Sparse projected-gradient method as a linear-scaling low-memory alternative to diagonalization in self-consistent field electronic structure calculations

Journal of Chemical Theory and Computation

Volumn 9, Issue 2, 2013, Pages 1043-1051

  Birgin, Ernesto G ^a   Martinez J M ^b   Martínez, Leandro ^b   Rocha, Gerd B ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84873690392     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct3009683     Document Type: Article

References (49)

1. Helgaker, T.; Jorgensen, P.; Olsen, J. Molecular Electronic-Structure Theory; John Wiley & Sons: New York, 2000; pp 433-502.
2. Sánchez-Portal, D.; Ordejón, P.; Artacho, E.; Soler, J. M. Density-functional method for very large systems with LCAO basis sets Int. J. Quantum Chem. 1997, 65, 453-461 (Pubitemid 127616617)
3. Pople, J. A.; Headgordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. Gaussian-1 Theory-A general procedure for prediction of molecular energies J. Chem. Phys. 1989, 90, 5622-5629
4. Pariser, R.; Parr, R. G. A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsatured Molecules. II J. Chem. Phys. 1953, 21, 767-777
5. Pople, J. A.; Santry, D. P.; Segal, G. A. Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures J. Chem. Phys. 1965, 10, S129-S135
6. Francisco, J. B.; Martínez, J. M.; Martínez, L. Globally convergent trust-region methods for Self-Consistent Field electronic structure calculations J. Chem. Phys. 2004, 121, 10863-10878 (Pubitemid 40020627)
7. Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. LAPACK Users' Guide 3rd ed.; Society for Industrial and Applied Mathematics: Philadelphia, PA, 1999.
8. Lehoucq, R. B.; Sorensen, D. C.; Yang, C. ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods; Society for Industrial and Applied Mathematics: Philadelphia, PA, 1998.
9. Pulay, P. Convergence acceleration of iterative sequences: the case of SCF iteration Chem. Phys. Lett. 1980, 73, 393-398
10. Millam, J. M.; Scuseria, G. Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations J. Chem. Phys. 1997, 106, 5569-5577 (Pubitemid 127590352)
11. Daniels, A. D.; Scuseria, G. Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms J. Chem. Phys. 1997, 107, 425-431
12. Daniels, A. D.; Scuseria, G. What is the best alternative to diagonalization of the Hamiltonian in large scale semiempirical calculations? J. Chem. Phys. 1999, 110, 1321-1328 (Pubitemid 129614666)
13. Francisco, J. B.; Martínez, J. M.; Martínez, L. Density-based globally convergent trust-region method for Self-Consistent Field electronic structure calculations J. Math. Chem. 2006, 40, 349-377 (Pubitemid 44777562)
14. Thögersen, L.; Olsen, J.; Yeager, D.; Jörgensen, P.; Salek, P.; Helgaker, T. The trust-region self-consistent field method: Towards a black box optimization in Hartree-Fock and Kohn-Sham theories J. Chem. Phys. 2004, 121, 16-27
15. Thögersen, L.; Olsen, J.; Köhn, A.; Jörgensen, P.; Salek, P.; Helgaker, T. The trust-region self-consistent field method in Kohn-Sham density-functional theory J. Chem. Phys. 2005, 123, 1-17
16. Yang, C.; Meza, J. C.; Lee, B.; Wang, L.-W. KSSSOLV - a MATLAB toolbox for solving the Kohn - Sham equations ACM Trans. Math. Softw. 2009, 36, 1-35
17. Yang, C.; Meza, J. C.; Wang, L.-W. A constrained optimization algorithm for total energy minimization in electronic structure calculations J. Comput. Phys. 2006, 217, 709-721 (Pubitemid 44340994)
18. Yang, C.; Meza, J. C.; Wang, L.-W. A trust region direct constrained optimization algorithm for the Kohn-Sham equation SIAM J. Sci. Comput. 2007, 29, 1854-1875
19. Darve, E. The Fast Multipole Method: Numerical Implementation J. Comput. Phys. 2000, 160, 195-240
20. Li, X.; Moss, C. L.; Liang, W.; Feng, Y. Carr-Parrinello density matrix search with a first principles fictitious electron mass method for electronic wave function optimization J. Chem. Phys. 2009, 130, 234115
21. Li, X.-P.; Nunes, R. W.; Vanderbilt, D. Density-matrix electronic-structure method with linear system-size scaling Phys. Rev. B 1993, 47, 10891-10894
22. Rubensson, E. H.; Zahedi, S. Computation of interior eigenvalues in electronic structure calculations facilitated by density matrix purification J. Chem. Phys. 2008, 128, 176101
23. Rubensson, E. H.; Rudberg, E.; Salek, P. Density matrix purification with rigorous error control J. Chem. Phys. 2008, 128, 074106
