesize and to isolate hybrid DNA-gold nanostructured materials have been discovered,1-7,8-1 further studies continue to fully characterize the structural, electronic, optical, transport, and other physical and chemical properties. This research represents a challenge for future investigations in Nanoscience and Nanotechnology because of the complexity of these materials, which are a complex mixture of inorganic and biological structures.1-9-1 The first investigations toward a full characterization of gold-based nano-structured materials have already begun. In a first stage, valuable information on the properties of each subsystem, metal particles and DNA, is being obtained. These separate properties will be fundamental in understanding the behavior of the hybrid materials.1-9-1 Along this direction, theoretical and experimental information on the shape and morphology of bare and passivated gold nanoclusters will be fundamental to fully predict and understand their electronic, optical, and other physical and chemical properties. This information is essential to optimizing their utilization as building blocks of the new molecular nanostructured materials.
OVERVIEW
The objective of this article is to describe recent theoretical advances on the study of the shape and morphology of bare and passivated gold nanoclusters of different sizes. A detailed knowledge of the most stable structural configurations of these nanostructures is a very active field of research because the cluster geometries are the starting point to study their electronic, optical, and other physical and chemical properties, which are relevant for the design and fabrication of gold-based nanostruc-tured materials. The main trend emerging from recent theoretical studies on structural optimizations of bare Au clusters in the size range up to 200 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer.1-10,11-1 Moreover, chiral structures have been obtained as the lowest-energy isomers of bare Au28 and Au55 clusters,1-12-1 whereas in the size range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers.1-11,13-1 For methylthiol-passivated gold nanoclusters [Au28(SCH3)16 and Au^SCH^J, structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure.1-12,14-1 These predictions on the existence and the stability of disordered configurations for bare and passivated gold nanoclusters have opened the possibility of constructing gold-based nanostructured materials, where the amorphous-like character of the gold nanoparticles could generate interesting electronic and optical behavior with potential nanotech-nological applications.
In the next section, we briefly describe the theoretical methodologies utilized to study the structural properties of bare and passivated gold nanoclusters, as well as the existing experimental techniques that provide useful information to complement the structural characterization of these systems. The trends on the most stable geometries of bare and passivated gold nanoclusters are then discussed including a recent prediction on the existence of chirality in such systems. Finally, some concluding remarks are presented.
THEORETICAL AND EXPERIMENTAL METHODOLOGIES
Several experimental studies have reported results on the properties of bare and thiol-passivated gold nanoclusters that constitute the building blocks of gold-based nano-structured materials. For example, structural information of bare and passivated gold nanoclusters of different sizes has been obtained using high-resolution transmission electron microscopy (HRTEM),[15-19] X-ray powder diffraction (XRPD),[20-23] scanning tunneling microscopy (STM),[24,25] and extended X-ray absorption fine structure (EXAFS).[26,27] Furthermore, optical spectrum measurements on the smallest gold particles (1-2 nm) have shown discrete electronic transitions indicating the existence of quantum size effects in these systems.[20] Despite the existence of these sophisticated experimental tools, several questions concerning the physical and chemical properties of bare and passivated gold nanoclusters remain unsolved or under debate.[9,11,12,14] For example, the current approach to determine nanocluster structures is based on the comparison between experimental HRTEM images[16,19] or XRPD and EXAFS structure factors1-20,21,26-1 with those calculated from geometrical models of these nanostructures. However, the actual experimental resolution is not sufficient to resolve the broad features shown in the XPRD patterns,[21,23] neither have the HRTEM images[16,19] allowed for a clear discrimination of the atomic positions of gold nanoclus-ters in the size range of 1-2 nm.
An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low-energy isomers (local minima) of clusters combines genetic algorithms and many-body potentials (to perform global structural optimizations over the cluster potential energy landscape), , ] with first-principles density functional theory (to confirm the stability and the energy ordering of the local minima).[9-14,33-36] This method has been recently utilized to study the structural properties of bare and passivated gold nanoclusters. In the initial stage of this approach, global unconstrained structural optimizations of bare gold nanoclusters of different sizes are performed using semiempirical many-body potentials, such as the Gupta potential,[37,38] and a genetic-symbiotic algorithm.[29,31,39,40] With this procedure, it is possible to obtain the distribution of lowest-energy isomers in a range of potential energy values for each cluster size.[28,29] From this distribution, representative isomers such as those with the lowest energy are selected, together with those isomers that are considered good candidates to be the lowest-energy minima, based on the existence of well-known symmetric structures for certain cluster sizes such as the truncated octahedron, icosahedron, or decahedron configurations.[12]
In the second stage of this approach, the first-principles methods, which do not depend on empirical parameterizations and have a reliable predictive power, are used to locally reoptimize the representative isomers obtained at the first stage. Specifically, unconstrained relaxations are performed using the forces calculated from density functional theory (DFT) in the local density (LDA) and generalized-gradient (GGA) approximations. The DFT calculations are performed using scalar relativ-istic norm conserving pseudopotentials and numerical atomic orbitals[41] or plane waves[42] as basis sets. For these quantum mechanical calculations, the atomic coordinates of each cluster, obtained from the global optimizations realized at the first stage, are used as initial conditions for the DFT relaxations.
