Sparse Projected-Gradient Method As a Linear-Scaling Low-Memory Alternative to Diagonalization in Self-Consistent Field Electronic Structure Calculations

Autor(es)

Birgin, Ernesto G. ^[1] ; Martinez, J. M. ^[2] ; Martinez, Leandro ^[3] ; Rocha, Gerd B. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Inst Math Stat & Sci Comp, Dept Appl Math, Campinas, SP - Brazil

^[3] Univ Estadual Campinas, Inst Chem, Campinas, SP - Brazil

^[4] Univ Fed Paraiba, Dept Chem, BR-58059900 Joao Pessoa, Paraiba - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF CHEMICAL THEORY AND COMPUTATION; v. 9, n. 2, p. 1043-1051, FEB 2013.
• Citações Web of Science: 10

Resumo

Large-scale electronic structure calculations usually involve huge nonlinear eigenvalue problems. A method for solving these problems without employing expensive eigenvalue decompositions of the Fock matrix is presented in this work. The sparsity of the input and output matrices is preserved at every iteration, and the memory required by the algorithm scales linearly with the number of atoms of the system. The algorithm is based on a projected gradient iteration applied to the constraint fulfillment problem. The computer time required by the algorithm also scales approximately linearly with the number of atoms (or non-null elements of the matrices), and the algorithm is faster than standard implementations of modern eigenvalue decomposition methods for sparse matrices containing more than 50 000 non-null elements. The new method reproduces the sequence of semiempirical SCF iterations obtained by standard eigenvalue decomposition algorithms to good precision. (AU)

• Processo FAPESP: 06/53768-0 - Métodos computacionais de otimização
• Beneficiário: José Mário Martinez Perez
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 10/16947-9 - Estrutura, dinâmica e função em proteínas: simulação computacional e desenvolvimento de algoritmos
• Beneficiário: Leandro Martinez
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 03/09169-6 - Desenvolvimento e aplicação de métodos numéricos para otimização contínua de grande porte
• Beneficiário: Ernesto Julián Goldberg Birgin
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 08/00468-4 - Sistemas KKT
• Beneficiário: Francisco Nogueira Calmon Sobral
• Linha de fomento: Bolsas no Brasil - Doutorado