24. Barrault, M.; Cancès, E.; Hager, W. W.; Le Bris, C. Multilevel domain decomposition for electronic structure calculations J. Comput. Phys. 2007, 222, 86-109
25. Goedecker, S. Linear scaling electronic structure methods Rev. Mod. Phys. 1999, 71, 1085-1123 (Pubitemid 129336905)
26. Szekeres, Z.; Mezey, P. G. Fragmentation selection strategies in linear scaling methods. In Linear-Scaling Techniques in Computational Chemistry and Physics, 1st ed.; Zaleny, R.; Papadopoulus, M. G.; Mezey, P. G.; Leszczynski, J., Eds.; Springer: New York, 2011; pp 147-156.
27. Stewart, J. J. P. Application of Localized Molecular Orbitals to the Solution of Semiempirical Self-Consistent Field Equations Int. J. Quantum Chem. 1996, 58, 139-146
28. Anikin, N. A.; Anisimov, V. M.; Bugaenko, V. L.; Bobrikov, V. V.; Andreyev, A. M. LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules J. Chem. Phys. 2004, 121, 1266-1270
29. Ordejón, P.; Artacho, E.; Soler, J. M. Self-consistent order-N density-functional calculations for very large systems Phys. Rev. B 1996, 53, 10441-10444
30. McWeeny, R. Some Recent Advances in Density Matrix Theory Rev. Mod. Phys. 1960, 32, 335-369
31. Palser, A. H. R.; Manolopoulos, D. E. Canonical purification of the density matrix in electronic structure theory Phys. Rev. B 1998, 58, 12704-12711 (Pubitemid 128655048)
32. Rudberg, E.; Rubensson, E. H.; Salek, P. Hartree-Fock calculations with linearly scaling memory usage J. Chem. Phys. 2008, 128, 184106
33. Rubensson, E. H.; Rudberg, E. Bringing about matrix sparsity in linear-scaling electronic structure calculations J. Comput. Chem. 2011, 32, 1411-1423
34. Rudberg, E.; Rubensson, E. H.; Salek, P. Kohn-Sham Density Functional Theory Electronic Structure Calculations with Linearly Scaling Computational Time and Memory Usage J. Chem. Theory Comput. 2011, 7, 340-350
35. Rubensson, E. H. Nonmonotonic Recursive Polynomial Expansions for Linear Scaling Calculation of the Density Matrix J. Chem. Theory Comput. 2011, 7, 1233-1236
36. Figueiredo, M. A.; Nowak, R. D.; Wright, S. J. Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems IEEE J. Sel. Top. Signal Proc. 2007, 1, 586-597 (Pubitemid 351276802)
37. Birgin, E. G.; Martínez, J. M.; Raydan, M.. Spectral Projected Gradient Methods. In Encyclopedia of Optimization, 2 nd ed.; Floudas, C. A.; Pardalos, P. M., Eds.; Springer: New York, 2009; pp 3652-3659.
38. Birgin, E. G.; Martínez, J. M.; Raydan, M. Nonmonotone spectral projected gradient methods on convex sets SIAM J. Optim. 2000, 10, 1196-1211
39. Birgin, E. G.; Martínez, J. M.; Raydan, M. Algorithm 813: SPG- Software for convex-constrained optimization ACM Trans. Math. Soft. 2001, 27, 340-349 (Pubitemid 33654982)
40. Birgin, E. G.; Martínez, J. M.; Raydan, M. Inexact Spectral Projected Gradient methods on convex sets IMA J. Num. Analys. 2003, 23, 539-559 (Pubitemid 37445929)
41. Griewank, A.; Walther, A. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Society for Industrial and Applied Mathematics: Philadelphia, PA, 2008, pp 37-65.
42. Francisco, J. B.; Martínez, J. M.; Martínez, L.; Pisnitchenko, F. I. Inexact Restoration method for minimization problems arising in electronic structure calculations Comput. Optim. Appl. 2011, 50, 555-590
43. Golub, G. H.; Van Loan, C. Matrix Computations; Johns Hopkins: Baltimore, MA, 1996.
44. Stewart, J. J. P. MOPAC2009, version 10.060W; Stewart Computational Chemistry: Colorado Springs, CO, 2009.
45. Rocha, G. B.; Freire, R. O.; Simas, A. M.; Stewart, J. J. P. A Reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I J. Comput. Chem. 2006, 27, 1101-1111
46. Martínez, J. M.; Martínez, L. Packing optimization for the automated generation of complex system's initial configurations for molecular dynamics and docking J. Comput. Chem. 2003, 24, 819-825
47. Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. Packmol: A package for building initial configurations for molecular dynamics simulations J. Comput. Chem. 2009, 30, 2157-2164
48. Maia, J. D. C.; Carvalho, G. A. U.; Mangueira, C. P., Jr.; Santana, S. R.; Cabral, L. A. F.; Rocha, G. B. GPU Linear Algebra Libraries and GPGPU Programming for Accelerating MOPAC Semiempirical Quantum Chemistry Calculations J. Chem. Theory Comput. 2012, 8, 3072-3081
49. Le Bris, C. Computational chemistry from the perspective of numerical analysis Acta Numer. 2005, 14, 363-444 (Pubitemid 40763886)