Assessing the performance of ab initio methods on static (hyper)polarizability predictions for silicon clusters. Si4 as a test case
Résumé
We have calculated static electric dipole (hyper)polarizabilities for a small silicon cluster, Si4. The molecular properties have been obtained from finite-field restricted-Hartree-Fock, Møller-Plesset perturbation theory, coupled-cluster and density functional theory calculations performed with carefully designed basis sets of gaussian-type functions. A large [8s6p5d2f] basis set is thought to provide near-Hartree-Fock quality results: αm̌ = 142.77 and Δα = 77.93 e2 a02 Eh-1 for the mean and the anisotropy of the dipole polarizability and γm̌ = 87.5 × 103 e4 a04 Eh-3 for the mean hyperpolarizability. Electron correlation has a rather small effect on αm̌ but a relatively strong one on Δα and γm̌. Our best values were obtained at the CCSD(T) level of theory with a [5s4p3d1f] basis set: αm̌ = 140.35, Δα = 83.78 e2 a02 Eh-1 and αm̌ = 106.3 × 103 e4 a04 Eh-3. At the same level of theory the differential (hyper)polarizability is αm̌ (Si4) - 4αm̌Si = -9.21 e2 a02 Eh-1 and is γm̌(Si4) - 4γm̌Si = -65.3 × 103 e4 a04 Eh-3. To our knowledge, this is the first complete calculation of the dipole (hyper)polarizability of this cluster to be reported in the literature.