Starting with a perturbation expansion for the Kleinman forbidden nonlinear optical coefficient

and for Miller\´s

, and making several approximations, we arrive at a simple result for the ratio of forbidden to allowed mixing nonlinearities (

), namely

. For second-harmonic generation (SHG) this can be expressed as

, which clearly shows the close connection between

and the linear dispersion. These expressions are shown to give good agreement with literature experimental values, as well as for our measurements on TeO
2for various input frequencies ω
1and ω
2(i.e.,

, and 3.76 eV).