# Growth behaviors and electronic structures of Na and Cu nanoclusters: The role of sp-d hybridization

10 Jul 2005-International Journal of Modern Physics B (World Scientific Publishing Company)-Vol. 19, pp 2421-2426

TL;DR: In this article, the effects of sp-d hybridization on the atomic and electronic structures of CuN clusters are discussed, which can be characterized into three regimes: planar, layered and 3D structures.

Abstract: Ab initio calculations of the atomic and electronic structures of CuN and NaN (N = 2 - 22) clusters show similar growth behaviors. These can be characterized into 3 regimes: planar, layered and 3D structures. Atomic structures lead to anomalies in the even-odd alternation behavior of the second order energy difference for N = 16 and 17 in both CuN and NaN. The effects of sp-d hybridization on the atomic and electronic structures of CuN clusters are discussed.

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TL;DR: The evolution of the structure and shape of the preferred configuration of Cu(n), n

Abstract: Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cun clusters over the size range n=8–20. For n=8–16, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n⩽6). For n=17 and beyond, there is a transition to compact structures containing an icosahedral 13-atom core. The calculated ground-state structures are significantly different from those predicted earlier in studies based on empirical and semiempirical potentials. The evolution of the structure and shape of the preferred configuration of Cun, n⩽20, is shown to be nearly identical to that found for Na clusters, indicating a shell-model-type behavior in this size range.

89 citations

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TL;DR: There is a similarity in the N dependence of the HOMO-LUMO gap between the three metal clusters, it is much stronger between the two noble metal clusters and the magic number is explicitly defined with a new criterion in the framework of total energy calculations.

Abstract: The geometric and electronic structures of NaN, CuN, and AgN metal clusters are systematically studied based on the density functional theory over a wide range of cluster sizes 2≤N≤75. A remarkable similarity is observed between the optimized geometric structures of alkali and noble metal clusters over all of the calculated cluster sizes N. The most stable structures are the same for the three different metal clusters for approximately half the cluster sizes N considered in this study. Even if the most stable structures are different, the same types of structures are obtained when the metastable structures are also considered. For all of the three different metal clusters, the cluster shapes change in the order of linear, planar, opened, and closed structures with increasing N. This structural-type transition leads to a deviation from the monotonic increase in the specific volume with N. A remarkable similarity is also observed for the N dependence of the cluster energy E(N) for the most stable geometric structures. The amplitude of this energy difference is larger in the two noble metal clusters than in the alkali metal cluster. This is attributed to the contribution of d electrons to the bonds. The magic number is explicitly defined with a new criterion in the framework of total energy calculations. In the case of NaN, a semiquantitative comparison between the experimental abundance spectra [Knight et al., Phys. Rev. Lett. 52, 2141 (1984)] and the total energy calculations is carried out. The changing aspect of the Kohn–Sham eigenvalues from N=2 to N=75 is presented for the three different metal clusters. The feature of the bulk density of states already appears at N=75 for all of three clusters. With increasing N, the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap clearly exhibits an odd-even alternation and converges to 0. Although there is a similarity in the N dependence of the HOMO-LUMO gap between the three metal clusters, it is much stronger between the two noble metal clusters. The growth aspect of the d band below the Fermi level of the noble metal clusters with increasing N is presented. A good correspondence is observed in the d characteristic of the electronic states between the cluster composed of 75 atoms and the bulk metal. The similarities observed in the N dependence of the geometric structures and E(N)s originate from the similarity in that of the electronic structures.

73 citations

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TL;DR: In this paper, the geometric and electronic structures of NaN, CuN, and AgN metal clusters are systematically studied based on the density functional theory over a wide range of cluster sizes 2=

Abstract: The geometric and electronic structures of NaN, CuN, and AgN metal clusters are systematically studied based on the density functional theory over a wide range of cluster sizes 2=

64 citations

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TL;DR: In this paper, optical absorption spectra in the UV-visible range (1.6 eV < ℏω < 5.5 eV) of mass selected neutral copper clusters were measured in a solid neon matrix at 7 K.

Abstract: We present optical absorption spectra in the UV-visible range (1.6 eV < ℏω < 5.5 eV) of mass selected neutral copper clusters Cu(n)(n = 1-9) embedded in a solid neon matrix at 7 K. The atom and the dimer have already been measured in neon matrices, while the absorption spectra for sizes between Cu(3) and Cu(9) are entirely (n = 6-9) or in great part new. They show a higher complexity and a larger number of transitions distributed over the whole energy range compared to similar sizes of silver clusters. The experimental spectra are compared to the time dependent density functional theory (TD-DFT) implemented in the TURBOMOLE package. The analysis indicates that for energies larger than 3 eV the transitions are mainly issued from d-type states; however, the TD-DFT scheme does not reproduce well the detailed structure of the absorption spectra. Below 3 eV the agreement for transitions issued from s-type states is better.

63 citations

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TL;DR: In this article, the 6-atom clusters of group IB noble metals have been investigated theoretically using the density functional calculation with a plane-wave basis (CASTEP), and their optimized structures, relative cluster's energies, atomic and bonding populations, spectra of the vibrational frequencies, energy gaps between the highest occupied and the lowest unoccupied molecular orbitals, and average polarizabilities per atom.

