Static Third-Order Polarizability Calculations for C₆₀, C₇₀, and C₈₄

Abstract

Valence electron contributions to the static molecular third-order polarizabilities (γ) are calculated for C 60 , C 70 , and two stable structures of C 84 (D 2 and D 2d ). The method utilized is based on the finite-field approach coupled with semiempirical polarization calculations on all-valence electrons. An increase in the third-order polarizability contributions is observed for molecular structures with a reduction in group symmetry, in agreement with recent experimental observations for these fullerenes. This increase is attributed mainly to the appearance of aromatic structures within the molecules as well as to the increase in molecular volume.Fullerenes are the subject of intensive research by many groups on several contents. There has also been a great deal of speculation about potential uses for fullerenes and their derivatives, ranging from electrochemistry and electronics (the latter based in part on the superconducting properties of alkalidoped fullerides) to catalysis, hydrogen storage, antiviral agents, and all-optical devices. 1 Associated with the delocalized π-conjugated electrons in fullerenes, their large nonlinear optical responses have been the subject of several recent experimental studies. 1-10 A wealth of experimental data concerning the thirdorder optical nonlinearities have been accumulated for the fullerenes C 60 , C 70 , and C 84 . The two most abundant fullerenes, C 60 and C 70 , have configurations with I h and D 5h symmetries, respectively. 11-14 C 84 has been recently synthesized, 15,16 and the most stable configurations have been determined to be D 2 and D 2d . 1,17 An interesting feature discovered by the experimental study is the increase of the third-order nonlinearity from C 60 to C 70 and to C 84 . 1 With the advances in the synthesis of macroscopic quantities of fullerenes, a theoretical understanding of the dependence of the nonlinear optical responses on the molecular symmetry and electronic properties is thus of particular interest.Theoretical calculations of third-order nonlinear effects have been carried out using various semiempirical and ab initio methods. π-electron calculations on unsaturated hydrocarbon chains have been used to predict third-order effects. 19 Ab initio methods applied to molecules with more than 15 atoms are extremely computer intensive. An alternative method using allvalence electrons and a semiempirical perturbation (sum-overstates approach) has generally been applied to molecules with less than 30 atoms. 20,21 In the present work, the procedure X

Third-order Optical Nonlinearities of Higher Fullerene and Carbon Nanotube

“…This discrepancy may arise from the truncation of the expansion in excited states in the explicit summation of contributions to the secondBrought to you by | MIT Libraries Authenticated Download Date | 5/10/18 11:08 PM order hyperpolarizability in SOS calculations [36]. In contrast, the second-order hyperpolarizabilities obtained in the FFA methods [48,34] are of the same order of magnitude. The described problems are absent in the analytical RPA approach [36].…”

“…From a geometric point of view, Moore et al [48,57] analyzed the static third-order polarizabilities 7 of CÖO, C70, fi ye isomers of C78 and two isomers of Cg4 in terms of three properties: (i) symmetry; (ii) aromaticity; (iii) size. The polarizability values were based on the finite field approximation (FFA), using a semiempirical Hamiltonian, and applied to the molecular structures obtained from density functional theory calculations.…”

“…The maximum interatomic distance and surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear polarizability a and second-order hyperpolarizability 7 in these molecules respond differently to geometrical properties [48,57]: a depends almost exclusively on the surface area, while 7 is affected by a combination of the Report number of aromatic rings, length and group order, in decreasing importance. In the case of a, valence electron contributions provide the same information as all-electron estimates [48,57], For the second-order hyperpolarizability 7, the best correlation coefficients are obtained when all-electron estimates are used and when the dependent parameter is ln(7) instead of 7 [48,57].…”

“…Since the ratios between different components of 7 are not known, a spatial average of 7 is given by [48] Report 7= (14) 7xxxx + 7i/yyy + Ifzzzz + ^"fxxyy + ^7 yyzz + ^7 zzxx 5 '…”

Nonlinear optical study of the five IPR isomers of C78 generated by capping C72 through C6

“…A large number of experimental data concerning the third-order optical nonlinearities have been accumulated for the fullerenes C 60 , C 70 , and C 84 . Also it has been noticed that γ values increases from C 60 to C 70 and to C 84 [26]. While comparing the more diversed hydrocarbons, γ per n π could be used [27,28], where n π refers to the number of π electrons.…”