Pekka Pyykkö recently published http://www.chem.helsinki.fi/~pyykko/pekka/PT.pdf" where he'd done ground-state calculations on the elements all the way up to 172(!), so you could start there (and references therein).
I personally can't really say offhand, relativistic (heavy-element) quantum chemistry isn't really my thing.
While I may be a theorist, theoretical properties of theoretical elements is a bit too "hard-core" even for me!
Why do the elements have to be stable to examine their properties? For most of the transuranium actinids, extensive experimental data on chemical reactivity are available and basic chemical experiments have been performed for up to element 106 or so.
Of course it is not simple to do experiments with single atoms which live for only a second or so, but nevertheless it is done. E.g. I found the following thesis ( in German, however): http://ubm.opus.hbz-nrw.de/volltexte/2000/96/pdf/diss.pdf