Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Abstract

Kohn−Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of firstprinciples molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn−Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, twopoint, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Harvesting Chemical Understanding with Machine Learning and Quantum Computers

“…According to the basic theorems of Hohenberg–Kohn in DFT, , there is a one-to-one correspondence between ρ and the external potential, υ ext , ρ ⇔ υ ext , suggesting that all properties associated with the system, including the total energy E , are functionals of ρ. DFT has been the most successful and widely applied approach in theoretical and computational chemistry in the last few decades to simulate the electronic structure of molecules and solids alike. , Even though the Kohn–Sham scheme of DFT employed Kohn–Sham orbitals to outcome the difficulty of approximating the kinetic energy density functional, it is not necessary to do so in principle. The DFT method without using orbitals is called orbital-free DFT (OF-DFT), which has been enjoying considerable research attention in recent literature. − …”

Some Recent Advances in Density-Based Reactivity Theory

“…OF-DFT (orbital-free DFT), , as the fourth density-based framework, is a DFT approach without using orbitals. It is contrary to the Kohn–Sham scheme of DFT, where Kohn–Sham orbitals were introduced to bypass the difficulty of approximating T S [ρ].…”

“…Different implementations of OF-DFT are possible. A recent review on OF-DFT is available in the literature . To apply OF-DFT for the purpose of enhancing chemical understanding has been our emphasis.…”

“…Lastly, for systems bounded together through noncovalent interactions, we quantified the effects of cooperativity and frustration, which are the energy gain or loss from the perspective of systems and individuals, respectively, due to the formation of molecular complexes, and then applied them to homochiral systems, where we established the Principle of Chirality Hierarchy . − Homochirality propensities observed in proteins and DNA are only special cases of such principle. These findings by us, together with those by others from the literature, were recently summarized and categorized into four density-based frameworks, i.e., CDFT, − DAQ (density associated quantities), ITA (information-theoretic approach), − and OF-DFT (orbital-free density functional). , These four frameworks form the foundation of the so-called density-based reactivity theory, which is the focus of this work …”

High-Quality Local Pseudopotentials for Metals

“…Following the Hohenberg–Kohn theorem, the orbital-free density functional theory (OF-DFT) , formulates a system’s energy only in terms of the electron density. This bypasses the computational complexities in the orbital-based methods, making OF-DFT a promising method for large-scale material simulations.…”