Bond dissociation energy (R3M+-L) and bond length (R-M and M-L) trends in the R3ML+ series of cation-ligand (L) complexes for M = carbon and silicon, and R = H, CH3 and F are derived from density functional theory calculations using the hybrid B3LYP exchange-correlation potential. The ligands studied are NH3, H2O, HCN, H2CO, MeCN, Me2O, Me2CO, FCN, F2O, F2CO, and NF3, where ligand binding to M is through the nitrogen or oxygen atom. For all ligand substrates, R3M+-L bond energies are calculated to decrease from carbenium to silicenium with R = H but to increase for R=methyl and fluorine. Also for these latter two cases, in going from the bare R3M+ cation to the ligand complexes, the R-M distances increase by more than twice as much for the carbenium than for the silicenium ions. These trends indicate the relative importance of a stabilizing R-M hyperconjugative interaction in the bare tert-butyl and trifluoromethyl cations compared with the other bare cations and all the cation-ligand complexes. Ab initio, multiconfiguration VBSCF calculations are carried out on model systems (AH(n)-MH2+; M = C, Si; AH(n) = CH3, SiH3, F), designed to mimic the R3M+ cations, in order to analyze the electronic structure of the R-M bend. The pi bond component, representing the hyperconjugative interaction, is found to preferentially stabilize CH3CH2+ over SiH3CH2+ and FCH2+ relative to FSiH2+. The fluorosilicenium cation shows significant pi donor effects. This analysis establishes the theoretical basis for the trends in energy and structural properties found for the R3M+ cations and cation-ligand complexes.