Abstract
First and second hyperpolarizabilities of small silicon clusters have been calculated using conventional ab initio methods systematically increasing the amount of electron correlation. Besides Si$_{5}$, 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.
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