Abstract: The 6-atom clusters of group IB noble metals have been investigated theoretically using the density functional calculation with a plane-wave basis (CASTEP). We have calculated their optimized structures, relative cluster’s energies, atomic and bonding populations, spectra of the vibrational frequencies, energy gaps between the highest occupied and the lowest unoccupied molecular orbitals, and average polarizabilities per atom. The stable structures we found are planar triangular, pentagonal pyramid, and capped trigonal bipyramid. For the Cu6 and Ag6 cluster, the planar structure energetically competes with the pyramid structure for the ground state. According to the population analyses, the s–d orbital hybridization is explicitly shown to be in association with the corner atoms of the planar structure. We found that the vibrational spectra of the clusters are structural dependent. The average polarizabilities for the planar structure of the Cu6 and Ag6 cluster are quite different from their other stable isomers. In contrast, the polarizabilities are about the same for all stable gold hexamers. Our calculations benefit a reliable geometry identification of the 6-atom noble metal clusters.

36 citations

##### References

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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

117,932 citations

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TL;DR: In this article, the electronic properties and the geometric structure of noble metal clusters were studied and the trend for the cohesive energy, ionization potentials, electron affinities, and highest accupied and lowest unoccupied molecular orbital gap was analyzed in detail for each noble metal and rationalized in terms of two-and three-dimensional electronic shell models.

Abstract: We present a systematic study of the electronic properties and the geometric structure of noble metal clusters ${X}_{n}^{\ensuremath{
u}}$ ($X=\mathrm{Cu}$, Ag, Au; $\ensuremath{
u}=\ensuremath{-}1,0,+1$; $n\ensuremath{\leqslant}13$ 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 $(\ensuremath{
u}=\ensuremath{-}1)$, neutral $(\ensuremath{
u}=0)$, and cationic $(\ensuremath{
u}=1)$ species of gold clusters with up to 12, 11, and 7 atoms, respectively. In contrast, the maximum size of planar clusters with $\ensuremath{
u}=\ensuremath{-}1,0,+1$ are $n=(5,6,5)$ 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 $s\text{\ensuremath{-}}d$ promotion energy and lead to hybridization of the half-filled $6s$ orbital with the fully occupied $5{d}_{{z}^{2}}$ 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 ${X}_{n}^{\ensuremath{
u}}$ clusters are in very good agreement with available experiments.

474 citations

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TL;DR: In this article, the results of extensive computer simulations of several sodium microclusters, using the Car-Parrinello method (unified density functional theory and molecular dynamics), were presented.

Abstract: We present the results of extensive computer simulations of several sodium microclusters, using the Car–Parrinello method (unified density‐functional theory and molecular dynamics). Dynamical simulated annealing strategies are adopted in the search for low‐energy minima of the potential energy surface. A detailed analysis of the results for both structural and electronic properties at temperatures in the 0–600 K range is carried out, which allows us for the first time to gain insight into the structural ‘‘growth’’ pattern, the extent of the validity of (spherical, spheroidal, and ellipsoidal) jellium models, and the effects of temperature. In particular, new and unforeseen structures are discovered for n=10, 13, 18, and 20 and we emphasize the constant presence of arrangements with local pentagonal symmetry for the low‐energy isomers as well as the similarity of the structural pattern with that of Lennard‐Jones systems. Shape transformations with increasing temperature are observed, ‘‘rigidity’’ and ‘‘nonrigidity’’ of the individual clusters examined, and the presence of distinct isomers is identified for the smaller ones. Closing of electronic shells is confirmed for Na8 and Na20 and—to a minor extent only—for Na18. Hybridization of cluster states of different angular momenta, which represents a deviation from the spherical shell model, is discovered in several cases and discussed in detail, also in correspondence with the presence of anisotropy of the electronic potential. In most cases, this hybridization is observed to increase with increasing temperature, in parallel with the increase of the eccentricity of the cluster shape. In spite of the relatively high atomic mobility, our results do not support a spherical liquid‐droplet picture for the atomic distribution.

240 citations

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TL;DR: High resolution UV-photoelectron spectra of cold mass selected Cun, Agn, and Aun- with n=53-58 show that only Cu55- and Ag55- exhibit highly degenerate states, a direct consequence of their icosahedral symmetry, as confirmed by density functional theory calculations.

Abstract: We present high resolution UV-photoelectron spectra of cold mass selected ${\mathrm{C}\mathrm{u}}_{n}^{\ensuremath{-}}$, ${\mathrm{A}\mathrm{g}}_{n}^{\ensuremath{-}}$, and ${\mathrm{A}\mathrm{u}}_{n}^{\ensuremath{-}}$ with $n=53--58$. The observed electron density of states is not the expected simple electron shell structure, but is strongly influenced by electron-lattice interactions. Only ${\mathrm{C}\mathrm{u}}_{55}^{\ensuremath{-}}$ and ${\mathrm{A}\mathrm{g}}_{55}^{\ensuremath{-}}$ exhibit highly degenerate states. This is a direct consequence of their icosahedral symmetry, as is confirmed by density functional theory calculations. Neighboring sizes exhibit perturbed electronic structures, as they are formed by removal or addition of atoms to the icosahedron and therefore have lower symmetries. Gold clusters in the same size range show completely different spectra with almost no degeneracy, which indicates that they have structures of much lower symmetry. This behavior is related to strong relativistic bonding effects in gold, as demonstrated by ab initio calculations for ${\mathrm{A}\mathrm{u}}_{55}^{\ensuremath{-}}$.

218 citations

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TL;DR: In this article, the authors study nine neutral copper clusters through the theoretical characterization of their molecular structures, binding energy, electronic properties, and reactivity descriptors, using density functional theory calculations with a hybrid functional combined with effective core potentials.

Abstract: In this paper we study nine neutral copper clusters through the theoretical characterization of their molecular structures, binding energy, electronic properties, and reactivity descriptors. Geometry optimization and vibrational analysis were performed using density functional theory calculations with a hybrid functional combined with effective core potentials. It is shown that reactivity descriptors combined with reactivity principles like the minimum polarizability and maximum hardness are operative for characterizing and rationalizing the electronic properties of copper clusters.

163 citations