The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al.). Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the beta-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near OK, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.