The lowest-energy structures of passivated gold clusters are obtained by performing local relaxations, using the forces calculated from the DFT-LDA-GGA first principles method, and starting from different cluster-ligands configurations.1-9,11,12,14,43-48-1 These include the lowest energy bare gold cluster geometries obtained by the procedure described above, with the passivating molecules placed on different adsorption sites (top, bridge, and hollow), as well as on random positions over the metal cluster surface.[9,11,12,14] For passivated gold clusters, a global structural optimization, of the type mentioned above for bare gold clusters, is more difficult to perform because of the lack of adequate model potentials that describe appropriately the interaction between the metal cluster and the organic passivating molecules. Nevertheless, some calculations of this kind have been reported in connection with gold-based nanostructured materials.
STRUCTURAL PROPERTIES OF BARE GOLD NANOCLUSTERS
Extensive theoretical studies on the geometrical structures of the most stable isomers of bare gold clusters have shown that these systems have interesting and perhaps unique peculiarities. For example, in the small-size regime (n < 13), quantum mechanical calculations of neutral and charged gold clusters1-34,36,50-54-1 indicate that the lowest-energy configurations correspond to planar (two-dimensional) structures. These results have been attributed to the nonadditivity of the many-body forces existing in small noble metal clusters1-50,51-1 and to the strong sp-d hybridization caused by the large relativistic effects present in the bonding and structure of gold clusters.[52,53- This planarity in the structures of small gold clusters is being considered as an important factor for the appearance of unusual catalytic activity, recently observed in these systems.
Fig. 1 Left: stable isomers and their energies (in eV) of the Au55 cluster. The three upper configurations correspond to amorphous gold clusters. The cluster shown on the top was the lowest-energy configuration obtained in the optimization procedure. The icosahedron and octahedron structures are local minima with higher potential energy. Right: vibrational spectra of the five isomers. The vertical axis shows the degree of degeneracy.
In the intermediate-size regime (n =12-55), structural optimizations of Aun clusters have shown that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest- energy ordered isomer.[9-12,29,30,32,33,35,36,55- This is especially surprising because the calculations include ''magic'' cluster sizes for which very compact ordered structures exist. Fig. 1 shows the lowest-energy structures calculated for the Au55 cluster.1-55-1 In this case, there are several amorphous-like structures, such as those shown in the three upper panels of Fig. 1, that have higher stability than the ordered icosahedral and cuboctahedral structures.
It was shown that the analysis of the cluster local stress can be used to understand the physical origin of the higher stability of disordered clusters with respect to their ordered isomers.[33,35- Specifically, it was found that the compact ordered structures are destabilized by the tendency of metallic bonds to contract at the surface because of the decreased coordination. The cluster amorphization is also favored by the relatively low energy associated with bond length and coordination disorder in metals.[33,35- Although these are the general effects of the metallic bonding, they are especially large in the case of gold because of the short range of the many-body forces existing in this system as compared with other metals.'55- The low spatial symmetry or lack of symmetry at all in the most stable configurations of intermediate-size gold nanoclusters opened the possibility of having distinct electronic and optical properties in such systems that are of interest for the fabrication of gold-based nanostructured materials.1-10-1 In fact, the atomic disorder in the gold nanocluster structures is reflected in the broad features present in their vibra-tional and electronic density of states (DOS), as compared with the sharper structure found in the DOS corresponding to high-symmetry ordered structures.[10-Such differences could lead to distinct optical responses according to the cluster size and structural symmetry. Fig. 2 displays a comparison of different physical properties, including the vibrational and electronic DOS, between disordered and ordered gold nanoclusters of different sizes.
