Surface modification of silicon with organic monolayers tethered to the surface by different linkers is an important process in realizing future miniaturized electronic and sensor devices. Understanding the roles played by the nature of the linking group and the chain length on the adsorption structures and stabilities of these assemblies is vital to advance this technology. This paper presents a density functional theory (DFT) study of the hydrogen passivated Si(111) surface modified with alkyl chains of the general formula H:Si(CH2)(n)CH2 and H:SiX(CH2)(n)CH3, where X = NH, O, S and n = (0, 1, 3, 5, 7, 9, 11), at half coverage. For (X)hexane and (X)dodecane functionalization, we also examined various coverages up to full monolayer grafting in order to validate the result of half covered surface and the linker effect on the coverage. We find that it is necessary to take into account the van der Waals interaction between the alkyl chains. The strongest binding is for the oxygen linker, followed by S, N, and C, irrespective of chain length. The result revealed that the sequence of the stability is independent of coverage; however, linkers other than carbon can shift the optimum coverage considerably and allow further packing density. For all linkers apart from sulfur, structural properties, in particular, surface-linker-chain angles, saturate to a single value once n > 3. For sulfur, we identify three regimes, namely, n = 03, n = 57, and n = 911, each with its own characteristic adsorption structures. Where possible, our computational results are shown to be consistent with the available experimental data and show how the fundamental structural properties of modified Si surfaces can be controlled by the choice of linking group and chain length.