Muon spin relaxation studies with DNA and related materials have shown distinct differences in the behaviour of double stranded DNA compared to single stranded DNA and the free bases. Studies are now in progress to completely characterise the muonium adducts of all the bases of relevance to DNA and RNA. In order to assist in the assignments and to gain an insight into the electronic structures and physical properties of the bases, ab initio DFT calculations have been performed. The hyperfine frequencies exhibited by the Mu adducts of adenine, cytosine, guanine, thymine and uracil were found to span a sufficiently wide range to allow the opportunity for distinction between addition sites within each base and between these bases when incorporated in the DNA strand. The results are presented and discussed.