In HRTEM studies'-56,57- on Au and Pd nanoparticles, images of polycrystalline and amorphous structures have been reported in the size range of a few nanometers, providing experimental evidence for the existence and the stability of disordered metal nanoclusters. Further experimental evidence in this direction was obtained through the qualitative agreement between the XRPD patterns measured for Au38 and Au75 clusters and those calculated using their disordered configurations.1-28,29-1 It can be noticed in Fig. 3 the level of agreement with the experimental results between the structure factors corresponding to the disordered and ordered clusters. However, the above comparisons are not completely fair because the experimental samples corresponded to thiol-passivated gold nanoclusters, whereas the calculated structures corresponded to bare gold particles. In fact, an obvious question is what the effect is of the thiol-passivating monolayer on the physical and chemical properties of gold nanoclusters.
Fig. 2 Cluster structures, distribution of interatomic distances, vibrational density of states, and total electronic density of states (DOS) for the lowest-energy amorphous and ordered isomers of Aun (n =38, 55, 75) nanoclusters. The DFT-LDA calculated difference in cluster energy between the lowest-energy amorphous isomer and the first-ordered structure is shown. The insets show the distribution of interatomic distances of the ordered isomers. Vibrational and electronic DOS results for the ordered isomers are also included for comparison (thinner lines).
Fig. 4 Distances of the gold (i =1-38) and sulfur (i=39-62) atoms from the cluster center of mass for the Au38(SCH3)24 nanocluster in the disordered (closed circles and stars) and the truncated octahedron fcc (open circles and diamonds) structures. The inset shows the relaxed disordered structure. Sulfur atoms are depicted as darker spheres and only one CH3 group is shown.
CHIRALITY IN GOLD NANOCLUSTERS
Although most of the theoretical results mentioned above on the degeneracy in energy of amorphous or disordered isomers with ordered structures for intermediate-size gold clusters have been obtained by several research groups,’9-14,28-33,35,36,55- and the calculated XRPD structure factors of the disordered gold clusters are in qualitative agreement with the experimental data,’28,29-direct confirmation of the existence of bare and thiol-passivated gold nanoclusters with low or no spatial symmetry has not been possible. This is mainly because of the lack of enough experimental resolution in HRTEM and XRPD measurements for cluster in the size range of 1-2 nm.’20,21- Nevertheless, a recent study using circular dichroism techniques found strong optical activity in the metal-based electronic transitions (across the near-infrared, visible, and near ultraviolet regions) of size-separated glutathione-passivated gold clusters in the size range of 20-40 atoms.’58- In this work, it was pointed out that the most plausible interpretation of these results is that the structure of the metal cluster core of the gold glutathione cluster compound would be inherently chiral.’58- Moreover, because the most abundant cluster in the experimental samples corresponds to the passivated cluster Au28(SG)16, where SG denote the glutathione adsorbate, a chiral structure with T point group for the Au28 cluster was proposed.’58-
In earlier studies, several structural, vibrational, and electronic properties of disordered gold nanoclusters have been reported.’10-12,55,59 Although an initial quantification of the amount and type of local disorder present in amorphous-like structures of Au55 was obtained,’55- no attempt to theoretically investigate the existence of chirality in gold nanoclusters has been reported. Very recently, a theoretical study on the existence and quantification of chirality in bare and thiol-passivated nanoclusters was published.’11,12- In this study, the asymmetrical structures corresponding to the lowest-energy configurations of several cluster sizes, obtained by the theoretical approach described above, have been analyzed to calculate their index of chirality.’11,12- This information is relevant for a proper interpretation of the circular dichroism measurements performed on glutathi-one-passivated gold nanoclusters.’11,12-
Because chirality is a geometrical property of the system, independent of its chemical and physical manifestations, it is possible to quantify chirality without reference to experimental measurements, but using the inherent structural symmetry of the clusters. Although in recent years several approaches have been developed to measure chirality,’60,61- the Hausdorff chirality measure (HCM) has emerged as the general method of choice for the quantification of chirality.’62,63- Within this approach, the degree of chirality is found by calculating the maximum overlap between the actual molecular structure and its mirror image, using the Hausdorff distance between the sets of atomic coordinates. By rotating and translating one structure with respect to the other, the optimal overlap can be calculated. The HCM is a continuous and similarity-invariant function of the molecular shape and is zero only if the molecule is achiral.’62,63- The advantage of this approach is that its numerical implementation for large cluster sizes in a three-dimensional space is straightforward.’11,12-
Fig. 5 Top panel: distances of the gold atoms from the center of mass and cluster geometry for the lowest-energy disordered ‘closed diamonds and inset (a)- and the T ‘open circles and inset (b)- isomers of the bare Au28 cluster. Bottom panel: distances of the gold (open diamonds) and sulfur (stars) atoms from the center of mass for the lowest-energy structure of the thiol-passivated Au28(SCH3)16 cluster. The closed diamonds denote the same gold atom distances as in the top panel. They are included to show at the same scale the degree of distortion and expansion of the gold metal cluster core upon passivation. The insets show the geometries of the chiral metal cores and the passivated clusters. Sulfur atoms are depicted as darker spheres.
