Assessing The Band Gap Problem By Improving Upon The Semilocal Exchange Hole Potential

An asymptotic corrected exchange hole potential analogous to Becke-Roussel [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)] is constructed by modeling the exchange hole using the generalized coordinate transformation based on density matrix expansion. The model potential is Laplacian free and the inhomogeneity present in the system is included in the momentum vector without affecting the uniform density limit. The parameters associated with the model exchange hole are fitted with the spherical atoms. The newly constructed potential along with Tran-Blaha modified Becke-Johnson (TBMBJ) [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] potential quite accurately produces the band gap of various materials ranging from semiconductor through insulators. The results for band gap are improved compared to the TBMBJ and other standard semilocal exchange functionals.