On the computation of large-scale self-consistent-field iterations

• Published in: Journal of mathematical chemistry Vol. 55; no. 5; pp. 1158 - 1172
• Main Authors: Gomes, F. M., Martínez, J. M., Raydan, M.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.05.2017; Springer Nature B.V
• Subjects: Chemistry; Chemistry and Materials Science; Computation; Consolidation; Eigenvalues; Eigenvectors; Electronic structure; Iterative methods; Linear algebra; Math. Applications in Chemistry; Matrix methods; Original Paper; Physical Chemistry; Theoretical and Computational Chemistry; Subspace projection matrix; Large-scale eigenvalue calculations; Electronic structure calculations
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-017-0731-2

The computation of the subspace spanned by the eigenvectors associated to the N lowest eigenvalues of a large symmetric matrix (or, equivalently, the projection matrix onto that subspace) is a difficult numerical linear algebra problem when the dimensions involved are very large. These problems appear when one employs the self-consistent-field fixed-point algorithm or its variations for electronic structure calculations, which requires repeated solutions of the problem for different data, in an iterative context. The naive use of consolidated packages as Arpack does not lead to practical solutions in large-scale cases. In this paper we combine and enhance well-known purification iterative schemes with a specialized use of Arpack (or any other eigen-package) to address these large-scale challenging problems.