Because of an inadvertent error in programming, some data presented in Figs. 8 and 9 of our paper are inaccurate. The new Fig. 8 with the corrected s , p , d angular decompositions of the Kohn-Sham levels of Au 20 and the new Fig. 9 with the corrected d characters of the optical excitations are presented below. The net effect of these corrections is to increase the d character of the optical excitations in both Ag n and Au n clusters. We note that the d-electron contributions to the optical excitations of Au n clusters are still, on average, larger than those of Ag n clusters. However, the difference between the d characters of the optical excitations of Ag n and Au n clusters is not as pronounced as we originally reported. These corrections do not affect the main conclusions of our paper. 0.00 0.05 0.10 0.15 1.5 2.0 2.5 3.0 Oscillator Strength Energy (eV) 83% 31% 12% 16% 8% 13% 34% 10% 13% 8% (3) HOMO−10 (98% d) (3) HOMO−9 (98% d) (2) HOMO−7 (14% sp, 86% d) (1) HOMO−6 (35% s, 42%p, 23% d) (3) HOMO−3 (95% d) (3) HOMO−2 (93% d) (3) HOMO−1 (39% s, 18% p, 43% d) (2) HOMO (27% s, 25% p, 48% d) (3) LUMO+1 (25% s, 41% p, 34% d) (3) LUMO+3 (31% s, 41% p, 28% d) (3) LUMO (23% s, 58% p, 19% d) 20 Au FIG. 8. ͑Color online͒ The Kohn-Sham energy levels ͑within LDA͒ of Au 20 that are involved in the excitations at 1.86 eV, 2.777 eV, and 2.785 eV. The degeneracies ͑in parentheses͒ and the angular characters of the occupied and unoccupied orbitals involved in the transitions are given next to the energy levels. The weights ͑in %͒ of the vc orbital pairs in the eigenvectors of the transitions are also shown. See the text for details.2 3 4 5 6 7 8 9 10 11 12 13 14 20 Cluster Size (atoms) 10 20 30 40 50 60 70 80 % d-character Au , Ec = 9 eV Au , Ec = 6 eV Au , Ec = 4 eV Ag , Ec = 9 eV Ag , Ec = 6 eV Ag , Ec = 4 eV n n n n n n FIG. 9. ͑Color online͒ The percentage of the d-character in the transitions calculated according to Eq. 2 for Au n ͑solid lines͒ as a function of n at cutoff energies E c =4,6, and 9 eV. Also shown are the same results for Ag n ͑dashed lines͒.

Static polarizabilities and optical absorption spectra for the ground state structures of gold clusters ͑Au n , n =2-14 and 20͒ are investigated from first principles within static and time-dependent density functional theory. The static polarizabilities of clusters with less than 14 atoms generally increase as a function of size modulated by even-odd oscillations. The polarizabilities of Au 14 and Au 20 are noticeably lower due to the shape transition from two-dimensional to three-dimensional structures at n = 14. The analyses of the optical absorption spectra calculated within the time-dependent local density approximation indicate that the d electrons in Au n clusters are significantly more involved in low-energy transitions and give rise to more quenched oscillator strengths ͑by screening the s electrons͒ than in Ag n clusters. These stronger effects of the d electrons in the optical properties of Au n are due to the larger degree of proximity of the s and d levels in the Au atom as compared to the Ag atom, which gives rise to stronger s-͑p͒-d hybridization in the molecular orbitals of Au n . The calculated spectra are found to be in good agreement with experimental data and results from earlier studies for the available sizes.

We present a series of electron energy-loss spectroscopy (EELS) studies on niobium (Nb) and its oxides (NbO, NbO2, and Nb2O5) to develop a reliable method for quantifying the oxidation state in mixed niobium oxide thin films. Our approach utilizes a combination of transmission electron microscopy and EELS experiments with density functional theory calculations to distinguish between metallic niobium and the different niobium oxides. More specifically, the differences in the near-edge fine-structure of the Nb M-edge and O K-edge provide sufficient information to determine the valence state of niobium. Based on these observed changes in the core-loss edges, we propose a linear relationship that correlates the peak positions in the Nb M- and O K-edges with the Nb valence state. The methods developed in this paper are also applied to ultrathin niobium oxide films to examine the effects of low-temperature baking on the films’ oxidation states.

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