Assessing the performance of ab initio methods on static (hyper)polarizability predictions for silicon clusters. Si4 as a test case

Abstract

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:  = 142.77 and Δα = 77.93 e²a²₀E⁻¹_h for the mean and the anisotropy of the dipole polarizability and  = 87.5 × 10³e⁴a⁴₀E⁻³_h for the mean hyperpolarizability. Electron correlation has a rather small effect on but a relatively strong one on Δα and . Our best values were obtained at the CCSD(T) level of theory with a [5s4p3d1f] basis set:  = 140.35, Δα = 83.78 e²a²₀E⁻¹_h and  = 106.3 × 10³e⁴a⁴₀E⁻³_h. At the same level of theory the differential (hyper)polarizability is (Si₄) − 4_Si = −9.21 e²a²₀E⁻¹_h and is (Si₄) − 4_Si = −65.3 × 10³e⁴a⁴₀E⁻³_h. To our knowledge, this is the first complete calculation of the dipole (hyper)polarizability of this cluster to be reported in the literature.