Frequently it is useful to compare experimental values of the hyperpolarizabilities bgr; and ggr; with calculated values. It is also often helpful to compare experimental values of bgr; obtained from dchyphen;electric field induced second harmonic generation (dchyphen;SHG) experiments, e.g., with values obtained using the solvatochromism method. In order to do this the hyperpolarizabilities must be defined using consistent conventions. In this paper, four commonly used conventions are discussed and simple factors for converting between them presented. In addition, the sumhyphen;overhyphen;states expression for the calculation of bgr; and ggr; is described and its correct use in comparing with hyperpolarizabilities obtained using other experimental and theoretical techniques discussed. As an illustration of the consistent use of conventions,abinitioand semiempirical calculations on parahyphen;nitroaniline are compared with experimental dchyphen;SHG values. This comparison highlights the difference between theoretical values of the hyperpolarizability with the molecule in a gas phase environment and experimental values obtained in polar solventsminus;a difference that has in the past been obscured by inconsistent choice of conventions. thinsp;
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