A brief review of orbital-free density functional theory methods: the fundamental and unique branches

First-principles calculations play a pivotal role in contemporary chemical studies. The most commonly employed algorithms are based on density functional theory (DFT), and in certain instances, the Hartree-Fock method is also utilized. Although these two methods can efficiently yield accurate results for small-to-medium-sized systems, they incur prohibitively high computational costs for systems containing 1000-100 000 atoms. However, capturing such scales is indispensable for replicating realistic complex reactions. Methods based on orbital-free density functional theory (OFDFT), which are expected to significantly reduce computational costs compared to DFT while maintaining quantum-scale accuracy, are thus garnering increasing attention. In this review, the independent-electron methods and the Hohenberg-Kohn theorem are briefly introduced initially. Subsequently, the most crucial component of OFDFT methods, namely, the TF model and its derivatives, is elaborated. A unique extended electron model (EEM) that incorporates geometric algebra into the wavefunction is also reviewed. The latest advancements in this field, particularly those driven by deep learning (DL), are presented in the final part of this review to offer an overview of the trends in OFDFT. This review aims to provide a fundamental understanding of OFDFT to audiences interested in adopting or developing these appealing methods in their research.