The accuracy and efficiency of a density functional is dependent on the basic ingredients it uses and how the ingredients are built into the functional as a whole. An iso-orbital indicator based on the electron density, its gradients, and the kinetic energy density, has proven an essential dimensionless variable that allows density functionals to recognize and correctly treat various types of chemical bonding, both strong and weak. Density functionals constructed around the iso-orbital indicator usually require dense real-space grids for numerical implementation that deteriorate computational efficiency, with poor grid convergence compromising the improved accuracy. Here, an improved iso-orbital indicator is proposed based on the same ingredients that retains the capability to identify the same chemical bonds while significantly relieving the requirement of dense grids. Furthermore, the improved iso-orbital indicator gives an improved recognition for tail regions of electron densities and is divergence-free for the exchange-correlation potential. The improved iso-orbital indicator is therefore expected to be the prime choice for further density functional development.
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