Efficient O($N$) divide-conquer method with localized natural orbitals

Abstract

An efficient O($N$) divide-conquer (DC) method based on localized natural orbitals (LNOs) is presented for large-scale density functional theories (DFT) calculations of gapped and metallic systems. The LNOs are non-iteratively calculated by a low-rank approximation via a local eigendecomposition of a projection operator for the occupied space. Introducing LNOs to represent the long range region of a truncated cluster reduces the computational cost of the DC method while keeping computational accuracy. A series of benchmark calculations and high parallel efficiency in a multilevel parallelization clearly demonstrate that the O($N$) method enables us to perform large-scale simulations for a wide variety of materials including metals with sufficient accuracy in accordance with development of massively parallel computers.

arXiv comment14 pages, 9 figures

References in corpus (14)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Maximally-localized generalized Wannier functions for composite energy bands
• Maximally localized Wannier functions: Theory and applications
• O(N) methods in electronic structure calculations
• Accurate and efficient linear scaling DFT calculations with universal applicability
• Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals
• Real-space electronic-structure calculations with timesaving double-grid technique
• Block bond-order potential as a convergent moments-based method
• Augmented orbital minimization method for linear scaling electronic structure calculations
• Stochastic linear scaling for metals and non metals
• Optimized multi-site local orbitals in the large-scale DFT program CONQUEST
• Efficient Calculations with Multisite Local Orbitals in the large-scale DFT Code CONQUEST
• Projection based embedding theory for solving Kohn-Sham density functional theory

Cited by in corpus (2)

• Large scale and linear scaling DFT with the CONQUEST code
• Electronic structures of crystalline and amorphous GeSe and GeSbTe compounds using machine learning empirical pseudopotentials