Efficient O( N ) divide-conquer method with localized single-particle 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.

Large scale and linear scaling DFT with the CONQUEST code

“…Both the three-layer and six-layer cores expand, and the expansion is largely isotropic, particularly in comparison to the shell. This is in agreement with previous theoretical and experimental work [9,39], in which the Si core is found to be under tensile strain.…”

“…Although we do not treat the ion permeation directly in this study, it is important to note the experimental result that the rate of the ion permeation is significantly changed by the replacement of the tryptophan (Trp) residues, which have dipole moments (approx. 2D), with other residues [6,[8][9][10]. When it is replaced with non-polar phenylalanine, the ion permeation rate is greatly reduced.…”

“…However, efficient use of systems of this size requires care to ensure that the parallel scaling of any given code remains efficient as the number of cores becomes large. A real-space formulation, and the use of local basis functions to represent the Kohn-Sham (KS) eigenstates, can help with the parallel efficiency of the code, and enables calculations on larger systems, often with several thousand atoms [2][3][4][5][6][7][8][9][10]. Moreover, there is no inherent reason why DFT implementations should scale with the cube of the system size [11]; in fact, with local basis functions, DFT can be formulated in a linear scaling approach [12,13].…”

Landing Proteins on Graphene Trampoline Preserves Their Gas-Phase Folding on the Surface

“…Our calculations employed a cutoff energy of 300 Ry, an electronic temperature of 300 K, and a supercell with dimensions of 51.33 Å ( X axis), 49.39 Å ( Y axis), and 50.00 Å ( Z axis). All calculations sampled only the gamma point of the k -mesh and used an electronic convergence criterion of 4 × 10 –8 hartree, employing the divide-conquer with localized natural orbitals (DC-LNO) method . The graphene was modeled by 960 C atoms, and the cyt c was modeled with a total of 1744 atoms as C 558 H 878 O 155 N 148 FeS 4 .…”

“…All calculations sampled only the gamma point of the k-mesh and used an electronic convergence criterion of 4 × 10 −8 hartree, employing the divide-conquer with localized natural orbitals (DC-LNO) method. 73 The graphene was modeled by 960 C atoms, and the cyt c was modeled with a total of 1744 atoms as C 558 H 878 O 155 N 148 FeS 4 . The relaxation calculations were performed until the forces in all atoms were below 4 × 10 −4 hartree/bohr.…”