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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 bymodeling the exchange hole using the generalized coordinate transformationbased on density matrix expansion. The model potential is Laplacian free andthe inhomogeneity present in the system is included in the momentum vectorwithout affecting the uniform density limit. The parameters associated with themodel exchange hole are fitted with the spherical atoms. The newly constructedpotential along with Tran-Blaha modified Becke-Johnson (TBMBJ) [F. Tran and P.Blaha, Phys. Rev. Lett. 102, 226401 (2009)] potential quite accurately producesthe band gap of various materials ranging from semiconductor throughinsulators. The results for band gap are improved compared to the TBMBJ andother standard semilocal exchange functionals.

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