Alkene complexes of silver(I) are studied by four computational methodologies: ab initio RHF, MP2, and MP4 computations, and density functional B3LYP computations, with a variety of all-electron and effective core potential basis sets. Methodological studies indicate that MP2/SBK(d) computations can adequately represent Ag(I)-alkene complexes, and this method is used to study Ag(I) complexes with one to six ethene ligands as well as with methyl-substituted ethene derivatives. The first two alkene ligands enter the coordination sphere of Ag(I) with approximately the same energy, in line with ICR experiments. The association enthalpies of additional complexing ethene ligands diminish progressively. Computations on methyl-substituted alkenes show that the observed trends in argentation chromatography are opposite to those observed and computed for the gas phase, and suggest strong medium effects in Ag(I) chromatography.