Tensor-structured algorithm for reduced-order scaling large-scale Kohn-Sham density functional theory calculations

Abstract

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn-Sham Hamiltonian and an $L_1$ localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2,000 electrons.

References in corpus (8)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• O(N) methods in electronic structure calculations
• Total energy global optimizations using non orthogonal localized orbitals
• Compressed Modes for Variational Problems in Mathematics and Physics
• DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations
• Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
• Parallel Tensor Compression for Large-Scale Scientific Data
• A subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization