Frontier Orbital Description of the Si(100) Surface: A Route to Symmetry-Allowed and Concerted [2 + 2] Cycloadditions

We present a conceptually simple frontier orbital description of an ideal Si(100) surface by extending the standard orbital description for a single Si dimer unit across the surface Brillouin zone. Density functional theory calculations are used to order the predicted frontier wave functions in terms of energy. When applied to the p(2 × 1) and c(4 × 2) reconstructions, this analysis provides a route for the controversial [2 + 2] cycloaddition reaction, which was previously thought to involve a violation of the Woodward−Hoffman rules. The calculated frontier states are shown to be a valuable aid in describing reactivity on Si(100) that is consistent with experiment and provides a rational means to predict allowed reaction products on Si(100).