Explicit nondivergent formulas for atomic and molecular dynamic hyperpolarizabilities

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  • David M. Bishop
    Department of Chemistry, University of Ottawa, Ottawa K1N 6N5, Canada

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<jats:p>Two methods are used to develop nondivergent, compact, sum-over-states formulas for dynamic hyperpolarizabilities up to fifth order. Expressions for both atoms and molecules are given; those at fourth and fifth order for the first time. The fifth-order formula is related to such nonlinear optical phenomena as stimulated hyper-Raman scattering and the self-induced intensity-dependent refractive index. Questions of time-reversal invariance are also discussed. Importantly, the derivations explicitly take into account secular divergences in a simple and clear way.  </jats:p>

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