Refractive properties of materials?
I can only answer your question about the relation between refractive indices and other properties with two examples.

When looking at dispersion interactions between particles in solution the Lifschitz Theory connects the refractive indices with the Hamaker constants.
The information about refractive indices is even used to choose materials in a way to cancel out dispersion interactions between particles of different kind. (I will attach a paper URL in the next days, just heard it from our professor in the lecture)

Another application of refractive indices is X-Ray NEXAFS spectroscopy and  many more spectroscopic methods involving electron or high energy light radiation. By the Kramers-Kronig relation it is possible to connect absorption constants and refractive indices. Especially one can find for example absorption edges.

Then here I found some probably interesting papers regarding your question. At least their references will be a good starting point. Unfortanetly I have no access and could only read the abstract: 

http://www.sciencedirect.com/science/article/pii/0020089165900205

http://www.sciencedirect.com/science/article/pii/0032395083902836