Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations

Abstract

We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core-subspace, spanned by the core eigenfunctions, and its complement, the valence-subspace, and thereby enables an efficient computation of the Fermi-operator expansion by reducing the expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The key ideas used in our approach are: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate non-orthogonal localized functions spanning the Chebyshev-filtered subspace; (ii) compute the Kohn-Sham Hamiltonian projected onto the valence-subspace; (iii) employ Fermi-operator expansion in terms of the valence-subspace projected Hamiltonian to compute the density matrix, electron-density and band energy. We demonstrate the accuracy and performance of the method on benchmark materials systems involving silicon nano-clusters up to 1330 electrons, a single gold atom and a six-atom gold nano-cluster. The benchmark studies on silicon nano-clusters revealed a staggering five-fold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of $\sim 10^{-4}Ha/atom$ with respect to reference calculations. Further, numerical investigations on gold suggest that spectrum splitting is indispensable to achieve meaningful accuracies, while employing Fermi-operator expansion.

arXiv comment12 pages, 5 figures

References in corpus (14)

• O(N) methods in electronic structure calculations
• Density functional study of Au${}_n$ (n=2-20) clusters: lowest-energy structures and electronic properties
• Daubechies wavelets as a basis set for density functional pseudopotential calculations
• Total energy global optimizations using non orthogonal localized orbitals
• Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
• Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
• Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach
• Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals
• Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
• Coarse-graining Kohn-Sham Density Functional Theory
• Pole-based approximation of Fermi-Dirac function
• Large-scale all-electron density functional theory calculations using an enriched finite element basis
• An efficient and accurate decomposition of the Fermi operator
• A subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization

Cited by in corpus (8)

• DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations
• DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization
• Large-scale all-electron density functional theory calculations using an enriched finite element basis
• Configurational forces in electronic structure calculations using Kohn-Sham density functional theory
• Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate
• Real-time time-dependent density functional theory using higher order finite element methods
• Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements
• Complexity Reduction in Density Functional Theory: Locality in Space and Energy