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Based on infinite one-dimensional single-electron periodic models oftrans-polyacetylene, we show analytically that the overall permutation symmetryof nonlinear optical susceptibilities is, albeit preserved in the molecularsystems with only bound states, no longer generally held for the periodicsystems. The overall permutation symmetry breakdown provides a fairly naturalexplanation to the widely observed large deviations of Kleinman symmetry forperiodic systems in off-resonant regions. Physical conditions to experimentallytest the overall permutation symmetry break are discussed.Comment: 7 pages, 1 figur

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