Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session F19: Real Space Methods for the Electronic Structure Problem: AlgorithmsFocus Session Live
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Sponsoring Units: DCOMP Chair: Leeor Kronik, Weizmann Institute of Science |
Tuesday, March 16, 2021 11:30AM - 12:06PM Live |
F19.00001: Towards an Accurate and Efficient Order-N Framework for Real-Space Condensed-Phase Hybrid Density Functional Theory Invited Speaker: Robert Distasio By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with hybrid DFT limits its applicability when treating large-scale and complex condensed-phase systems. To overcome this limitation, we have devised a highly accurate and linear-scaling (order-N) approach based on a local (MLWF) representation of the occupied space that exploits sparsity when evaluating the EXX interaction in real space [1]. In this work, we present a detailed description of the theoretical and algorithmic advances that are needed to perform hybrid DFT based ab initio molecular dynamics (AIMD) simulations of large-scale finite-gap condensed-phase systems using this approach. This is followed by a critical assessment of the accuracy and parallel performance of the exx algorithm when performing AIMD simulations of liquid water and several ice phases in the canonical (NVT) and isobaric-isothermal (NpT) ensembles. With access to high-performance computing (HPC) resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of systems containing 500-1000 atoms with a wall time cost comparable to semi-local DFT. In the strong-scaling limit, this cost is split evenly between computation, communication, and processor idling; as such, we also discuss a three-pronged strategy that directly attacks each of these contributions and reduces the overall wall time cost by approximately an order of magnitude for large-scale heterogeneous systems. With these developments, this work takes us one step closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level. |
Tuesday, March 16, 2021 12:06PM - 12:18PM Live |
F19.00002: Accelerating real-space methods by discontinuous projection John Pask, Qimen Xu, Phanish Suryanarayana By virtue of multiple advances over the past two decades, real-space electronic structure methods have surpassed planewave methods in large-scale calculations of isolated and extended systems alike. Combining advances in both finite-difference and finite-element methods, we discuss a new approach to accelerate real-space methods further still, while retaining the simplicity, systematic convergence, and parallelizability inherent in the methodology. The key idea is to compress the large, sparse real-space Hamiltonian by projection in a strictly local, systematically improvable, discontinuous basis spanning the occupied subspace. We show how this basis can be constructed and employed to reduce the dimension of the real-space Hamiltonian by up to three orders of magnitude. Molecular dynamics step times of a few minutes for systems containing thousands of atoms demonstrate the scalability of the methodology in a discontinuous Galerkin formulation. Results for 1D, 2D, and 3D systems demonstrate the additional advantages afforded by the new projection formulation [1]. |
Tuesday, March 16, 2021 12:18PM - 12:30PM Live |
F19.00003: Polynomial-filtered Spectrum Slicing Method for Real-space Pseudopotential Density Functional Theory Calculations James Chelikowsky, Kai-Hsin Liou, Chao Yang First-principles electronic structure calculations are a popular avenue to understanding and predicting properties of materials. However, solving the electronic structures of the materials of interest, such as complex biomolecules, nanostructures, and interfacial systems can involve many atoms, e.g., systems with over 10,000 atoms. Systems of this size pose a challenge to current electronic structure software. We will present the recent work of a spectrum slicing algorithm, which is implemented in a real-space pseudopotential density functional theory code, PARSEC. The spectrum slicing method builds an additional layer of parallelization on top of the Chebyshev-filtered subspace iteration. Our approach provides more flexibility to fully utilize the computing power of modern distributed parallel computers. We will demonstrate the scalability of the algorithm and discuss outstanding challenges. |
Tuesday, March 16, 2021 12:30PM - 12:42PM Live |
F19.00004: Space-filling Curves for Real-space Pseudopotential Density Functional Theory Calculations Kai-Hsin Liou, Ariel Biller, Leeor Kronik, James Chelikowsky Pseudopotential density functional theory is a popular approach to predict material properties and to explain experimental observations. With this approach implemented in real space, we are able to simulate systems of tens of thousands of atoms as routine work. Real-space methods discretize the simulation domain and are advantageous when simulating confined or semi-periodic systems, such as charged defects and interfaces. Among real-space methods, finite difference methods are easier to implement. The Hamiltonian matrix is often large but sparse, which requires an efficient implementation of matrix–vector multiplications. Using space-filling curves, we can construct a real-space grid with excellent locality. Consequently, the communication overhead can be reduced and is more balanced. We will also demonstrate the improved scalability of the matrix–vector multiplications, which is beneficial to polynomial filtering based eigensolvers. |
Tuesday, March 16, 2021 12:42PM - 12:54PM Live |
F19.00005: Real-space Density Functional Theory for large length and time scales Phanish Suryanarayana In this talk, previous and current efforts of the speaker to develop efficient real-space formulations and massively parallel implementations for Density Functional Theory (DFT) will be discussed. These include (i) SPARC: A general purpose framework for performing large-scale electronic structure calculations based on DFT; (ii) Cyclic+Helical DFT: A framework for studying systems possessing cyclic and/or helical symmetry, with application to bending and torsional deformations of nanostructures; and (iii) SQDFT: A linear-scaling framework for studying materials under extreme conditions. Overall, the speaker will discuss how the above developments enable electronic structure simulations at large length and time scales. |
Tuesday, March 16, 2021 12:54PM - 1:06PM Live |
