I was reading a bit about this technique, Density Functional based Tight binding (DFTB). It's claimed it can provide a speed improvement of several fold when compared to plain DFT, still giving acceptable results. I downloaded one of its free implementations, the DFTB+ package, and started to work on their tutorial. The problem is, like a semiempirical method, this technique demands parameters. In DFTB the parameters are downloaded separately, as a series of files for each bonded element pair. The problem is, in the page linked as the repository for such parameter files, the options listed don't cover every possible element pair in the periodic table. I my case, I'm interested in heavier members of the alkaline earth group, Sr and Ba. But the only elements in this group with parameter files available are Mg and Ca.
So, I wonder if there is a workaround, short of doing the parametrization on my own, what I imagine would probably be a whole research project on itself, and far beyond my league. Perhaps that repository page just doesn't list every Slater-Koster file in existence, ond others may be found somewhere.