Abstract
We present a tensor-structured algorithm for efficient large-scale density functional theory (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 L1 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 2000 electrons.
Highlights
Density functional theory (DFT) has been the workhorse of abinitio materials simulations for over three decades, providing many key insights into materials properties and materials behavior
In an attempt to enable DFT calculations on largescale systems that are critical to understanding many aspects of complex materials phenomena, many efforts over the past three decades have focused on developing reduced-order scaling algorithms for electronic structure calculations[3,4,5,6,7,8,9,10,11,12,13]
We have presented a tensor-structured algorithm, where the Tucker tensor basis is constructed as a tensor product of localized 1-D functions whose span closely approximates the eigensubspace of a suitably constructed additive separable approximation to the Kohn–Sham Hamiltonian
Summary
Density functional theory (DFT) has been the workhorse of abinitio materials simulations for over three decades, providing many key insights into materials properties and materials behavior. In an attempt to enable DFT calculations on largescale systems that are critical to understanding many aspects of complex materials phenomena, many efforts over the past three decades have focused on developing reduced-order scaling algorithms for electronic structure calculations[3,4,5,6,7,8,9,10,11,12,13] These approaches have either relied on a localized representation of the single-electron wavefunctions (such as Wannier functions5) or the exponential decay of the density-matrix in real-space, and have been demonstrated to provide close to linear-scaling complexity for materials with a gap. This translates to substantial speed-ups over Quantum Espresso (QE), a widely used state-of-the-art plane-wave DFT code[19,20], with speed-ups of ~8fold for metallic nano-particles containing ~2000 atoms
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