A new tight-binding band structure calculation method is described. This method, which is based on the Fenske-Hall molecular orbital technique, should be extremely useful in the study of the bulk and surface electronic structure of inorganic materials. The approximations used in the Fenske-Hall method are reviewed, and the extension of this approach to periodic band structure calculations is outlined. Results of calculations for bulk MoS2 are in good agreement with previous experimental and theoretical results. Results of calculations for two-dimensional MoS2 slabs exposing (100) edge planes provide a description of coordinatively unsaturated Mo and S atoms on these edges. Coordinative unsaturation at the Mo atoms introduces new surface states near the Fermi level. Coordinative unsaturation at the S atoms leads to high-energy occupied bands that can be attributed to S lone pair electrons. Surface bonds between Mo atoms and terminal S atoms are stronger than bulk Mo-S bonds, suggesting that terminal S atoms may be more difficult to remove from the edges of MoS2 than bridging S atoms. Bonding in a single two-dimensional layer of MoS2 is found to be more ionic than the bonding in the full three-dimensional structure. This effect is also observed in one-dimensional MoS2 ribbons that expose (100) edge planes. The simplified one-dimensional ribbons will be used for further studies of the electronic structure of the edge planes of MoS2.