TD-DFT Studies on sp- and sp2-Hybridized Single Vacancy-Defected [60]Fullerene: Electronic Excitation and Nonlinear Optical Properties of C59 [9-4] and C59 [8-5] Isomers

By removing one carbon atom from [60]Fullerene (C60), two different isomers (C59 [9-4] and C59 [8-5]) are generated for the C59 cluster. Inspired by their structural and electronic properties, we, theoretically, studied the static and frequency-dependent electronic (hyper)polarizabilities of sp- and sp2-hybridized isomers in vacuum by TD-DFT calculations. The simulated absorption spectra showed that all absorption bands of C59 [9-4] and C59 [8-5] are attributed to pi ->pi and n ->pi* transitions. Regarding their nonlinear optical properties, it is found that the frequency-dependent polarizability anisotropy alpha(anisotropy)(lambda = 1064.80 nm) of C59 [8-5] is 4 times larger than the static regime, revealing a notable polarization anisotropy, due to the delocalized pi electrons around the vacancy defect. By decreasing the incident wavelengths from lambda = 1908 nm to lambda =589.08 nm, the dispersion of optical nonlinearity of C59 [8-5] has achieved the maximum at beta(xxx) (lambda = 1064.8 nm) = 38.150 au and (gamma(xxxx) (lambda = 589.08 nm) = -9.896 x 10(7) au), indicating that the resonance effect of the hyperpolarizability amplified with the decrease of incident wavelengths. Hyperpolarizability density analyses in X and Z directions displayed that the conspicuous negative rho((3))(xxx)((r) over right arrow) and -z rho((3))(zzz)((r) over right arrow) are more expanded on the C59 [8-5] cage when the main contributions stem from the pi electrons instead to the sp-hybridized carbon.