Sum rules which connect spectral moments of linear and nonlinear optical susceptibilities of nonrelativistic many-electron systems to their ground state properties 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.