Orbital-free density functional theory: Linear scaling methods for kinetic potentials, and applications to solid Al and Si

Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data

Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.

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

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 first-principles 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, two-point, 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.

Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks

We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from an input electron density. The output of the network is used as a nonlocal correction to conventional local and semilocal kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. The density which minimizes the total energy given by the functional is examined in detail. We identify several avenues to improve on this exploratory work, by reducing numerical noise and changing the structure of our functional. Finally we examine the features in the density learned by the neural network to anticipate the prospects of generalizing these models.

Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system

Regular to chaotic transition takes place in a driven van der Pol oscillator in both classical and quantum domains.

Quantum molecular dynamics simulations of transport properties in liquid and dense-plasma plutonium

We have calculated the viscosity and self-diffusion coefficients of plutonium in the liquid phase using quantum molecular dynamics (QMD) and in the dense-plasma phase using orbital-free molecular dynamics (OFMD), as well as in the intermediate warm dense matter regime with both methods. Our liquid metal results for viscosity are about 40% lower than measured experimentally, whereas a previous calculation using an empirical interatomic potential (modified embedded-atom method) obtained results 3-4 times larger than the experiment. The QMD and OFMD results agree well at the intermediate temperatures. The calculations in the dense-plasma regime for temperatures from 50 to 5000 eV and densities about 1-5 times ambient are compared with the one-component plasma (OCP) model, using effective charges given by the average-atom code INFERNO. The INFERNO-OCP model results agree with the OFMD to within about a factor of 2, except for the viscosity at temperatures less than about 100 eV, where the disagreement is greater. A Stokes-Einstein relationship of the viscosities and diffusion coefficients is found to hold fairly well separately in both the liquid and dense-plasma regimes.