Fast diagonalisation of nonlocal pseudopotential Hamiltonians
- 1 January 1989
- journal article
- Published by IOP Publishing in Journal of Physics: Condensed Matter
- Vol. 1 (3) , 525-540
- https://doi.org/10.1088/0953-8984/1/3/004
Abstract
The calculation of band structure and total energy of solids involves the search for the few lowest (M) eigenvectors and eigenvalues of large matrices (size N × N). Standard algorithms which diagonalise the matrix entirely scale as N3, while procedures for extracting only a subset of M eigenvalues and eigenvectors scale as MN2. Two methods are described which aim at finding the lowest eigenvalues and corresponding eigenvectors of a nonlocal pseudopotential Hamiltonian. Both approaches lead to an algorithm which scales roughly as MN4/3.Keywords
This publication has 32 references indexed in Scilit:
- Ab initiocalculations of bismuth properties, including spin–orbit couplingPhysica Scripta, 1988
- Structural, Dymanical, and Electronic Properties of Amorphous Silicon: Anab initioMolecular-Dynamics StudyPhysical Review Letters, 1988
- Elastic Constants of Crystals from Linear-Response TheoryPhysical Review Letters, 1987
- Nonlocal pseudopotentials in molecular-dynamical density-functional theory: Application toPhysical Review Letters, 1987
- Predicting New Solids and SuperconductorsScience, 1986
- Unified Approach for Molecular Dynamics and Density-Functional TheoryPhysical Review Letters, 1985
- Pseudopotentials that work: From H to PuPhysical Review B, 1982
- Relativistic norm-conserving pseudopotentialsPhysical Review B, 1982
- Ground State of the Electron Gas by a Stochastic MethodPhysical Review Letters, 1980
- The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matricesJournal of Computational Physics, 1975