Reduced electronic density matrices, effective Hamiltonians, and nonlinear susceptibilities of conjugated polyenes

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The ground state single-electron reduced density matrix is shown to contain the essential chemical bonding information relevant for calculating the nonlinear optical response of conjugated polymers. Applications to a series donor-acceptor substituted Hexatrienes demonstrate the interplay of electronic structure and dynamics, and the correlation between off-resonant polarizabilities and reduced density matrix. The construction of an effective Hamiltonian using the reduced density matrix is discussed.