Static polarizability and second hyperpolarizability tensors are computed for a series of polyenes, polyynes, and cumulenes by ab initio SCF theory. Numerically stable finite field (FF) calculations can be achieved by using polynomial fits of either energy or induced dipole moment as a function of field strength. The nonlinear expansion coefficients from these fits correspond to the microscopic nonlinear optical property. Our results from fully coupled (FF) ab initio calculations for polarizability are in good agreement with those derived from uncoupled (sum-over-states) ab initio methods. The hyperpolarizabilities do not compare as well. A qualitative description of the chain length dependence of polarizability and hyperpolarizability for moderately long chains is discussed in terms of an empirical function. Diffuse orbital basis functions are required for qualitatively correct hyperpolarizabilities of small conjugated systems or for that matter any small molecule. For example, the average second hyperpolarizability, 7, of ethylene is computed to be -13, 1.7, and 726 au with STO-3G, 6-31G, and augmented 3-21G basis sets, respectively. The value computed with the augmented basis set agrees, within a factor of 2, with the experimental value of 1500 au. The valence set for the carbon atoms is augmented with diffuse s, p, and two Cartesian d sets, or subsets of these. The inclusion of diffuse polarization functions drastically alters the computed second hyperpolarizabilities. The results are nearly insensitive to the choice of valence set but are highly dependent on the basis set quality. We also describe the use of a corresponding orbital analysis to aid in the interpretation of ab initio results obtained by either FF or analytic derivative methods. The computed polarizability and hyperpolarizability and the and components indicate that the contribution due to the orbitals is much more significant than the orbitals. Both contributions change sign in going from the ethylenic and acetylenic chains to the cumulenic systems. The polarization of -electron density by the field is illustrated by contour surfaces of derivative -electron-density functions. Contour maps of the first derivative of charge density with respect to the field (a) for an acetylenic chain are nearly periodic, corresponding to localized polarization, whereas the third derivative density (7) corresponds to longer range charge shifts.
The third order nonlinear optical susceptibility has been measured by degenerate four wave mixing in a 33-μm-thick biaxial film of a conjugated aromatic heterocyclic polymer, poly-p-phenylenebenzobisthiazole, commonly known as PBT, which has a very high mechanical strength due to its rigid rod conformation as well as environmental stability and a high laser damage threshold. For the first time, the response of the optical nonlinearity in the π-electron conjugated system has been experimentally verified to be in subpicoseconds. The value of χ(3) is found to be about an order of magnitude larger than that of CS2. The measurement at two different wavelengths suggests that they are nonresonant χ(3) values. The measured anisotropy of χ(3) as a function of angular orientation at two different sets of laser polarization is explained by using the tensor properties of χ(3) in an anisotropic medium.
The electronic third-order nonlinear optical interaction in a solution cast film of a polydiacetylene has been studied by degenerate four wave mixing. The results demonstrate a subpicosecond response and a very high χ(3) value. The χ(3) value changes considerably during the thermally induced conformational transition in the film in which the effective π-electron conjugation is reduced.
Resonant third-order nonlinear optical susceptibility χ(3) of poly-N-vinyl carbazole: 2,4,7-trinitrofluorenone composite polymer photoconductor has been measured at 602 nm for various compositions by picosecond degenerate four-wave mixing. The origin of effective third-order nonlinearity of this system is attributed to the charge–transfer excitation which creates thermalized correlated electron–hole pairs. The optical nonlinearity of this polymeric system is characterized by a long relaxation time of hundreds of picoseconds. A progressive enhancement of the signal intensity and hence effective χ(3) accompanied by an increase in the decay rate of the degenerate four-wave mixing signal has been observed with an increase in the mole fraction of trinitrofluorenone.
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