The exact formula is derived from the "sum over states" (SOS) quantum mechanical model for the frequency dispersion of the nonlinear refractive index coefficient n for centrosymmetric molecules in the off-resonance and non-resonant regimes. This expression is characterized by interference between terms from two-photon transitions from the ground state to the even-symmetry excited states and one-photon transitions between the ground state and odd-symmetry excited states. When contributions from the two-photon terms exceed those from the one-photon terms, the non-resonant intensity-dependent refractive index n>0, and vice versa. Examples of the frequency dispersion for the three-level SOS model are given. Comparison is made with other existing theories.
