Explore semi-local non-interacting kinetic energy functional and non-additive non-interacting kinetic energy functional with neural network models*

The non-interacting kinetic energy (KE) functional of Density Functional Theory (DFT) has been for many decades an object of study for orbital-free DFT and density embedding methods. Due to its comparatively large magnitude and to its highly non-local dependence on the density, the non-interacting KE functional remains extremely challenging to approximate accurately as an explicit functional of the densities. One of the most successful approximations, especially for modeling solid metals and semiconductors, is non-local functional. However, recent calculations show that the meta-GGA level of approximation seems to be capable of yielding comparable accuracy. We explore the full potential of the meta-GGA form for the non-interacting KE functional by using neural network models with exact conditions enforced. Moreover, the non-additive non-interacting kinetic energy (NAKE), defined as the difference between the non-interacting KE of the entire system and the sum of the fragment kinetic energies, can be approximated as one separate quantity. We explore NAKE functionals designed for covalently-bonded fragments and fractional electrons in Partition-DFT.