Odd–even oscillations in structural and optical properties of gold clusters A. Nijamudheen a , Ayan Datta b, * a Department of Chemistry, Cochin University of Science and Technology (CUSAT), Cochin 680022, Kerala, India b School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, CET Campus, Thiruvananthapuram 695016, Kerala, India article info Article history: Received 11 December 2009 Received in revised form 11 January 2010 Accepted 11 January 2010 Available online 18 January 2010 Keywords: Au-clusters Odd–even effects DFT-calculations Optical properties Woodward–Fieser rules abstract Density Functional Theory (DFT) calculations suggests odd–even oscillations in structural, geometrical and optical properties of neutral Au-clusters (n = 2–20). Such odd–even oscillations are understood on the basis of the presence of SOMO in the case of the odd-membered clusters. An analysis of the Mulliken spin-density shows that the negative charges are localized on the edge-atoms on the clusters while the core-atoms are electron deficient. Interestingly, the color of the clusters also shows an odd–even oscilla- tion. A rule similar to the Woodward–Fieser rules is proposed for predicting the average red-shift in vis- ible spectra in these nanoclusters. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Gold nanoclusters are subject of intense research due to their fundamental and fascinatingly different behavior from bulk [1– 3]. The fact that a noble metal undergoes a drastic physical and chemical transformation into a potent, shape and size selective cat- alyst [4,5] opens up a huge prospect in the area of nanotechnology and allied applications in bio-medical research [6,7]. Structural and electronic features of small Au n clusters (n 6 20) have studied using photoelectron spectroscopy (PES) and compu- tational studies mostly using the Density Functional Theory (DFT) [8–10]. The finite-size effects which lead a non-monotonous behavior in the stability and geometries have been well character- ized. Based on these studies, we now have a broad consensus that at n t  14, the neutral Au-clusters undergo a transformation from planar to 3D structures [11]. The stability of small planar gold-clus- ters like Au 6 has been explained on the basis of d-orbital aromatic- ity [12] while the stability of highly symmetric tetrahedral clusters like Au 20 is attributed to 3D aromaticity [13]. Such an understand- ing of nano-systems from fundamental and well known principles in organic chemistry is very intuitive and desirable. Interestingly, these clusters also are known to exhibit odd–even oscillations in their binding energies [8]. Odd–even oscillations are omnipresent across chemistry including melting point of molecular solids [14], magnetic exchange interactions in metal-clusters [15], packing efficiencies of molecules in self-assembled mono-layers (SAM) [16] and non-linear optical (NLO) properties of D(donor)-bridge- A(acceptor) chromophores [17]. In this article, we critically inves- tigate such odd–even oscillations in various structural and elec- tronic properties of Au-clusters from first principles. Such odd– even oscillations are also predicted in the optical properties of these clusters. Based on this study, we suggest a general trend for predicting the UV–vis absorbtion spectra for various sizes of Au-nanoparticles that is conceptually complementary to the well-known Woodward–Fieser rules [18] for predicting the k max of organic chromophores. 2. Results and discussions The structures of the Au-clusters were optimized using the DFT method using the B3PW91 hybrid functional [19]. We have used the Las Alamos 19-electron shape-consistent ECP (LANL2DZ) basis set [20]. This ECP is bench-marked with respect to scalar-relativis- tic Dirac–Fock theory and includes mass–velocity and Darwin terms. Hence, the relativistic corrections are satisfactorily ac- counted by this basis set. All the structure calculations were fol- lowed by vibrational analyses to ensure all-positive frequencies for these clusters. We use the Gaussian 03 Suite for our calcula- tions [22]. In Fig. 1, the structures for the minimum energy geom- etries for Au n (n = 2–20) are shown. The shapes of these clusters are in harmony with previous calculations using different level of the- ories [9,10,21]. Interestingly, the structures of Au 19 , Au 18 , Au 17 and Au 16 are derived from the T d structure of Au 20 by sequential re- moval of one Au-atom from each of the four edges, respectively, and subsequent relaxation to balance the dangling charges. It is 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.01.023 * Corresponding author. E-mail address: ayan@iisertvm.ac.in (A. Datta). Journal of Molecular Structure: THEOCHEM 945 (2010) 93–96 Contents lists available at ScienceDirect Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem