  We performed ab initio simulations aimed at identifying the atomistic and
electronic structure origin of the high valence and conduction band, and band
gap tunability of halide perovskites. We found that the two key ingredients are
the overlap between bivalent cation and halide atomic orbitals, and the
electronic charge of the bottom of the conduction band (CBM) state on the Sn or
Pb atoms. In particular, we found that lower gaps are associated to higher
negative antibonding overlap, and higher CBM charge on the bivalent cation.
Both overlap and CBM charge on Sn/Pb can be tuned by the chemical nature of
halide, bi and monovalent cation, as well as the symmetry of crystal structure.
On the basis of our results we provide some practical rules to tune the valence
band maximum, conduction band minimum, and band gap in this class of materials.
