The present study is focused on the optical properties of the
The transition metal silver has the particular property of a filled d-shell causing its chemistry to be mainly dominated by the s-valence electron. As the most “alkali-like” group-11 element, it has been well studied in a number of theoretical investigations,1–3 especially due to the strong surface plasmon absorption in the visible regime observed in silver clusters and nanoparticles.4–9,52 In order to understand the size-dependent physical and chemical properties of such nano-sized silver particles, small clusters consisting of only a few atoms are ideal model systems.10–13 The relatively large s-d separation means that the optical response is mainly associated with s-electrons while d-electrons are only partially involved in the excitations.14 The Nilsson-Clemenger model,15 taking only the 5s-electrons into account, leads to absorption spectra in good qualitative agreement with experiments.16 Further, it has been shown that the jellium model is valid at high temperatures, whereas a molecular picture is more appropriate at low temperatures.17 However, especially at small sizes, a quantum chemical treatment becomes important since the electronic structure of the sub-nanometer particles becomes more discrete. In order to probe the optical response of small silver clusters, photodissociation spectroscopy18–24 and rare-gas matrix spectroscopy14,16,25 have been reported previously. Very recently, Ito et al. presented optical spectra of
Previously, Weis et al. performed ion mobility measurements on
In this article, we present the photodissociation spectrum of the
The experimental setup is described in detail elsewhere.24 Briefly, cluster cations are produced by pulsed laser vaporization and separated with time-of-flight mass spectrometry. The optical response is probed by longitudinal photodissociation spectroscopy with a tunable ns-laser pulse from an optic parametric oscillator, pumped by the third harmonic of an Nd:YAG laser. Spectra are recorded by monitoring the ion signal depletion upon photon absorption using the Lambert–Beer law and assuming perfect overlap between the dissociation laser and molecular beam.
In the search of the decamer cation configuration space, the pool-BCGA uses the plane-wave self consistent field code within the Quantum Espresso36 package in local optimizations, where 11 electrons for each Ag atom are treated explicitly and the remaining 36 core electrons are captured by ultrasoft Rabe-Rappe-Kaxiras-Joannopoulos pseudopotentials,38 employing the Perdew-Burke-Ernzerhof (PBE)39 xc functional. Local optimization is performed with an electronic self consistency criterion of 10−5 eV, and total energy and force convergence threshold values of 10−3 eV and 10−2 eV/Å, respectively. The lowest lying putative GM candidates are subsequently locally optimized using NWChem v6.3,40 employing an extensive 19-electron def2-tzvpp basis set and the corresponding effective core potential (def2-ecp) of Weigend and Ahlrichs.41 The long-range corrected xc functional LC-ωPBEh33 is used in order to accurately recover the asymptotic behaviour of the exchange correlation potential, since this has proven to reliably reproduce vertical electronic excitation spectra.4,6,8,24,33,34 The theoretical description of optical properties of clusters based on TDDFT calculations is easily applicable and widely used, in particular due to the low computational costs associated with the single-reference character.42 In minimizations the BP-8643,44 and M06-L45 functionals are also studied for comparison purposes. The energy is calculated using a grid of high density (xfine integration grid, tight optimization criterion). The integral precision is set to 10−9 eV while the tolerance on linear dependencies in the overlap matrix has been set to 10−6 eV since diffuse basis sets are prone to linear dependencies. Additionally, harmonic frequency analyses are performed in order to verify whether the considered geometries are true minima on the potential energy surface.
For all geometries resulting from the DFT optimizations, electronic excitation spectra are calculated using spin-unrestricted TDDFT (at the LC-wPBEh/def2-tzvpp level with NWChem v6.3.40) with 50 excited state roots to be determined. The optical response calculations are compared to the experimental photodissociation spectrum in Figure 3. It is clear that only isomer a qualitatively reproduces the signature of the experimental spectrum, while all other isomers show features which do not match the experimental observation. The pool-BCGA results and local relaxations, as well as the measured absorption spectrum point to isomer a being the GM and the only species present in the molecular beam experiment.
In order to compare these results to previous ion mobility experiments, three commonly used theoretical models for calculating the collision cross section of a given ion structure have been used. The EHSS model, the trajectory method including either partial charges (CT-TR) or a uniform charge distribution (EQ-TR), and the projection approximation (PA) are used in order to elucidate the structure of
In general, all of the postulated isomers can fit the experimental ion mobility data as nearly all collision cross section calculations, for the different models, remain in the experimental error range. Hence, spectroscopy is necessary for the unambiguous assignment in the case of
In conclusion, we have strong evidence that we have identified the true GM structure of the
We acknowledge financial support by the DFG (Grant No. SCHA 885/10-2) and the Merck'sche Gesellschaft für Kunst und Wissenschaft e.V. The calculations reported here have been performed on the following HPC facilities: The University of Birmingham BlueBEAR facility (Ref. 51); the MidPlus Regional Centre of Excellence for Computational Science, Engineering and Mathematics, funded under EPSRC Grant No. EP/K000128/1; and via our membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/F067496), this work made use of the facilities of ARCHER, the UK’s national high-performance computing service, which is provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc. and NAG Ltd, and funded by the Office of Science and Technology through EPSRC’s High End Computing Programme.