The Potential Blind Spot of the τ-Dependent Exchange Density Functional Approximations

Density functional theory (DFT) predicts the existence of an exact functional that allows one to obtain the energy and electron density of the ground state of any molecular system. Although the exact functional is not known, its approximations have become the workhorse of quantum chemistry. In this work, we demonstrate that exchange parts of all τ-dependent meta-GGAs (e.g., TPSS, r²SCAN, M06-L, and so on), which are often the methods of choice in current materials modeling, have the same blind spot as much simpler GGAs (e.g., PBE) on two-electron densities, highlighting the scarcity of data about electron density available to a functional. We demonstrate that to overcome this blind spot, a meta-GGA functional should incorporate nonclassic ingredients such as the Laplacian of electron density, which finally becomes possible with the rise of machine learning techniques for the construction of density functional approximations.