TDDFT Study of the Optical Absorption Spectra of Bare Gold Clusters Robertson W. Burgess and Vicki J. Keast* School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia ABSTRACT: Time-dependent density functional theory (TDDFT) was used to calculate the optical absorption spectra of gold clusters of 20-171 atoms. The spectra for the smallest clusters agree with previous results, and the spectra for the largest clusters show features consistent with classical Mie theory. The systematic exploration of particles of sizes within these two extremes has allowed the trends linking optical absorption spectra and particle size and symmetry to be identified. A transition from molecular-like spectra to a more classical response is observed. ■ INTRODUCTION Metal nanoparticles are currently of great technological interest due to their unique optical properties. 1-3 They can show absorption that is highly nonlinear with radiation intensity, a tunable absorption, and the potential for the manipulation of light using structures smaller than one wavelength. 4-10 Gold particles can be fabricated to bridge the middle ground between individual atoms and bulk materials in a continuous fashion. 10-13 Quantum effects become apparent in small clusters, and a classical description of their properties is no longer adequate. 14-16 Optical properties of materials can be calculated with time- dependent density functional theory (TDDFT), 17 although the computational requirements are substantially larger than for ground-state density functional theory (DFT) calculations. As a consequence, structures investigated with TDDFT often contain fewer atoms than when ground-state DFT is applied. TDDFT has been used calculate the optical absorption cross section for gold clusters of 20 atoms or less. 18-23 In systematic study, Idrobo et al. 22 compared their results to other workers and showed that the calculated absorption peak positions for the same cluster can vary depending on the computational method used. This can limit our capacity to draw robust conclusions about the relationship between cluster structure and optical response, if we attempt to do this by comparing results between different workers who may have used different computational approaches. Some recent studies on larger clusters have included thiolate- coated clusters with 25, 24,25 38, 26 and 55 atoms. 27 Initially, moving to clusters with a larger number of atoms required making a approximations such as the jellium approximation 28 and only calculating the static dipole polarizability of the clusters. 29 One application of TDDFT without these approximations was for silver tetrahedral clusters up to 120 atoms in size. 30 More recently, there have been a number of calculations of gold, silver, and alloy clusters reaching sizes of over 100 atoms. 31-35 In order to reduce calculation times, the spectra have only been calculated in an energy range up to 2.5- 3 eV in gold and 5-6 eV in silver. As a consequence, often just the first one or two features appear in the calculated spectrum. All of these studies have investigated highly symmetrical structures where full use of the reduction of computation time using symmetry considerations could be employed. Use of the time-propagation method in TDDFT, which scales favorably with system size, has allowed an extended energy range in the optical absorption spectrum to be calculated for pure and alloyed noble metal clusters up to 147 atoms in size, 36,37 although these were again high-symmetry structures. In this paper, the optical absorption cross section of gold clusters in the range between 10 and 171 atoms will be calculated using the time-propagation method in TDDFT. These cluster sizes span the gap between small clusters, where systematic studies have been performed, and almost reach the limit of where classical calculations are known to be accurate. Covering this range of cluster sizes in a single set of calculations has allowed the identification of trends linking cluster size and absorption spectra. In particular, the size of clusters at which the absorption spectra adopt features similar to that predicted by Mie theory 38 can be identified. The calculations did not enforce symmetry to the electron density, enabling the spectra of structures without any planes of symmetry, including a rod- shaped cluster, to be calculated. This allowed the impact of symmetry and shape on the optical absorption spectra to be investigated. ■ COMPUTATIONAL DETAILS A total of 24 gold clusters were generated and are listed in Table 1. Two structures, the lowest energy flake arrangements Received: August 26, 2013 Revised: January 15, 2014 Published: January 16, 2014 Article pubs.acs.org/JPCC © 2014 American Chemical Society 3194 dx.doi.org/10.1021/jp408545c | J. Phys. Chem. C 2014, 118, 3194-3201