Treecode-accelerated Green iteration for Kohn-Sham density functional theory

We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on a reformulation of the Kohn-Sham equations in which the eigenvalue problem in differential form is converted into a fixed-point problem in integral form by convolution with the modified Helmholtz Green's function. In each self-consistent field (SCF) iteration, the fixed-points are computed by Green Iteration, where the discrete convolution sums are efficiently evaluated by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in TAGI include a-priori adaptive mesh refinement, Fejer quadrature, singularity subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate convergence of the SCF and Green Iterations. Ground state energy computations of several atoms (Li, Be, O) and small molecules (H-2, CO, C6H6) demonstrate TAGI's ability to efficiently achieve chemical accuracy. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

TAGI is a real-space computational method for all-electron Kohn-Sham Density Functional Theory that uses specialized Green Iteration and treecode acceleration to speed up convergence, with various techniques to improve efficiency and accuracy in energy calculations for atoms and small molecules.