We present a systematic study of the electronic properties and the geometric structure of noble metal clusters X n (X = Cu, Ag, Au; =−1,0, +1; n ഛ 13 and n =20), obtained from first-principles generalized gradient approximation density functional calculations based on norm-conserving pseudopotentials and numerical atomic basis sets. We obtain planar structures for the ground state of anionic ͑ =−1͒, neutral ͑ =0͒, and cationic ͑ =1͒ species of gold clusters with up to 12, 11, and 7 atoms, respectively. In contrast, the maximum size of planar clusters with =−1,0, +1 are n = ͑5,6,5͒ for silver and (5,6,4) for copper. For X 20 we find a T d symmetry for gold and a compact C s structure for silver and copper. Our results for the cluster geometries agree partially with previous first-principles calculations, and they are in good agreement with recent experimental results for anionic and cationic gold clusters. The tendency to planarity of gold clusters, which is much larger than in copper and silver, is strongly favored by relativistic effects, which decrease the s-d promotion energy and lead to hybridization of the half-filled 6s orbital with the fully occupied 5d z 2 orbital. That picture is substantiated by analyzing our calculated density matrix for planar and three-dimensional clusters of gold and copper. The trends for the cohesive energy, ionization potentials, electron affinities, and highest accupied and lowest unoccupied molecular orbital gap, as the cluster size increases, are studied in detail for each noble metal and rationalized in terms of two-and three-dimensional electronic shell models. The most probable fragmentation channels for X n clusters are in very good agreement with available experiments.

We analyse the transition state energies for 249 hydrogenation/dehydrogenation reactions of atoms and simple molecules over close-packed and stepped surfaces and nanoparticles of transition metals using Density Functional Theory. Linear energy scaling relations are observed for the transition state structures leading to transition state scaling relations for all the investigated reactions. With a suitable choice of reference systems the transition state scaling relations form a universality class that can be approximated with one single linear relation describing the entire range of reactions over all types of surfaces and nanoclusters.

There has been substantial progress in the description of adsorption and chemical reactions of simple molecules on transition-metal surfaces. Adsorption energies and activation energies have been obtained for a number of systems, and complete catalytic reactions have been described in some detail. [1][2][3][4][5][6][7] Considerable progress has also been made in the theoretical description of the interaction of molecules with transition-metal oxides, [8][9][10][11][12][13][14][15][16][17][18][19] sulfides, [20][21][22][23][24][25] and nitrides, [26][27][28][29] but it is considerably more complicated to describe such complex systems theoretically. Complications arise from difficulties in describing the stoichiometry and structure of such surfaces, and from possible shortcomings in the use of ordinary generalized gradient approximation (GGA) type density functional theory (DFT).[30]Herein we introduce a method that may facilitate the description of the bonding of gas molecules to transitionmetal oxides, sulfides, and nitrides. It was recently found that there are a set of scaling relationhips between the adsorption energies of different partially hydrogenated intermediates on transition-metal surfaces.[31] We will show that similar scaling relationships exist for adsorption on transition metal oxide, sulfide, and nitride surfaces. This means that knowing the adsorption energy for one transition-metal complex will make it possible to quite easily generate data for a number of other complexes, and in this way obtain reactivity trends.The results presented herein have been calculated using self-consistent DFT. Exchange and correlation effects are described using the revised Perdew-Burke-Ernzerhof (RPBE) [32] GGA functional. It is known that GGA functionals give adsorption energies with reasonable accuracy for transition metals. [32,33] It is not clear, however, whether a similar accuracy can be expected for the oxides, sulfides, and nitrides, although there are examples of excellent agreement between DFT calculations and experiments, for example, with RuO 2 surfaces.[9] In our study we focused entirely on variations in the adsorption energies from one system to another, and we expected that such results would be less dependent than the absolute adsorption energies on the description of exchange and correlation.For the nitrides, a clean surface and a surface with a nitrogen vacancy were studied. For MX 2 -type oxides or sulfides, an oxygen-or sulfur-covered surface with an oxygen or sulfur vacancy was studied. The structures of the clean surface considered in the present work and their unit cells are shown in Figure 1. The adsorption energies given below are for the adsorbed species in the most stable adsorption site on the surface.By performing calculations for a large number of transition-metal surfaces of different orientations, [31] it was found that the adsorption energy of intermediates of the type AH x is linearly correlated with the adsorption energy of atom A (N, O, S) according to Equation (1):Here the scali...

