Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session A44: RealSpace Methods for the Electronic Structure Problem IFocus

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Sponsoring Units: DCOMP Chair: James Chelikowsky, University of Texas at Austin Room: 704 
Monday, March 2, 2020 8:00AM  8:36AM 
A44.00001: Exploiting Orbital Locality in Real Space to Enable LargeScale CondensedPhase Ab Initio Molecular Dynamics with Hybrid Density Functional Theory Invited Speaker: Robert Distasio By including a fraction of exact exchange (EXX), hybrid functionals reduce the selfinteraction error in semilocal density functional theory (DFT), and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with hybrid DFT has limited its applicability when treating largescale condensedphase systems. To overcome this limitation, we have devised a linearscaling yet formally exact approach that utilizes a local representation of the occupied orbitals to exploit the sparsity in the realspace evaluation of the quantum mechanical exchange interaction in finitegap systems. Here, we present a detailed description of the theoretical and algorithmic advances required to perform ab initio molecular dynamics (AIMD) simulations of largescale condensedphase systems with hybrid DFT. We focus our theoretical discussion on integrating this approach into the framework of CarParrinello AIMD, and provide a comprehensive description of our algorithm, which is implemented in the opensource Quantum ESPRESSO program and employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the highperformance computing (HPC) resources available on supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when performing AIMD simulations of liquid water in the canonical (NVT) and isobaricisothermal (NpT) ensembles. With access to HPC resources, we demonstrate that our algorithm enables hybrid DFT based AIMD simulations of condensedphase systems containing ~1000 atoms with a walltime cost that is comparable to semilocal DFT. In doing so, this work takes us one step closer to routinely performing AIMD simulations of largescale condensedphase systems for sufficiently long timescales at the hybrid DFT level of theory. 
Monday, March 2, 2020 8:36AM  8:48AM 
A44.00002: Improving the Scalability of CondensedPhase Hybrid Density Functional Theory: Computation, Communication, and Load Balancing HsinYu Ko, Junteng Jia, Marcos Andrade, Zachary Sparrow, Robert Distasio Ab initio molecular dynamics (AIMD) simulations at the hybrid density functional theory (DFT) level provide a semiquantitative description of complex condensedphase systems such as molecular liquids and crystals. For finitegap systems, we have developed a linearscaling and formally exact algorithm for computing the exact exchange interaction in real space based on a localized representation of the occupied orbitals (e.g., maximally localized Wannier functions). Although a massively parallel implementation of this algorithm in Quantum ESPRESSO already enables hybrid DFT based AIMD simulations of condensedphase systems containing 5001000 atoms, we have identified three nearly equal contributions to the walltime cost of this approach: computation events, communication overhead, and processor idling due to workload imbalance. In this work, we present a threepronged strategy that we have employed to attack these contributions and reduce the overall walltime cost by approximately an order of magnitude. 
Monday, March 2, 2020 8:48AM  9:00AM 
A44.00003: SPARCX: Realspace Density Functional Theory for large length and time scales Phanish Suryanarayana In this talk, previous and current efforts of the speaker to develop efficient realspace formulations and massively parallel implementations for Density Functional Theory (DFT) will be discussed. These include (i) SPARC: A general purpose framework for performing largescale electronic structure calculations based on DFT; (ii) Cyclic DFT: A framework for studying systems possessing cyclic symmetry, with application to the bending deformations in nanostructures; (iii) Helical DFT: A framework for studying systems possessing helical symmetry, with application to the torsional deformations in nanostructures; and (iv) SQDFT: A linearscaling 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. 
Monday, March 2, 2020 9:00AM  9:12AM 
A44.00004: A Scalable Eigensolver for Realspace Pseudopotential Density Functional Theory: A Polynomialfiltered Spectrum Slicing Method KaiHsin Liou, Chao Yang, James Chelikowsky Firstprinciples electronic structure calculations are a popular avenue for 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 require descriptions of systems with many atoms, e.g., systems with over 10,000 atoms. Systems of this size pose a challenge to current electronic structure computation software. We will present recent work using a spectrumslicing algorithm, which is implemented in a realspace pseudopotential density functional theory code, PARSEC. The spectrum slicing method builds an additional layer of parallelization on top of the Chebyshevfiltered 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. 
Monday, March 2, 2020 9:12AM  9:24AM 
A44.00005: TreecodeAccelerated Green's Iteration for KohnSham DFT Nathan Vaughn, Robert Krasny, Vikram Gavini We present a realspace method for KohnSham Density Functional Theory based on an integral equation formulation of the KohnSham equations, called TreecodeAccelerated Green's Iteration (TAGI). In this approach, the eigenvalue problem for the KohnSham differential operator is converted to a fixed point problem for an integral operator by convolution with a Green's function, then the fixed points are computed using Green's iteration. Essential to this method is the accurate and efficient evaluation of the convolution integrals arising in the iteration. TAGI achieves accuracy and efficiency through the use of adaptive mesh refinement to represent the fields, singularity subtraction schemes to reduce the quadrature error due to the singular Green's functions, and a GPUaccelerated treecode to reduce the computational complexity of the convolution integrals. We have performed allelectron calculations on nonperiodic systems and demonstrated systematic convergence to chemical accuracy with respect to tightly converged reference values. 
