Optical Absorption Spectra of Ag11 Isomers by First-Principles Theoretical Spectroscopy with Time-dependent Density Functional Theory

📝 Abstract

The optical absorption spectrum of the three most stable isomers of the Ag11 system was calculated using the time-dependent density functional theory, with the generalized gradient approximation for the exchange and correlation potential, and a relativistic pseudopotential parametrization for the modelling of the ion-electron interaction. The computational scheme is based on a real space code, where the photoabsorption spectrum is calculated by using the formalism developed by Casida. The significantly different spectra of the three isomers permit the identification of the ground-state configuration predominantly present in the laboratory beams in base to a comparison between the calculated photoabsorption spectrum of the most stable configuration of Ag11 and the measured spectra of medium-size silver clusters trapped in noble gas Ar and Ne matrices at different temperatures. This assignment is confirmed by the fact that this isomer has the lowest calculated energy.

💡 Analysis

The optical absorption spectrum of the three most stable isomers of the Ag11 system was calculated using the time-dependent density functional theory, with the generalized gradient approximation for the exchange and correlation potential, and a relativistic pseudopotential parametrization for the modelling of the ion-electron interaction. The computational scheme is based on a real space code, where the photoabsorption spectrum is calculated by using the formalism developed by Casida. The significantly different spectra of the three isomers permit the identification of the ground-state configuration predominantly present in the laboratory beams in base to a comparison between the calculated photoabsorption spectrum of the most stable configuration of Ag11 and the measured spectra of medium-size silver clusters trapped in noble gas Ar and Ne matrices at different temperatures. This assignment is confirmed by the fact that this isomer has the lowest calculated energy.

📄 Content

Optical Absorption Spectra of Ag11 Isomers by First-Principles Theoretical Spectroscopy with Time-dependent Density Functional Theory Jos´e I. Mart´ınez1, ∗and Eva M. Fern´andez1, † 1Center for Atomic-scale Materials Design, Department of Physics NanoDTU, Technical University of Denmark, DK-2800 Lyngby (Denmark) (Dated: April 26, 2022) The optical absorption spectrum of the three most stable isomers of the Ag11 system was calculated using the time-dependent density functional theory, with the generalized gradient approximation for the exchange and correlation potential, and a relativistic pseudopotential parametrization for the modelling of the ion–electron interaction. The computational scheme is based on a real space code, where the photoabsorption spectrum is calculated by using the formalism developed by Casida. The significantly different spectra of the three isomers permit the identification of the ground-state configuration predominantly present in the laboratory beams in base to a comparison between the calculated photoabsorption spectrum of the most stable configuration of Ag11 and the measured spectra of medium-size silver clusters trapped in noble gas Ar and Ne matrices at different temperatures. This assignment is confirmed by the fact that this isomer has the lowest calculated energy. PACS numbers: 77.22.–f,61.46.Bc,31.15.Ew Keywords: silver, cluster, photoabsorption spectrum, density functional theory I. INTRODUCTION The study of transition and noble metal clusters has fo- cused considerable attention along the last years due to the different properties detected respect to their corresponding bulk-phases. Additionally, these cluster properties have de- monstrated to be strongly dependent on the cluster size. On the other hand, noble metal clusters, and silver clusters in par- ticular, present important applications from the scientific and technological point of view in interesting researching fields such as catalysis [1, 2, 3, 4, 5, 6], and optics [7, 8, 9, 10]. The structural and electronic properties of silver clus- ters [11, 12, 13, 14, 15, 16] have been widely studied, however unlike the optical properties [11, 17, 18, 19, 20, 21, 22, 23]. The optical absorption spectra of silver clusters have been studied for more than two decades ago. Fedrigo et al. [19, 20] found that AgN (N≤40) clusters show a simple dominant peak in the low energy region, exceptions were attributed to the coexistence of low energy isomers. These results were confirmed theoretically for small-sized silver clusters (n=5- 8) [11]. On the other hand, Idrobo et al. [18] have recently carried out calculations of the absorption spectra of Ag11 for different structural isomers, however no full agreement with experiments was found. On the other hand, experimental optical spectroscopy, aided by recent advances in the corresponding theoretical tools, has proved to be a powerful means for obtaining information about the geometrical and electronic structure of molecules and small clusters. Since the structure of a cluster is gene- rally not directly accessible experimentally, its characteriza- tion must be done with a combination of experiment and the- ory. In previous works we have shown how a comparison of the measured optical spectrum with theoretical calculations ∗Electronic address: jimartinez@fysik.dtu.dk †Electronic address: efernand@fysik.dtu.dk for different isomeric forms of a given cluster can provide a useful diagnosis of the geometrical structure of the clus- ter [24, 25]. However, conventional optical absorption spec- troscopy experiments for studying transition and noble metal clusters are difficult due to several technical issues, such as the extremely low density of the produced clusters, and theoreti- cal spectroscopy is a perfect framework to complement most of experimental analysis. In this paper, we present calculations of the optical ab- sorption spectra of the three most stable isomeric forms of the Ag11 cluster up to 8 eV by using an extremely accurate technique for treating the electronic excitations: the time- dependent density functional theory (TDDFT) [26, 27, 28] under the formalism developed by Casida et al. [29, 30]. Our motivations for this work have been the following: (a) first, to show a comparison between the present first- principles TDDFT results and the available experimental mea- surements, in order to improve the description of previous theoretical studies by reducing the numerical uncertainty; (b) since significant differences have been found among the spec- tra of the different isomers of Ag11 (see Fig. 1), to propose the comparison of experimental and TDDFT absorption spectra as a powerful tool to elucidate between the different isomeric forms of small clusters; and (c) finally, to predict Ag11 pho- toabsorption spectrum for energies higher than 5.5 eV, a range of energies which has not been considered in previous experi- mental or theoretical studies for this system (our calculations extend the rang

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