The HCM for the lowest-energy structures of the bare and passivated gold nanoclusters can be calculated using their relaxed Cartesian coordinates measured with respect to the cluster center of mass.’11,12- Through an inversion operation, the coordinates of the mirror-image clusters are obtained. By calculating the maximum overlap between a given cluster and its mirror image, the HCM is obtained. This corresponds to the minimum value of the Hausdorff distance between the sets of atomic coordinates of both structures. To obtain the minimum Hausdorff distance, the mirror cluster is translated and rotated around the original cluster in the three-dimensional space generating different configurations. For each configuration, the Hausdorff distance with respect to the original cluster is calculated. The minimum of these values, normalized by the largest interatomic distance in the cluster, corresponds to the HCM.’11,12-
Chiral structures, with HCM values different from zero, have been obtained for the lowest-energy isomers of bare (Au28 and Au55) and thiol-passivated ‘Au28(SCH3)16 and Au38(SCH3)24- gold nanoclusters using the HCM approach.’11,12- For the lowest-energy isomers of bare Au38 and Au75 clusters, the HCM index of chirality is zero. These values are expected because the lowest-energy structures corresponding to these sizes have one plane of symmetry and therefore are achiral. By comparing the HCM index of chirality of bare and passivated gold nanoclusters, an interesting theoretical predic-tion,’11,12- to be confirmed experimentally, indicates that the effect of the passivating thiol monolayer is strong enough to distort the bare cluster geometry, producing chiral metal cores that give rise to intense chiroptical activity. This effect could change an achiral cluster into a chiral one as in the Au38 case or increase the index of chirality in an already chiral structure as in the Au28 cluster.’11,12-
The HCM values calculated for bare and passivated clusters have been compared with the corresponding values of other chiral nanostructures such as the D2-C78 and D2-C84 fullerenes. It shows that the chiral gold clusters are as chiral as those fullerenes.’11,12- However, it remains to be seen if clusters with different chirality can be detected experimentally. In this respect, circular dichroism spectroscopy seems to be an appropriate technique to study the above effect, as has been suggested by the optical activity measurements in passivated gold-glutathione cluster compounds.’58- At present, it is expected that novel and interesting properties emerge from the chiral character of metal clusters that could be useful for new applications.
CONCLUSION
Along this article, several trends and predictions on the most stable configurations of bare and passivated gold nanoclusters, obtained through a theoretical approach that incorporates ”state-of-the-art” techniques,’39-42-have been discussed. The main conclusion emerging from these studies indicates the existence of many topologi-cally interesting low-symmetry, disordered structures, nearly degenerate in energy.’9-14,28-36- Specifically, planar,[34,36,50-54] low-symmetry,[9-12,28-33,35,36,55,59] chi-ral,[11,12] and defective[13] structures have been obtained as the most stable configurations for bare gold clusters in the size range of 3-200 atoms. On the other hand, highly distorted structures were found for gold clusters with 20-40 atoms upon passivation with thiol monolayers.[9,11,12,14] Experimental techniques such as HRTEM,[16,56,57] XRPD,[23] and circular dichroism[58] have now been used to provide further evidence to support the above predictions.
The existence and the stability of disordered structures of bare and passivated gold nanoclusters have opened the possibility of using these amorphous-like nanostructures as building-blocks of gold-based nanostructured materials, where the nanoscale disorder may produce interesting behavior with potential nanotechnological applications. Although most of the results on disordered nanostructures described in this article have focused on gold nanoclus-ters, other metals may have similar structural behavior as indicated by recent theoretical studies.[59] One important characteristic of the structural nanoscale disorder existing in gold clusters is that it is not a result of kinetic or temperature effects,[64] but of the complexity of the cluster potential energy landscape generated by the special bonding mechanisms involving Au atoms, where nonad-ditive,[50,51] relativistic,[52,53] and strong sp-d hybridization1-52,53-1 effects are present.
