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.