Computing the Self-Consistent Field in Kohn-Sham Density Functional Theory

Abstract

A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory. The aims of this work are two-fold. First, we explore the properties of Kohn-Sham density functional theory as it pertains to the convergence of self-consistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the \textsc{scf}-$x_n$ suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner.

References in corpus (20)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Perspective on density functional theory
• Ab initio Random Structure Searching
• Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals
• O(N) methods in electronic structure calculations
• Ensemble density-functional theory for ab-initio molecular dynamics of metals and finite-temperature insulators
• GW method with the self-consistent Sternheimer equation
• The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
• A time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities
• A density functional study of lithium bulk and surfaces
• Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations
• C2x: a tool for visualisation and input preparation for Castep and other electronic structure codes
• N-representability of two-electron densities and density matrices and the application to the few-body problem
• Robust Mixing for Ab-Initio Quantum Mechanical Calculations
• Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity
• An Efficient and Robust Technique for Achieving Self Consistency in Electronic Structure Calculations
• Applicability of Kerker preconditioning scheme to the self-consistent density functional theory calculations of inhomogeneous systems
• A rapidly converging algorithm for solving the Kohn-Sham and related equations in electronic structure theory
• On the equivalence of LIST and DIIS methods for convergence acceleration
• Symmetry breaking in the self-consistent Kohn-Sham equations

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• Convolutional network learning of self-consistent electron density via grid-projected atomic fingerprints
• Variational Polaron Equations Applied to the Anisotropic Fröhlich Model
• A robust and efficient line search for self-consistent field iterations
• Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low rank approximation of the dielectric matrix
• Rigorous body-order approximations of an electronic structure potential energy landscape
• Exact static linear response of excited states from ensemble density functional theory
• Multipolar Fermi-surface deformation in a Rydberg-dressed Fermi gas with long-range anisotropic interactions
• Crystalline Solutions of Kohn-Sham Equations in the Fractional Quantum Hall Regime
• Variational first-principles approach to self-trapped polarons
• Convergence analysis of direct minimization and self-consistent iterations
• Quantum-Enhanced Neural Exchange-Correlation Functionals
• Resta-like preconditioning for self-consistent field iterations in the linearized augmented planewave method