Boron vacancies at the Si( 111):B-root 3 surface are model systems in the comprehension of strongly correlated semiconductor surfaces. By using scanning tunneling spectroscopy, the origin of the single-vacancy electronic structure is addressed. It is shown to originate from the localization of a well-identified dangling-bond surface state with significant B character. The bivacancy defect, which is characterized by energy-split bonding and antibonding states, is interpreted within the textbook diatomic molecule picture. From the hopping parameter, we determine the bandwidth of the surface state from which the impurity state derives and evaluate the strength of many-body effects. Our analysis supports the realization of the Mott-Hubbard insulator state in half-filled dangling-bond surface states on root 3-reconstructed surfaces, as proposed recently for SiC(0001), Sn/Ge(111), and Sn/Si(111). DOI: 10.1103/PhysRevB.87.075427