Construction of Laplacian dependent meta-generalized gradient approximation functional based on iso-orbital systems

Kohn-Sham (KS) orbital dependence in a meta-generalized-gradient-approximation (mGGA) functional [1] arises from the kinetic energy density. The orbital dependence can be “de-orbtialized” by replacing the kinetic energy density in terms of the gradient and Laplacian of the electron density [2, 3], with the motivation to cut down the computational cost. Here, we aim to develop a Laplacian dependent mGGA functional without the de-orbitalization that is based on iso-orbital densities, including hydrogen density, gaussian density, and cuspless hydrogen density whose analytic forms are known. We will test the resulting Laplacian-dependent mGGA on other one-electron systems, including the hydrogen molecule cation, H₂⁺, which is a prototypical system for demonstrating the self-interaction error intrinsic to semilocal density functionals (e.g., mGGAs).