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

We have calculated static electric dipole (hyper) polarizabilities for a small silicon cluster, Si-4. The molecular properties have been obtained from finite-field restricted-Hartree-Fock, Moller-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: (alpha) over bar =142.77 and Deltaalpha=77.93 e(2) a(0)(2) E-h(-1) for the mean and the anisotropy of the dipole polarizability and (gamma) over bar =87.5x10(3) e(4) a(0)(4) E-h(-3) for the mean hyperpolarizability. Electron correlation has a rather small effect on (alpha) over bar but a relatively strong one on Deltaalpha and (gamma) over bar. Our best values were obtained at the CCSD(T) level of theory with a [5s4p3d1f] basis set: (alpha) over bar =140.35, Deltaalpha=83.78 e(2) a(0)(2) E-h(-1) and (gamma) over bar =106.3x10(3) e(4) a(0)(4) E-h(-3). At the same level of theory the differential (hyper) polarizability is (alpha) over bar (Si-4)-4 (alpha) over bar (Si) = -9.21 e(2) a(0)(2) E-h(-1) and is (gamma) over bar (Si-4)-4 (gamma) over bar (Si) = -65.3x10(3) e(4) a(0)(4) E-h(-3). To our knowledge, this is the first complete calculation of the dipole (hyper) polarizability of this cluster to be reported in the literature.