Electronic structure of metal clusters

Photoemission spectra of valence electrons in metal clusters, together with threshold ionization potential measurements, provide a coherent picture of the development of the electronic structure from the isolated atom to the large metallic cluster. An insulator-metal transition occurs at an intermediate cluster size, which serves to define the boundary between small and large clusters. Although the outer electrons may be delocalized over the entire cluster, a small cluster remains insulating until the density of states near the Fermi level exceeds 1/kT. In large clusters, with increasing cluster size, the band structure approaches that of the bulk metal. However, the bands remain significantly narrowed even in a 1000-atom cluster, giving an indication of the importance of long-range order. The core-electron binding-energy shifts of supported metal clusters depend on changes in the band structure in the initial state, as well as on various final-state effects, including changes in core hole screening and the coulomb energy of the final-state charge. For cluster supported on amorphous carbon, this macroscopic coulomb shift is often dominant, as evidenced by the parallel shifts of the core-electron binding energy and the Fermi edge. Auger data confirm that final-state effects dominate in cluster of Sn and some other metals. Surface atom core-level shifts provide a valuable guide to the contributions of initial-state changes in band structure to cluster core-electron binding energy shifts, especially for Au and Pt. The available data indicate that the shift observed in supported, metallic clusters arise largely from the charge left on the cluster by photoemission. As the metal-insulator transition is approached from above, metallic screening is suppressed and the shift is determined by the local environment.     

Electronic structure of small copper clusters

An all-electron ab initio LCAO -MO SCF calculation has been carried out for the electronic structure of small copper clusters (Cu_n, n = 2–6). The basis set superposition error occurring in the calculation, the equilibrium configuration of Cu₃, the bond energy in the clusters, and the localized d-hole in excited and ionized states of Cu₂ are closely examined.     

Electronic structure of clusters modeling silica

Self-consistent-field-Xα-scattered wave calculations on clusters Si₂O₇^6? and H₆Si₂O₇ modeling silica have been performed. Incorporation of Si 3d orbitals produces significant changes in the overall valence structure. In addition to σ Si — O bonds, there exists a bonding π character due to the participation of O 2p and Si 3d. Hydrogen terminators do not seem to correct edge effects for these π states.     

Electronic shell structure in Cs-O clusters

Unusually high ionization energies have been observed for Cs-O clusters having certain sizes and composition, namely for Cs_2n+zO_n with z=8, 18, 34, 58 and 92. The anomalies are well-defined for clusters containing from 1 to 7 oxygen atoms. The indicated values of z are identical to the number of electrons in closed shells of angular momentum.     

Electronic structure of Cr clusters on graphite

The electronic structure of small chromium clusters deposited by evaporation onto clean polycrystalline graphite has been studied by means of Auger, X-ray Photoemission (XPS) and Electron Energy Loss (EELS) spectroscopies. The XPS results show an increase in the binding energy of both core levels and valence band reducing the cluster size. The EELS measurements show a variation of the intensity ratio of L₃-to-L₂ ionization core edges. We interpret this change as due to different redistribution, within the clusterd-band, of the empty states above the Fermi level. As a consequence the XPS results may also be attributed to sizeable change of the electronic structure of the small clusters.     

Electronic and geometrical structure of noble metal clusters

We investigate the electronic and structural properties of small (N 20) and medium sized (N 500) clusters of Cu, using the first principles Tight-Binding Linear Muffin-Tin Orbitals (TB-LMTO) method in connection with the real-space recursion scheme. We find the electronic structure resembling the one of simple alkali metal clusters: Pronounced shell closing effects can be identified in the ionization potentials as well as in the HOMO-LUMO gaps for the magic sizesN=8, 20, 34 and 40. The low-energy equilibrium geometries show considerable Jahn-Teller distortions, just as in the case of alkali metals.This article was processed using Springer-Verlag T_EX Z.Physik D macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Electronic structure and stability of charged beryllium clusters

Electronic structure studies on neutral, singly and doubly ionized Be _n clusters (n≤5) have been carried out in order to investigate the stability and observability of charged clusters. Our studies employ wave function expansion in terms of gaussian type orbitals and have been carried out within local spin density formalism. It is shown that although small doubly ionized clusters are unstable, they are protected from fragmentation by energy barriers. We illustrate this explicitly for trimers by presenting a Born-Oppenheimer surface of Be₃, Be ₃ ⁺ and Be ₃ ⁺⁺ . It is argued that depending on their geometries, the observable doubly charged clusters can be generated through a one or two photons ionization. We also present results on the distribution of “hole charge” in doubly ionized clusters and show that a small cluster exhibits metallic like behaviour in regard to distribution of missing electronic charge.     

Electronic shell structure in multiply charged silver clusters

Silver clusters are generated by standard laser vaporization technique and ionized via multiphoton ionization. Time-of-flight mass spectrometry reveals singly, doubly and triply charged clusters, Ag _n ^z+ (z=1,2,3). The spectra show, for all charge states, intensity variations, indicating enhanced stabilities for cluster sizes with closed electronic configurations in accord with the spherical jellium model.     

Electronic structure and magic number of alkaline metal clusters

The results of LCAO-Xα calculations for Li_n-clusters (n=2 ... 13) are presented. The origin of magic numbers in cluster beams of alkaline metals is investigated and connected with an electronic shell structure as also obtained in spherical jellium calculations.     

Electronic structure and magnetic properties of TMRh12 clusters

We report an experimental study of energy pooling collisions involving Cs atoms in the 6P and 5D states. The 5D state was populated by a cw dye-laser tuned to the cesium dipole-forbidden transition 6S → 5D at 685.0 nm. The 6P state was populated by subsequent radiative relaxation of the 5D state. The 6P population density was determined from the absorption of a cw diode-laser probe beam. The population densities of the 5D state and the higher, by energy pooling excited states were determined by measuring the corresponding fluorescence intensities relative to the fluorescence intensity from the optically thin quasi-static wings of the cesium D ₂ line. The rate coefficient for the process Cs*(6P)+Cs*(6P)→Cs**(6D)+Cs(6S) is found to be (4.2±0.13)×10^?10 cm³ s^?1 at T=570 K. In addition, estimates of the rate coefficients for the processes Cs*(6P)+Cs*(5D)→Cs**(7D)+Cs(6S) and Cs*(5D)+ Cs*(5D)→Cs**(7F)+Cs(6S) are given.     

Electronic structure and thermodynamic properties of dimeric mixed-valence clusters

A many-electron theory is proposed for exchange and tunneling levels of dimeric mixed-valence clusters. Transition-metal ions are examined, and it is established that the parameters of the Heisenberg and double-exchange interactions depend on the configuration of the d_n-electronic states. Temperature dependences are constructed for the effective magnetic moments and the electronic heat capacity.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 2, pp. 148–157, March–April, 1987.     

Electronic structure and bonding in clusters: Theoretical studies

The electronic structures of small Al _n ,n=5, 9, 13, clusters with bulk geometry are studied using the ab initio Hartree-Fock-LCAO method. The cluster ground states have always multiplicity higher than the lowest possible value. However, the energy difference between ground and lowest low spin state decreases with increasing cluster size. The energy range of the Al _n cluster valence levels is comparable with the width of the occupied part of the 3sp band in bulk Al. The different binding mechanisms that arise when a CO molecule interacts with Al _n clusters in different coordination sites are analyzed in detail with the constrained space orbital variation (CSOV) method. Electrostatic and polarization contributions to the interaction are found to be important. Among charge transfer (donation) contributions π electron transfer from Al _n to CO corresponding to π backbonding is energetically more important than σ electron transfer from CO to Al _n characterizing the σ bond.     

Electronic structure and magnetic properties of small manganese oxide clusters

To investigate the electronic structure and magnetic properties of manganese oxide clusters, we carried out first-principles electronic structure calculations for small MnO clusters. Among various structural and magnetic configurations of the clusters, the bulklike [111]-antiferromagnetic ordering is found to be favored energetically, while the surface atoms of the clusters exhibit interesting electronic and magnetic characteristics which are different from their bulk ones. The distinct features of the surface atoms are mainly attributed to the reduction of Mn coordination numbers and the bond-length contractions in the clusters, which may serve as a key factor for the understanding of physical and chemical properties of magnetic oxide nanoparticles.     

