Important note: It is strongly recommended not to use KKR dielectric function models in the list of materials directly. Please work with objects of type 'Dielectric function model' and use in their susceptibility list a KKR susceptibility. This kind of susceptibility makes use of a KKR dielectric function model internally.

In some cases one has only a formula for the imaginary part of the dielectric function. This is especially true for interband transitions where quantum mechanical expressions can be derived from the band structure of a material.

Fortunately, with a little luck the missing real part can be constructed from the imaginary part using the Kramers-Kronig-Relation (KKR) that connects real and imaginary part of susceptibilities.

Of course, there are some restrictions and requirements. The imaginary part of the dielectric function must be known in a wide spectral range. To be specific, from 0 to infinity. Using a finite maximum frequency instead of infinity is acceptable only if the imaginary part approaches smoothly zero as its high frequency limit.

In addition, the KKR relation can only be used with certain numbers of data points, namely powers of 2 (256, 512, 1024, 2048, 4096, 8192, 16384). This is due to the fact that the Hilbert transformation that brings you from the imaginary to the real part of the susceptibility is realized in SCOUT using two successive Fourier transforms. These are programmed as so-called Fast Fourier Transforms (FFT) which are limited to the restricted number of data points.

Using KKR dielectric function models you can mix susceptibility types that require a KKR construction of the real part with those that have explicit expressions for real and imaginary part. The algorithm used for the computation of the final dielectric function is the following:

•First the imaginary parts of all KKR susceptibilities are summed up

•Then the KKR step is done to construct the corresponding real part

•Then all the 'normal' susceptibility terms are added that do not require a KKR transformation

Although the computational effort is large the time to perform the KKR on modern computers is still in a range that you should definitely consider using KKR dielectric function models for 'fitting' work. This is especially true for UV spectroscopy.

Up to now the following KKR susceptibilities have been implemented:

•Free formula

•OJL model

•Campi_Coriasso

•Tauc-Lorentz