A theoretical study of the Fermi surface for a square lattice of group 6 transition metal atoms shows that although most of this surface is made up of closed loops, it results from the weak hybridization of both one-dimensional (1D) and two-dimensional Fermi surfaces. Our study shows that the number of 1D portions of the Fermi surface can be changed by chemisorption. These 1D features of the Fermi surface may well be the origin of some structural instabilities observed in clean and hydrogen covered surfaces. The influence of the coverage, nature of the chemisorbed species, and interlayer interactions on the surface is reported.