Size and Electric Dipole (Hyper)polarizability in Small Cadmium Sulfide Clusters:  An ab Initio Study on (CdS)_n, n = 1, 2, and 4

Abstract

We report conventional ab initio and B3LYP/DFT calculations for the static electric (hyper)polarizability of small CdS clusters. Our results indicate a strong reduction of the (per atom) mean dipole polarizability with size, supporting the recent LDA findings by Troparevsky and Chelicowsky [J. Chem. Phys. 2001, 114, 943]. The same trend is observed for the second dipole hyperpolarizability. The computational complexity of the determination of the electric properties varies considerably with cluster size. B3LYP and conventional ab initio values are not in good agreement for the monomer but the gap is drastically reduced for the dimer and the tetramer.The electric properties of cadmium sulfide clusters are currently of interest due to the dramatic increase of work on semiconductor particles and their potential applications in materials science. 1 As applications vary from electronic/optical properties 2,3 to solar cell technology 4 and DNA analysis, 5 nanomaterials-oriented synthetic work on CdS clusters is actively pursued by many research groups. 6-8 The emergence of nonlinear susceptibility measurements on CdS clusters, 9 nanoparticles, 10-12 and thin films of CdS nanocrystals 13 is worth noticing. Little theoretical work has been published on (CdS) n . The electric (hyper)polarizability of the monomer was studied by Raptis et al. 14 The structure of (CdS) n was investigated by Joswig et al. 15 We are aware of only one study on the polarizability of cadmium sulfide clusters, a pseudopotential approach based on the local density approximation (LDA). 16 Troparevsky and Chelikowsky 16 showed that the mean dipole polarizability per atom of (CdS) n decreases rapidly with cluster size, approaching the bulk limit of 23.7 e 2 a 0 2 E h -1 from the tetramer onward. The aim of this paper is to present conventional ab initio and density functional theory (DFT) results for the static dipole (hyper)polarizability of (CdS) n , n ) 1, 2, and 4. We have designed a basis of Gaussian-type functions (GTF) especially for this kind of molecular system. We expect to obtain clear indications for the performance and relative merit of these two important classes of theoretical methods in CdS cluster calculations. A most important part of our investigation is to offer a first aperçu on the nonlinear polarizability of small CdS clusters and to compare the observed trends to those available for the linear polarizability. Overall, given the scarcity of ab initio work on (CdS) n , we expect the present gleanings of computational experience to be of use to future endeavors by other researchers.A detailed presentation of the theoretical methods used in this paper may be found in standard references. 17-21 Thus, along with the self-consistent field (SCF) we rely on Møller-Plesset perturbation theory (MP) and coupled-cluster (CC) techniques. The MP based methods are MP2, SDQ-MP4, and MP4, second, partial, and complete fourth-order, respectively. The highest order methods are CCSD (single and double CC) and its † Permanent address:

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