Electronic structure of diamagnetic and paramagnetic hexanuclear chalcohalide clusters of rhenium

Hexanuclear chalcohalide clusters of rhenium(III) of general formula [Re(6)S(4+x)Cl(10-x)](x-) with x = 1-4 have been studied using quantum chemical DFT calculations. The optimized structures reproduce the geometrical features found from X-ray data for the members of the series. The relative stability of different stereoisomers for the mono- and dianions has been estimated. The analysis of the tetraanion series [Re(6)Q(8)X(6)](4-) with Q = S, Se and X = Cl, Br, I, and CN demonstrates the influence of the mu(1)- and mu( 3)-ligands on the strength of Re-apical ligand bond. It is shown that the tetragonal distortion found for the stable oxidized paramagnetic species [Re(6)S(8)Cl(6)]*(3-) results from the Jahn-Teller effect for a doubly degenerate electronic state.     

Electronic structure studies on deprotonation of dithiophosphinic acids in water clusters

We report herein a computational study of proton transfer reactions between dithiophosphinic acids (HAs) and water clusters using B3LYP and MP2 methods. The ground-state and transition-state structures of HA-(H(2)O)(n) (n = 1, 2, 3) cluster complexes have been calculated. The influence of water molecules on energy barrier heights of proton transfer reactions has been examined in the gas phase and solution for bis[o-(trifluoromethyl)phenyl]- and bis(2,4,4-trimethylpentyl)dithiophosphinic acids (HA1 and HA2, respectively). Gas-phase calculations indicate that electron-withdrawing substituents and trifluoromethyl groups in the ortho position favor deprotonation of HA1 when three water molecules are included in the cluster. This suggests that at least three water molecules are necessary to solvate the abstracted proton in the presence of the anion. In the case of HA2, the electron-donating groups favor the reverse proton transfer reaction, namely, protonation of dithiophosphinate anion. Bulk solvent effects have been modeled for aqueous and organic media with the CPCM model. The calculated results show that polar solvents can lower the activation energy for less energetically stable transition states that have more localized charges.     

Electronic structure of clusters of 3d elements in layered oxide systems

Sverdlovak State Pedagogical Institute. Institute of Chemistry, Ural Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 20–25, January–February, 1991.     

Electronic properties of divalent-metal clusters

The transition from van der Waals to metallic bonding expected to occur in divalent-metal clusters (e.g., Be _n , Mg _n , Hg _n ) as a function of cluster size is discussed. Theoretical results for several electronic properties reflecting this transition in Hg _n -clusters are briefly reviewed and compared with available experiments. The limitations of the present theory particularly concerning the role of correlations and van der Waals interactions are discussed and possible improvements are suggested.     

Electronic shell structure and metal clusters: the self-consistent spheroidal jellium model

The electronic properties of small metal particles within the recently proposed self-consistent spheroidal jellium model [1] are further explored and compared to recent experimental data. Physical properties investigated include ionization potentials, electron affinities and the binding energy of neutral monomers to cationic clusters. The formalism is applied within the size-range 2≦N≦41, but could easily be extended beyondN=41. Finally, we discuss briefly the implications for the study of the dynamical response of open-shell clusters. In sharp contrast to earlier studies the functional is now corrected for self-interaction error, in a way first proposed by Pedew and Zunger [2]. This enables us to calculate reliable values for the electron affinities within ajellium-based model. This has the advantage, that we can calculate the affinities for Cu for all particle numbers for which experimental data are available. In all cases investigated we obtain excellent agreement with experiment, with pronounced shell-effects both for the electron affinities and for the binding energies, confirming in this way that the abundances map the relative stability of (Me) _N clusters, with Me being a sp-metal atom (Na, K, Li, Cu, Ag, Au etc.).     

Electronic and atomic structure of Na,Mg, Al and Pb clusters

Density functional theory is used to study the electronic and atomic structure of small clusters of Na, Mg, Al and Pb. We study the quantityE _N?1–E _N , which has relevance to the processes of cluster growth and evaporation (E _N is the total energy of the cluster withN atoms). By comparing the results of the jellium model with those of a more realistic model (although still simple) we are able to appreciate “structural” effects beyond the “electronic-shell effects” which form the essence of the predictions of the jellium model. The calculations predict formation of atomic shells and appreciable reconstruction as the cluster grows.