  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.
