Generalized sum rules for optical nonlinearities of many-electron systems

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Abstract
Sum rules which connect spectral moments of linear and nonlinear optical susceptibilities of nonrelativistic many‐electron systems to their ground stateproperties are derived. These sum rules provide a direct connection between chemical bonding and optical properties and may assist in constructing tight‐binding Hamiltonians for the effective modeling of electronic spectroscopy. In the time‐dependent Hartree–Fock approximation, the only relevant ground state information is the Hartree–Fock ground stated reduced single‐electron density matrix.