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

Abstract

Abstract Static and frequency-dependent electronic dipole polarisability, α, and second hyperpolarisability, γ, of the cyclopentadiene homologues C4H4XH2 (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 〈γe〉(−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 〈αe〉 and to 8–16% of 〈γe〉(−ω;ω,ω,−ω), while they are somewhat lower in the furan series. The transversal γxxxx 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.