応用物理学会春季・秋季学術講演会

Large-scale ab initio modeling is required to model properties of materials at realistic time and length scales. The near-cubic scaling of Kohn Sham DFT with system size limits routine modeling to systems on the order of 100 atoms. This scaling is due to reliance on orbitals. Orbital-Free DFT (OF-DFT) avoids orbitals and allows for near-linear scaling; up to 10⁵ atoms can be routinely modeled on a desktop. The Achilles’ heel of OF-DFT is the poor quality of available kinetic energy functionals (KEF) which replace the non-interacting kinetic energy T or kinetic energy density (KED) t(r) based on orbitals with a functional of electron density only. This problem is so bad that as of today, OF-DFT cannot be used in applications beyond light metals. We present the results of applying machine learning using neural networks (NN) to learn the KS KED of bulk light metals (Li, Mg, Al), a bulk semiconductor (Si) and molecules (H₂O and C₆H₆). We train the NN using terms of the 4^th order gradient expansion as inputs. We achieve ultra-low fit errors with no NN overfitting (contrary to other works). KS KED can be reproduced very accurately for Li, Mg, and Al; most importantly, a very good fit was also achieved for Si - a much more difficult case. A decent fit was achieved for H₂O KED, but not for C₆H₆. We also highlight the critical role played by the type of pseudopotential as well as by KED data distribution, suggesting directions of further research.