Petascale Orbital-Free Density Functional Theory Enabled by Small-Box Algorithms

Abstract

Orbital-free density functional theory (OFDFT) is a quantum-mechanics-based method that utilizes electron density as its sole variable. The main computational cost in OFDFT is the ubiquitous use of the fast Fourier transform (FFT), which is mainly adopted to evaluate the kinetic energy density functional (KEDF) and electron-electron Coulomb interaction terms. We design and implement a small-box FFT (SBFFT) algorithm to overcome the parallelization limitations of conventional FFT algorithms. We also propose real-space truncation of the nonlocal Wang-Teter KEDF kernel. The scalability of the SBFFT is demonstrated by efficiently simulating one full optimization step (electron density, energies, forces, and stresses) of 1,024,000 lithium (Li) atoms on up to 65,536 cores. We perform other tests using Li as a test material, including calculations of physical properties of different phases of bulk Li, geometry optimizations of nanocrystalline Li, and molecular dynamics simulations of liquid Li. All of the tests yield excellent agreement with the original OFDFT results, suggesting that the OFDFT-SBFFT algorithm opens the door to efficient first-principles simulations of materials containing millions of atoms.

The Importance of Being Inconsistent

“…The quasicontinuum-DFT approach (QCDFT) [PZHC08], combining the coarse-graining idea of multiscale methods [CLK05] with the coupling strategy of QM/MM (Quantum-Mechanics / Molecular-Mechanics) [SHFM96; GT02; FG05], allows for the simulation of multimillion atoms via orbital-free DFT embedding. Explicit treatment of a few million atoms has been demonstrated via linear-scaling orbital-free DFT algorithms [HC09;CJZ+16]. These, however, rely on approximations to the non-interacting kinetic energy functional T s [n], which are neither sufficiently accurate nor general.…”

libKEDF: An accelerated library of kinetic energy density functionals

“…We evaluated all KEDFs on real‐space grids with sizes up to 1280 × 1280 × 1280 on a tiger/CPU node with 128 GB RAM, unless the data set could not fit in the main memory. This is comparable to the largest size (1024 × 1024 × 1024 in real space) reported in the literature for a one‐million atom liquid lithium MD simulation employing tens of thousands of CPUs . Future hardware development will enable us to routinely study such systems with libKEDF.…”

“…This is comparable to the largest size (1024 3 1024 3 1024 in real space) reported in the literature for a one-million atom liquid lithium MD simulation employing tens of thousands of CPUs. [23] Future hardware development will enable us to routinely study such systems with libKEDF.…”

“…Lastly, excellent performance is generally required for consumer codes to adopt any library. Particularly in the case of OFDFT, we argue that good performance for large systems will advance adoption for computationally expensive simulations such as OFDFT molecular dynamics (MD), Monte–Carlo (MC), and nanoscale structure optimizations . These gains will lend insight into important challenges in materials science.…”

Multiscale Molecular Dynamics Model for Heterogeneous Charged Systems

“…MD codes based on Kohn-Sham-Mermin density functional theory (DFT) can reach scales of about 10 Å, at the price of severely limiting the method to uniform properties of matter, and the method also becomes more expensive at higher temperatures. Thus, orbital-free DFT (OFDFT) methods have been developed [15][16][17][18][19][20][21][22][23] to overcome some of these limitations. For zero-temperature systems with fixed nuclei, finite element methods have been successful in scaling OFDFT calculations to very large systems [24]; however, coupling this approach to the MD equations of motion would require an adaptive mesh generation routine to be run at each time step for each configuration of nuclear coordinates, which could introduce a significant bottleneck to the simulation.…”