No comments on anomalous, but if wavelength is at the boundary of interband transition, than broader gap results, naturally, in decrease of refractive index at fixed wavelength. This is crucial for laser diode operation, and Zhores Alferov received Nobel prize for this

Higher band gap materials in general have lower refractive index; but, there exists no rigorous quantitative relation between the two. There exists the empirical Moss Rule which is EGXn4 = 77 (band gap times 4th power of refractive index = 77). The inverse relation between band gap and refractive index can be qualitatively explained. 

Anomalous dispersion occurs in case of dielectric relaxation at lower frequencies where dielectric constant decreases with frequency. As dielectric constant and refractive index are related, it means that refractive index will decrease with frequency in this situation. This is, therefore,called anomalous dispersion. However, in practice, anomalous word is not used and we simply call it dielectric dispersion.