# Electron correlation theory and experimental measurements of the third-order nonlinear optical properties of conjugated linear chains

#### Abstract

Comprehensive theoretical and experimental studies of the magnitude, sign, dispersion, and length dependence of the third order molecular susceptibility $\gamma\sb{ijkl}$(-$\omega\sb4$;$\omega\sb1$, $\omega\sb2$, $\omega\sb3$) demonstrate that the microscopic origin of the nonresonant third order nonlinear optical properties of conjugated linear chains is determined by the effects of electron correlation due to electron-electron repulsion. Multiple-excited configuration interaction calculations of $\gamma\sb{ijkl}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$, $\omega\sb3$) for the archetypal class of quasi-one dimensional conjugated structures known as polyenes reveal for the first time the principal role of strongly correlated, energetically high-lying, two photon $\sp1$A$\sb{\rm g}$ virtual states in the largest of the two dominant, competing virtual excitation processes that determine $\gamma\sb{ijkl}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$). It is also found in studies of the effects of conformation on $\gamma\sb{ijkl}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$) that the origin of the third order optical properties remains basically the same for the all-trans and cis-transoid polyenes, and the results for the two conformations are unified by a common power law dependence of the dominant tensor component $\gamma\sb{xxxx}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$) on the physical end-to-end length L of the chain with an exponent of 3.5. Calculations for a noncentrosymmetric conjugated chain demonstrate that virtual excitation processes involving diagonal transition moments that are forbidden in centrosymmetric structures lead to a more than an order of magnitude enhancement in $\gamma\sb{xxxx}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$) compared to the analog centrosymmetric structure. Experimental measurements of the dispersion in the isotropically averaged dc-induced second harmonic susceptibility $\langle\gamma$(-2$\omega;\omega,\omega$,0)$\rangle$ and third harmonic susceptibility $\langle\gamma$(-3$\omega$;$\omega$,$\omega$,$\omega$)$\rangle$ in two important polyene structures confirm the electron correlation description of $\gamma\sb{ijkl}$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$). The measured values of $\langle\gamma$(-2$\omega$;$\omega$,$\omega$,0)$\rangle$ and $\langle\gamma$(-3$\omega$;$\omega$,$\omega$,$\omega$)$\rangle$ at several near infrared fundamental wavelengths for hexatriene, the N = 6 carbon site polyene chain, are in excellent agreement with the calculated magnitude, sign, and dispersion. Corresponding measurements for $\beta$-carotene, a substituted N = 22 polyene chain, together with the results for hexatriene, also verify the calculated power law dependence of $\langle\gamma$(-$\omega\sb4$;$\omega\sb1$,$\omega\sb2$,$\omega\sb3$)$\rangle$ on L. It was further found in the course of the experimental measurements that the common reference standard for the macroscopic susceptibility $\chi\sp{(3)}$(-3$\omega$;$\omega$,$\omega$,$\omega$) is too large by a factor of 2.0, and an improved standard value is proposed.

#### Subject Area

Condensation|Optics|Molecules

#### Recommended Citation

Heflin, James Randolph, "Electron correlation theory and experimental measurements of the third-order nonlinear optical properties of conjugated linear chains" (1990). Dissertations available from ProQuest. AAI9112573.
https://repository.upenn.edu/dissertations/AAI9112573

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