Theoretical investigation of the dipole polarisability and second hyperpolarisability of cyclopentadiene homologues C4H4XH2 (X=C, Si, Ge, Sn)

Abstract Static and frequency-dependent electronic dipole polarisability, α , and second hyperpolarisability, γ , of the cyclopentadiene homologues C 4 H 4 XH 2 (X=C, Si, Ge, Sn) were calculated by ab initio HF, MP2 and DFT-B3LYP methods using Sadlej POL basis sets, including vibrational and relativistic effects. The latter calculations were extended also to the furan homologues for comparison. The results show that both α and γ values increase monotonically as the heteroatom size increases. The energy values of the electronic transitions to the two lowest singlet 1 1 B 2 and 2 1 A 1 excited states decrease not uniformly as the heteroatom becomes heavier and the two-state model approximation is not adequate to explain the evolution of the (hyper)polarisability along the series, which indeed is essentially determined by the heteroatom property. Frequency dispersion correction on α increases down the group, by contrast γ dispersion is highest in cyclopentadiene and almost constant, at a lower value, in the heavier homologues. Electron correlation correction on the calculated properties is positive and rather large on γ . HF relativistic effects on 〈 α 〉 and 〈 γ 〉 are of little importance for both stannole and tellurophene and cannot account for the observed large discrepancy between the experimental and theoretical 〈 γ e 〉(− ω ; ω , ω ,− ω ) value in the latter compound. Vibrational contributions are calculated for the optically-heterodyned optical Kerr process (OHD-OKE). They are non negligible and show a clear heavy atom dependence. In the cyclopentadiene series they amount to 4–10% of 〈 α e 〉 and to 8–16% of 〈 γ e 〉(− ω ; ω , ω ,− ω ), while they are somewhat lower in the furan series. The transversal γ xxxx value is higher in the cyclopentadiene than in the furan series by ca. 30–40%, suggesting that α - α ′ -linked cyclopentadiene homologues can be considered as valid alternatives to the corresponding furan homologues in projecting π-conjugated oligomers and polymers for NLO applications.