There has been substantial progress in the description of adsorption and chemical reactions of simple molecules on transition-metal surfaces. Adsorption energies and activation energies have been obtained for a number of systems, and complete catalytic reactions have been described in some detail. [1][2][3][4][5][6][7] Considerable progress has also been made in the theoretical description of the interaction of molecules with transition-metal oxides, [8][9][10][11][12][13][14][15][16][17][18][19] sulfides, [20][21][22][23][24][25] and nitrides, [26][27][28][29] but it is considerably more complicated to describe such complex systems theoretically. Complications arise from difficulties in describing the stoichiometry and structure of such surfaces, and from possible shortcomings in the use of ordinary generalized gradient approximation (GGA) type density functional theory (DFT).[30]Herein we introduce a method that may facilitate the description of the bonding of gas molecules to transitionmetal oxides, sulfides, and nitrides. It was recently found that there are a set of scaling relationhips between the adsorption energies of different partially hydrogenated intermediates on transition-metal surfaces.[31] We will show that similar scaling relationships exist for adsorption on transition metal oxide, sulfide, and nitride surfaces. This means that knowing the adsorption energy for one transition-metal complex will make it possible to quite easily generate data for a number of other complexes, and in this way obtain reactivity trends.The results presented herein have been calculated using self-consistent DFT. Exchange and correlation effects are described using the revised Perdew-Burke-Ernzerhof (RPBE) [32] GGA functional. It is known that GGA functionals give adsorption energies with reasonable accuracy for transition metals. [32,33] It is not clear, however, whether a similar accuracy can be expected for the oxides, sulfides, and nitrides, although there are examples of excellent agreement between DFT calculations and experiments, for example, with RuO 2 surfaces.[9] In our study we focused entirely on variations in the adsorption energies from one system to another, and we expected that such results would be less dependent than the absolute adsorption energies on the description of exchange and correlation.For the nitrides, a clean surface and a surface with a nitrogen vacancy were studied. For MX 2 -type oxides or sulfides, an oxygen-or sulfur-covered surface with an oxygen or sulfur vacancy was studied. The structures of the clean surface considered in the present work and their unit cells are shown in Figure 1. The adsorption energies given below are for the adsorbed species in the most stable adsorption site on the surface.By performing calculations for a large number of transition-metal surfaces of different orientations, [31] it was found that the adsorption energy of intermediates of the type AH x is linearly correlated with the adsorption energy of atom A (N, O, S) according to Equation (1):Here the scali...

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We study, from first-principles quantum mechanical calculations, the structural and electronic properties of several low-lying energy equilibrium structures of isoelectronic Si n M clusters ͑M =Sc − ,Ti,V + ͒ for n = 14-18. The main result is that those clusters with n = 16 are more stable than its neighbors, in agreement with recent experimental mass spectra. By analyzing the orbital charge distribution and the partial orbital density of states, that special stability is rationalized as a combination of geometrical ͑near spherical cagelike structure for n =16͒ and electronic effects ͑l-selection rule of the spherical potential model͒. The structures of the two lowest energy isomers of Si 16 M are nearly degenerate, and consist of the Frank-Kasper polyhedron and a distortion of that polyhedron. The first structure is the ground state for M =V + , and the second is the ground state for Ti and Sc − . For the lowest energy isomers of clusters Si n M with n = 14-18, we analyze the changes with size n, and impurity M of several quantities: binding energy, second difference of total energy, HOMO-LUMO gap, adiabatic electron affinity, addition energy of a Si atom, and addition energy of an M impurity to a pure Si n cluster. We obtain good agreement with available measured adiabatic electron affinities for Si n Ti.

We study why gold forms planar and cage-like clusters while copper and silver do not. We use density functional theory and norm-conserving pseudo-potentials with and without a scalar relativistic component. For the exchange-correlation (xc) functional we use both the generalized gradient (GGA) and the local density (LDA) approximations. We find that planar Aun structures, with up to n = 11, have lower energy than the three-dimensional isomers only with scalar-relativistic pseudopotentials and the GGA. In all other calculations, with more than 6 or 7 noble metal atoms, we obtain three dimensional structures. However, as a general trend we find that planar structures are more favorable with GGA than with LDA. In the total energy balance, kinetic energy favors planar and cage structures, while xc-energy favors 3D structures. As a second step, we construct cluster structures having only surface atoms with O h , T d , and I h symmetry. Then, assuming one valence electron per atom, we select those with 2(l + 1) 2 electrons (with l integer), which correspond to the filling of a spherical electronic shell formed by node-less one electron wave functions. Using scalar relativistic GGA molecular dynamics at T = 600K, we show that the cage-like structures of neutral Au32, Au50, and Au162 are meta-stable. Finally, we calculate the static polarizability of the two lowest energy isomers of Aun clusters as a means to discriminate isomers with planar (or cagelike) geometry from those with compact structures. We also fit our data to a semi-empirical relation for the size dependent polarizability which involves the effective valence and the kinetic energy components for the homogeneous and inhomogeneous electron density. Analyzing that fit, we find that the dipole polarizability of gold clusters with planar and cage-like structures corresponds to the linear response of 1.56 delocalized valence electrons, suggesting a strong screening of the valence interactions due to the d-electrons.

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