Resolution of the Band Gap Prediction Problem for Materials Design

An important property with any new material is the band gap. In order to design new materials in silico, it is critical to have an accurate and computationally inexpensive tool for predicting band gaps. Standard density functional theory (DFT) methods are computationally efficient, but grossly underestimate band gaps. Hybrid density functionals are known to improve band gap predictions, but the computational cost in the overwhelmingly popular plane-wave basis set codes used for solids is a serious drawback. Exact exchange can be evaluated much more efficiently using localized Gaussian basis functions; however, the most readily available Gaussian basis periodic quantum chemistry code lacked spin-orbit coupling. This seriously limited the range of compounds that can be studies. In this thesis, spin-orbit coupling was implemented in the periodic, Gaussian basis set code CRYSTAL. Using the modified code, band gaps were computed using the B3PW91 hybrid density functional for 70 compounds spanning the entire periodic table and a factor of 500 in band gap (0.014 - 15 eV). To benchmark the quality of the hybrid method, we compared to the rigorous GW many-body perturbation theory method. Surprisingly, the MAD for B3PW91 is about 1.5 times smaller than the MAD for GW. Furthermore, B3PW91 is three to four orders of magnitude faster computationally. We also show that increasing (decreasing) the amount of exact exchange compared to B3PW91 leads to systematic overestimates (underestimates) of band gaps. Finally, we show that the pathological vanishing of the density of states at the Fermi level of a metal cannot be observed in practical calculations of real metals. Thus, we believe that B3PW91 is a practical tool for predicting the band gaps of materials before they are synthesized while being computationally efficient enough for high-throughput applications and represents a solution to the band gap prediction problem for materials design