Is the huge calcite birefringence accounted for by first principles?

The birefringence in calcite is huge (possibly the largest?). The question is, why is it so special? why is such kind of materials so rare?

In other words, is it explained by first principles?

By google, I just found a paper predicting the birefringence in some material. See http://pubs.acs.org/doi/abs/10.1021/jp506744s

A simple calculation would start out by doing this for a single CO$_3^{2-}$ ion (or for an ion with a 1+ charge), and then apply Clausius-Mosotti.