Theory of atomic additivity in molecular hyperpolizabilities

Hyperpolarizability is a function of frequency. This is called dispersion. Because of the Kramers-Kronig relations, researchers expect that a material that is dispersing light is also absorbing it. Where there is both dispersion and absorption, the molecular polarizabilities are complex functions of the frequency. This led researchers to consider atomic additivity in both the real and imaginary parts of the ordinary and hyperpolarizabilities. This effort is desirable not only from a theoretical point of view, but also because of the existence of a large body of complex refractive index data, which may be used to test the additivity principle with the complex valued ordinary dipole polarizability.