Photoabsorption spectra of sodium clusters

Abstract

Absolute photoabsorption cross sections of free neutral sodium clusters containing from N =3 to 40 atoms are presented. Investigation of a wide continuous range of cluster sizes reveals the size development of the photoabsorption behavior. In the smallest clusters the absorption is moleculelike.A transition to collective electronic excitations (surface plasmons) occurs in the size range of N =3 to 5. For clusters with N=6 to 12 atoms the surface plasma resonances are particularly well defined, and their positions are consistent with the predictions of an ellipsoidal shell model. The cluster shapes can be deduced from the observed resonance positions; the data provide a sensitive measurement of the relative axis lengths of ellipsoidal clusters. For clusters containing N~3 atoms, the plasma resonances do not always coincide with the positions predicted by the ellipsoidal shell model. In addition to these resonances, which dominate the spectra, there are three distinct wavelength regions within which absorption occurs for all investigated clusters.

Photoabsorption in sodium clusters on the basis of time-dependent density-functional theory

“…These observations strongly point to occurring collective plasmon excitations, which have also been observed experimentally. [9][10][11]25,52 In total, we have found an excellent agreement with the experimental obtained absorption spectra of Wang and co-workers. 12,13 The spectra also match well with those of Bonačić-Koutecký and co-workers [16][17][18] and others.…”

Highly Fluorescent Noble-Metal Quantum Dots

“…Identical to that for gas phase alkali metal nanocluster electronic absorption (27,44), the transition energy scaling with inverse cluster radius indicates that electronic structure is solely determined by the Au nanocluster free electron density and nanocluster size. Analogous to the protoplasmonic transitions in gas phase alkali clusters (26,44), our observations suggest that the free electron shell-filling model corresponds exactly to the spherical jellium approximation -the simplest model for explaining delocalized, free conduction electron behavior relative to the atomic cluster core, and an excellent basic model explaining plasmon absorption in large nanoparticles (23,25,42).…”

“…Since free electrons are piled up in metal clusters with constant electron density, Fermi energies of "free electron" metals only depend on the electron density (ρ 0 ) or the Wigner-Seitz radius (r s ) of the metals [5] By combining equations 4 and 5, a very simple relation of frequency, particle radius, and Fermi energy can be derived (23,25,27,30,40) [6] This simple relation explains how the electronic structures of metallic clusters scale with the number of free electrons, and has been confirmed by many gas phase studies that clearly indicate strong size-dependent transitions from single electron intraband resonances to collective plasmon oscillation in few atom metal clusters (1,2,(24)(25)(26)(27)43,44). These studies typically photodissociate the clusters, however, and do not probe the lowest lying transitions.…”

“…Both regimes scale with inverse cluster radius as the delocalized free electron states giving rise to nanocluster fluorescence become sufficiently dense at larger sizes that they enable the Au nanoparticle plasmon absorptions and generate the characteristic N −1/3 scaling of the plasmon width. Consequently, the size dependent transition frequencies of our water soluble Au nanoclusters are the small size limit of the plasmon absorption within bulk metals and provide a smooth connection between atomic and metallic behavior with true protoplasmonic fluorescence that is well-described at all sizes by the spherical jellium model (26).…”

“…While nicely demonstrated in the gas phase for alkali metals (23)(24)(25)(26)(27), Au (28)(29)(30) and Ag clusters (31)(32)(33) offer not only the opportunity for maintaining metallic properties in aqueous solutions, but also great promise as a new class of biolabels. Much fundamental and applied work continues in our laboratory and in others (34)(35)(36)(37)(38) on these materials due to their exciting optical properties.…”