Recent experimental work has shown that the addition of styrene molecules to hydrogen-terminated Si(001) surfaces leads to the formation of one-dimensional molecular structures through a radical-initiated surface chain reaction mechanism. These nanometric structures are observed to be directed parallel to the dimer rows on the H-Si(001)-(2 x 1) surface and perpendicular to the same rows on H-Si(001)-(3 x 1). Using periodic density functional theory (DFT) calculations, we have studied the initial steps of the radical chain mechanism on the H-Si(001)-(3 x 1) surface and compared them to analogous results for H-Si(001)-(2 x 1). On the H-Si(001)-(3 x 1) surface, one of the crucial steps of the surface chain reaction, namely, the abstraction of a H atom from a nearby surface hydride unit, is found to have a somewhat smaller activation energy in the direction perpendicular to the dimer rows (H abstraction from the nearest dihydride site) than along the rows (H abstraction from a neighboring dimer). Additionally, due to the steric repulsion between the styrene molecules and the SiH2 subunits, growth along the dimer rows is not thermodynamically favorable on the (3 x 1) surface. On the other hand, due to the absence of the SiH2 subunits, growth parallel to the Si dimer rows becomes favored on the H-Si(001)-(2 x 1) surface.