Eur. Phys. J. D 22, 217–227 (2003) DOI: 10.1140/epjd/e2003-00014-0 T HE EUROPEAN P HYSICAL JOURNAL D A correlation study of small silver clusters M.N. Huda and A.K. Ray a Department of Physics, The University of Texas at Arlington, P.O. Box 19059, Arlington, Texas 76019, USA Received 16 April 2002 / Received in final form 12 September 2002 Published online 21 January 2003 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2003 Abstract. The formalisms of many body perturbation theory and coupled cluster theory have been used to study the electronic and geometric structures of neutral, cationic, and anionic small silver clusters. Hay- Wadt relativistic effective core potentials replacing the twenty-eight core electrons and a Gaussian basis set have been used. Topologically different clusters and clusters belonging to different symmetry groups have been identified and studied in detail. Full geometry optimizations have been carried out at four different correlated levels of theories. Ionization potentials, electron affinities, and fragmentation energies of the optimized clusters have been compared with other experimental and theoretical results available in the literature. No convergence problems are encountered at the various levels of correlated theories. This is noteworthy since it has been claimed in the literature that for d elements the MP series does not converge very well. PACS. 71.15.Nc Total energy and cohesive energy calculations – 73.22.-f Electronic structure of nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals 1 Introduction Clusters are distinctly different from their bulk-state, and exhibit many specific properties, which distinguishes their studies as a completely different branch of science named “Cluster Science”. Ideas like “super-atoms”, “magic num- bers” or “fission” in clusters [1–3] provokes a wider class of scientists to study this “relatively” new area of the phys- ical sciences. Growing interest in the stabilities of small clusters and the evolution of bulk properties from cluster properties is also due to the emergence of a new science called nanoscience and its potential in industrial applica- tions. Moreover, a complete understanding of the physics of clusters, employing different theoretical models, is itself a demanding topic in many body physics. In the study of metal clusters, silver has received particular attention be- cause of two reasons: one is theoretical in that the silver has d-electrons at the outer orbitals, overlapped by the partially filled s-orbitals, which makes the study of silver clusters interesting and challenging; the second one is ap- plied because of the importance of silver in photographic and catalytic processes [4]. There is, in fact, a recent growth of experimental work concerning different aspects of silver clusters [5–13]. Spasov et al. [14] used energy-resolved collision-induced dissociation (CID) method to study fragmentation pat- terns, cross-sections, and dissociation energies of anionic silver clusters (Ag - n , n = 2–11). The main reaction chan- nels were found to be the loss of an atom and also the loss of a dimer, with the dimer less favored for odd n values. The dissociation energies for the loss of an atom showed a e-mail: akr@uta.edu strong odd-even alternation. Photoelectron spectra of sil- ver clusters were studied by Handschuh et al. [15] at dif- ferent photon energies to explore the electronic structures of individual clusters. They observed sharper spectral pat- terns of Ag clusters than the corresponding alkali metal clusters which, according to the authors, might be due to the stronger bonding in silver clusters. This can be inter- preted as the result of overlapping of the outer d and s orbitals, which gives rise to van der Waals type attractive force. Femtosecond NeNePo (negative to neutral to pos- itive) spectroscopy was used to study the structural dy- namics of Ag 3 clusters [16], and the wave packet dynamics along the coordinate of the linear-to-triangular rearrange- ment on the ground state potential surface was reported in details by Boo et al. [17]. The authors also commented about breaking of the degeneracy of the neutral Ag 3 state due to strong Jahn-Teller effect. Between the two possible valence electronic configu- ration 2 D(4d 9 5s 2 ) and 2 S(4d 10 5s 1 ), we found the former state to be at 4.22 eV higher than the latter one at the fourth-order many-body perturbation theory level (MP4) of calculation and the 2 P(4d 10 5p 1 ) state at 3.28 eV higher. Though the chemistry is primarily due to the valence s- electrons, the electronic properties and the stability of the clusters are strongly dominated by the filled d-electrons screening the oscillator strength of valence electrons [18]. As pointed out by Luh et al. [19] in their studies of d- band quantum well states, the d-electrons have more lo- calized wave functions and experience a larger correlation effect and have smaller energy dispersions and group ve- locities, for silver 4d shell is almost like a shallow core- level. Moreover, d and outer s valence electron correlation