Dear Maria,
very happy to hear that you are using sTDA!
MATAGA_NISHIMOTO_CEXP and MATAGA_NISHIMOTO_XEXP were added to enable more flexibility in the parameter choice, with CEXP referring to the parameter dubbed alpha in Eq. 28 in Ref.
https://pubs.acs.org/doi/full/10.1021/acs.jctc.2c00144, identical with the parameter alpha of the original Grimme paper, parameterizing Coulomb contributions.
MATAGA_NISHIMOTO_XEXP analogously refers to parameter beta in Eq. 29 of the reference above, also dubbed beta in the original Grimme paper, parameterizing Exchange contributions.
FRACTION is referring to a_EX in Eq. 29, thus resembling the coupling parameter to define the amount of exact exchange as it is in hybrid functionals.
DO_EXCHANGE enables to switch off exchange contributions completely.
Depending on the chosen ground-state reference, it is important to adjust not only the amount of exact exchange, but also CEXP and XEXP. In the sTDA manual of Grimme and also in corresponding papers, several values for alpha and beta are suggested depending on the GS functional, differing significantly from the standard choice alpha = 1.42 + a_EX *0.48 and beta = 0.2 + a_EX*1.83. However, parameterization was based on molecular test sets and depending on your systems, it might be beneficial to reoptimize these parameters.
Hope this helps, also happy to discuss further questions.
Best regards,
Anna