Ab initio investigation on the nonlinear optical properties of silicon clusters Si n (n=3–8)

First and second hyperpolarizabilities of small silicon clusters have been calculated using conventional ab initio methods systematically increasing the amount of electron correlation. Besides Si₅, upon successive addition of electron correlation in the MP2, MP3, MP4, CCSD, and CCSD(T) series, all clusters display the same behavior: i) the HF γ_// values are the smallest, ii) the MP2 γ_// values the largest, and iii) the latter values are good approximate to the reference CCSD(T) results because the overestimation is smaller than 10%. Contrary to the polarizability per Si atom, which decreases with the cluster size until reaching the bulk limit, the average second hyperpolarizability per Si atom presents a sawtooth behavior with maxima in γ_// associated with even numbers of Si and minima with odd numbers of Si atoms.