Comprehensive study of sodium, copper, and silver clusters over a wide range of sizes 2≤N≤75

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 meta-stable 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 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 defined in the framework of total energy calculations for the first time. In the case of NaN , a semi-quantitative comparison between the experimental abundance spectra (Knight et al., Phys. Rev. Lett. 52, 2141Lett. 52, (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 HOMO-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.

Research Update: Density functional theory investigation of the interactions of silver nanoclusters with guanine

“…57 Their results for Ag 3-6 are comparable to those described above with one disparity. Their study suggests that the triangular Ag 3 is the lowest energy isomer by 0.028 eV whereas we calculate the linear isomer to be more stable by ∼0.06 eV.…”

“…The lowest energy isomer for the neutral system is planar in agreement with previous work that suggested that the 2D-3D transition for the neutral Ag cluster does not occur until Ag [6][7] . 57 The linear structures are no longer contenders for the lowest energy isomer as they are more than 1.0 eV less stable than the most favorable isomers (Table I). The +1 cationic system now exhibits a three-dimensional lowest-energy structure denoted 3D bowtie.…”

σ-Holes on Transition Metal Nanoclusters and Their Influence on the Local Lewis Acidity

“…In broad terms, the most favorable atomic conformation, magnetic spin-state and electronic valence configuration vary largely for clusters of different TM elements. A common feature is that as the size of the cluster grows, the favorable structure converges towards the compact, close-packed, bulk structure of the corresponding metal [53][54][55][56]. However, at the (sub) nanometer scale, it has been established that clusters of e.g., Rh, Ru, and Ir, adopt an open cubic structure, whereas 3d clusters of Cu, Au and Pd are often found to be compact and possibly disordered [14,57].…”

On the work function and the charging of small (r≤ 5 nm) nanoparticles in plasmas

“…The DFT calculations were performed by modeling small Cu nanoparticles [19] in the range of 1 to 38 atoms with different charges ranging from +1 to -2 (to avoid mixed nomenclature we use the term nanoparticles for all sizes, even down to single atoms). These were geometry optimized using the Berny algorithm [20] to find the local energy-minima structures (see figures in Appendix), thus obtaining the relaxed energy.…”