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A new model is presented to describe the quantum confinement and surface passivation effects of nanoclusters. The quantum well depth (φ) and the band gap width (E[sub g]) of nanoclusters are independent concepts, because the $\phi$ depends on the surface electron density while the E[sub g] is a function of the crystal field of the solid. The φ and E[sub g] can be correlated with the joint physical and chemical effects, which are quite simple but have rarely been noticed. It is suggested that the bond contraction at the surface and the rise in the surface-to-volume ratio (γ), as well as the cluster interaction, enhance intrinsically the crystal field and hence the band gap E[sub g]. Reaction with electronegative elements, such as oxygen and nitrogen, widens extrinsically the E[sub g] by producing holes below the Fermi level [Appl. Phys. Lett.72, 1706 (1998)]. The formulation agrees well with experimental observations on the band gap enlargement by reducing particle size. [ABSTRACT FROM AUTHOR]