Scaling of the second hyperpolarisabilities of conjugated carbon systems: polyynes versus polyenes and fullerenes

A Sum over Molecular Orbitals scheme with an ab initio 6-31G basis set is used to calculate the static second hyperpolarisabilities, γ, of the eight linear polyynes ranging from C20H2 to C160H2. The values nearly parallel, with a negative offset, those obtained for the same number of carbons, N, for polyenes. In analogy with H(CH)2nH, γ/N vs. N saturates for HC2nH at N∼50. Further comparison with the fullerenes is presented.