Density matrix expansion based semi-local exchange hole applied to range separated density functional theory

Exchange hole is the principle constituent in density functional theory, which can be used to accurately design exchange energy functional and range separated hybrid functionals coupled with some appropriate correlation. Recently, density matrix expansion (DME) based semi-local exchange hole proposed by Tao-Mo gained attention due to its fulfillment of some exact constraints. We propose a new long-range corrected (LC) scheme that combines meta-generalized gradient approximation (meta-GGA) exchange functionals designed from DME exchange hole coupled with the ab-initio Hartree-Fock (HF) exchange integral by separating the Coulomb interaction operator using standard error function. Associate with Lee-Yang-Parr (LYP) correlation functional, assessment and benchmarking of our functional using well-known test set shows that it performs remarkably well for a broad range of molecular properties, such as thermochemistry, noncovalent interaction and barrier height of chemical reactions.