With the miniaturization of a solid, quantum and interface effects become increasingly important. As a result, the band structure of a nanometric semiconductor changes: the band gap expands, the core level shifts, the bandwidth revises, and the sublevel separation within a band increases. Unfortunately, such a thorough change goes beyond the scope of currently available models such as the `quantum confinement' theory. A consistent understanding of the factors dominating the band-structure change is highly desirable. Here we present a new approach for the size-induced unusual change by adding the effect of surface-coordination deficiency-induced bond contraction to the convention of an extended solid of which the Hamiltonian contains the intraatomic trapping interaction and the interatomic binding interaction. Agreement between modelling predictions and the observed size dependency in the photoluminescence of Si oxides and some nanometric III-V and II-VI semiconductors, and in the core-level shift of Cu-O nanosolids has been reached. Results indicate that the spontaneous contraction of chemical bonds at a surface and the rise in the surface-to-volume ratio with reducing particle size are responsible for the unusual change of the band structure of a nanosolid.