Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Hückel model

Based on one-dimensional single-electron infinite periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, although preserved in bound-state molecular systems, no longer generally held in periodic systems. The overall permutation symmetry breakdown provides a natural explanation of the widely observed large deviations of Kleinman symmetry in off-resonant regions of periodic systems. Finally, physical conditions to experimentally test the overall permutation symmetry breakdown are discussed.