Monday, March 2, 2020 9:24AM  9:36AM 
A44.00006: Accelerating realspace methods by discontinuous projection John Pask, Qimen Xu, Phanish Suryanarayana By virtue of multiple advances in the past two decades, realspace electronic structure methods have surpassed planewave methods in largescale calculations of isolated and extended systems alike. Combining advances in both finitedifference and finiteelement methods over the decades, we discuss a new approach to accelerate realspace methods further still, while retaining the simplicity, systematic convergence, and parallelizability inherent in the methodology. The key idea is to compress the large, sparse realspace 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 realspace 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 [1]. Results for 1D, 2D, and 3D systems demonstrate the additional advantages afforded by the new projection formulation [2]. 
Monday, March 2, 2020 9:36AM  9:48AM 
A44.00007: A Spacefilling Curve Based Grid Partition to Accelerate Realspace Pseudopotential Density Functional Theory Calculations Ariel Biller, KaiHsin Liou, Deena Roller, Leeor Kronik, James Chelikowsky Density functional theory (DFT) has become a popular tool to verify, explain, and predict experimental discoveries in materials. In conjunction with pseudopotentials, we can now achieve simulations of systems with tens of thousands of atoms as “routine work.” Realspace DFT has advantages when simulating confined or semiperiodic systems, such as defects, charged systems, and interfaces. Within a finitedifference method, the Hamiltonian matrix is often large and sparse, and requires an efficient implementation of matrixvector multiplication. We will show through spacefilling curves that we can construct a realspace grid whose grid points have excellent locality. Consequently, the communication between compute nodes is reduced. We will also demonstrate that this spacefilling curve based grid partition improves the scalability of the matrixvector multiplications, which is beneficial to polynomial filtering based eigensolvers. 
Monday, March 2, 2020 9:48AM  10:00AM 
A44.00008: Reduce Noise in Stochastic Density Functional Theory Ming Chen, Daniel Neuhauser, Roi Baer, Eran Rabani Large scale density functional theory (DFT) calculations are necessary for understanding the physics of complex materials. Steep numerical scaling of conventional DFT methods prohibits the routine application to large systems containing tens of thousands of electrons. An alternative to conventional DFT is based on representing the density and density matrix using stochastic sampling of the occupied subspace, allowing for linear or even sublinear scaling DFT method at the cost of introducing a wellcontrolled statistical error. It becomes an important task to develop approaches that reduce the stochastic noise in order to improve accuracy and reliability of stochastic DFT. Two different noise reduction techniques have been introduced in stochastic DFT. One is based on decomposing the system into overlapped fragments and the other approach divides the occupied subspace into subspaces according to energy windows. Both noise reduction techniques can significantly reduce the noise level in electronic structures, which leads to orders of magnitude reduction in computational costs. This talk will provide a look into both methods including analysis of noise reduction, scaling, and performance. Illustrations will be given for semiconductor materials with nearly 16,000 electrons. 
Monday, March 2, 2020 10:00AM  10:12AM 
A44.00009: A general approach towards continuous translational symmetry in finite difference realspace calculations Tian Qiu, Leeor Kronik, Andrew Marshall Rappe We have developed a new scheme to install pseudopotentials on a finite realspace grid that significantly reduces unphysical fluctuations of quantities for fractional gridpoint 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 gridpoint shifts and is designed to minimize the "egg box" effect for fractional gridpoint 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 exchangecorrelation 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 threedimensional case. 
Monday, March 2, 2020 10:12AM  10:24AM 
A44.00010: Discrete discontinuous basis projection (DDBP) method for largescale electronic structure calculations. Qimen Xu, Phanish Suryanarayana The large number of grid points per atom required for accurate realspace KohnSham Density Functional Theory (DFT) calculations restricts their efficiency. In this work, we present an approach to accelerate such calculations several fold, without loss of accuracy, by systematically reducing the cost of the key computational step: the determination of the KohnSham orbitals spanning the occupied subspace. This is achieved by systematically reducing the dimension of the discrete eigenproblem that must be solved, through projection into a highly efficient discrete discontinuous basis. In calculations of quasi1D, quasi2D, and bulk metallic systems, we find that accurate energies and forces are obtained with 8–25 basis functions per atom, reducing the dimension of fullmatrix eigenproblems by 13 orders of magnitude. 
Monday, March 2, 2020 10:24AM  10:36AM 
A44.00011: Fast allelectron density functional theory calculations in solids using orthogonalized enriched finite elements Nelson David Rufus, Bikash Kanungo, Vikram Gavini We present a computationally efficient approach to perform realspace allelectron KohnSham DFT calculations for bulk solids using an enriched finite element (FE) basis, wherein the classical FE basis are augmented with atomcentered numerical basis functions constructed from atomic solutions to the KohnSham problem. We term these atomcentered numerical basis functions as enrichment functions. Notably, to improve the conditioning we orthogonalize the enrichment function with respect to the classical FE basis, without compromising on the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix blockdiagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based acceleration technique to efficiently compute the occupied eigenspace in each selfconsistent iteration. We demonstrate the accuracy and efficiency for periodic unitcells and supercells, ranging up to 5000 electrons (containing as many as 500 atoms). We observe a staggering 50100x speedup over the classical FE basis. We also benchmark with (L)APW(+lo) basis for accuracy and performance. Finally, we demonstrate parallel scalability for a system with ~216 Si and C atoms. 
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