F19.00006: General Approach for Reducing Continuous Translational Symmetry Errors in Finite Difference Real-Space Calculations Tian Qiu, Leeor Kronik, Andrew Marshall Rappe We have developed a new scheme to install pseudopotentials on a finite real-space grid that significantly reduces unphysical fluctuations of quantities for fractional grid-point shifts in real space. Instead of interpolating the potential on the grid, this scheme chooses a reference position and use a translation method to represent positions of atoms in real space. This translation is exact for integer grid-point shifts and is designed to minimize the "egg box" effect for fractional grid-point shifts. It provides nonlocal but banded representations for local potentials and is compatible with nonlocal pseudopotential operators. As a demonstration, this scheme is tested in one dimension for three types of potentials: a local ionic potential, a local ionic potential plus a nonlocal operator, and a local ionic potential plus the Hartree and exchange-correlation potential. Fluctuations of examined quantities are reduced by four orders, four orders, and three orders, respectively. This scheme does not require the manipulation of grids and can be easily extended to the three-dimensional case. |
Tuesday, March 16, 2021 1:06PM - 1:18PM Live |
F19.00007: Configurational forces in density functional theory calculations using orthogonalized enriched finite elements. Nelson David Rufus, Vikram Gavini Real-space all-electron Kohn-Sham DFT calculations can be efficiently performed using orthogonalized enriched finite element (FE) basis, wherein the classical (standard) FE basis are augmented with atom-centered numerical basis functions (enrichments) that are appropriately orthogonalized with respect to the underlying FE basis. Orthogonalized enriched FE basis improves the numerical conditioning of the basis as well as renders the overlap matrix block-diagonal, greatly simplifying its inversion. In this work, we extend the framework to compute configurational forces which arise from the variational derivative of the Kohn-Sham energy functional with respect to the position of the material point x. This allows us to compute the ionic forces as well as stresses in periodic systems. We establish the accuracy of the formulation, by comparing the computed forces and stresses for various benchmark systems with those obtained from finite-differencing the ground-state energy. We also benchmark our calculations against Gaussian basis for isolated systems and LAPW basis for periodic systems. We finally demonstrate the capability of this approach to obtain relaxed structures for large-scale systems. |
Tuesday, March 16, 2021 1:18PM - 1:30PM Live |
F19.00008: Boost Efficiency for Stochastic Density Functional Theory with a Unified Strategy Ming Chen, Roi Baer, Daniel Neuhauser, Eran Rabani
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Tuesday, March 16, 2021 1:30PM - 1:42PM Live |
F19.00009: An improved method for computing dynamical conductivity Minsu Ghim, Ji Hoon Ryoo, Cheol-Hwan Park Recently, methods for computing dynamical conductivity including anomalous Hall and spin Hall conductivity from first principles, have been developed. [1,2] The analytic tetrahedron interpolation method was suggested, and the Wannier interpolation scheme allowed computation with a dense grid. [3] With the aid of these, we present further technical improvements in the tetrahedron method for both the real part and the imaginary part of conductivity. |
Tuesday, March 16, 2021 1:42PM - 1:54PM Live |
F19.00010: Enabling Linear Scaling Exact Exchange for Heterogeneous Systems Hsin-Yu Ko, Zachary Sparrow, Marcos Andrade, Owen L. Crane, Brian Ernst, Peace Kotamnives, Yan Yang, Yang Yang, Eric G. Fuemmeler, Robert Distasio Hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT) and provide a semi-quantitative description of the electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with evaluating the exact exchange (EXX) interaction limits hybrid DFT from treating large-scale condensed-phase systems. To address this challenge, we have developed a linear-scaling real-space approach that exploits the sparsity in the EXX interaction using local orbitals (MLWFs). The resulting massively parallel algorithm (exx) provides an accurate evaluation of all EXX quantities and enables hybrid DFT based ab initio molecular dynamics (AIMD) of large-scale finite-gap systems with a wall time cost comparable to semi-local DFT [1]. Since exx was optimized to treat homogeneous systems, its performance degrades when treating highly anisotropic heterogeneous systems with multiple phases and/or components. In this work, we discuss three major theoretical and algorithmic advances that enable efficient and accurate hybrid DFT based AIMD of large-scale heterogeneous systems, and showcase the extended exx module when treating a complex solid-liquid interface. |
Tuesday, March 16, 2021 1:54PM - 2:06PM Live |
F19.00011: Maximally Localized Wannier Functions for Strictly Local Projectors Pratik Sathe, Fenner Harper, Rahul Roy The localization properties of band projectors and their associated Wannier functions are closely related. In particular, a band projector in a 1d lattice is strictly local (SL) if and only if there exists an associated Wannier basis consisting of compactly supported wavefunctions [1]. We improve the bound on the degree of localization of Wannier functions associated with SL projectors. Specifically, we show that for an SL projector with a maximum hopping distance of b, it is always possible to obtain compactly supported Wannier functions with spatial support of at most 2b cells. Additionally, these wavefunctions are the corresponding maximally localized (generalized) Wannier functions in the presence (absence) of translational invariance, within a size b supercell representation of the lattice. Based on this result, we propose a method for the construction of arbitrary SL projectors in 1d, and demonstrate its potential for constructing model flat-band Hamiltonians in 1d. |
Tuesday, March 16, 2021 2:06PM - 2:18PM Live |
F19.00012: Electronic structure of dimers at finite temperature with density matrix quantum Monte Carlo Hayley Petras, William Van Benschoten, James Shepherd We show our recent efforts to benchmark molecular dimers using density matrix quantum Monte Carlo which calculates the exact-on-average electronic density matrix. Molecular systems are chosen for their affordability and we will comment on how our findings relate to solids and warm dense matter. |
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