Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices. (English) Zbl 0766.65037
The configuration interaction method is used to calculate electronic wavefunctions for the ground state and excited states of atoms and molecules. It leads to the formation of a large, real, symmetric matrix for which the lowest eigenvalues and associated eigenvectors must be found. The Davidson algorithm is the most widely used approach for matrices of this type. A number of improvements to the usual implementation of that algorithm are discussed and some results are presented.
The quasi degenerate variational perturbation theory, which is an alternative method for calculating electronic wavefunctions, is also considered. The similarities and differences between this approach and the Davidson algorithm are discussed. Some results that compare the performance of the two algorithms for similar matrices are given.
The quasi degenerate variational perturbation theory, which is an alternative method for calculating electronic wavefunctions, is also considered. The similarities and differences between this approach and the Davidson algorithm are discussed. Some results that compare the performance of the two algorithms for similar matrices are given.
Reviewer: Z.Dżygadło (Warszawa)
MSC:
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
Keywords:
configuration interaction method; electronic wavefunctions; large, real, symmetric matrix; lowest eigenvalues; eigenvectors; Davidson algorithm; quasi degenerate variational perturbation theory; performanceReferences:
| [1] | Roos, B. O., Chem. Phys. Lett., 15, 153 (1972) |
| [2] | Olsen, J.; Jørgensen, P.; Simons, J., Chem. Phys. Lett., 169, 463 (1990) |
| [3] | Davidson, E. R., (Diercksen, G. H.F.; Wilson, S., Methods in Computational Molecular Physics (1983), Reidel: Reidel Dordrecht) |
| [4] | Cave, R. J.; Davidson, E. R., J. Chem. Phys., 89, 6798 (1988) |
| [5] | Morgan, R. B.; Scott, D. S., SIAM J. Sci. Stat. Comput., 7, 817 (1986) · Zbl 0602.65020 |
| [6] | Lanczos, C., J. Res. Nat. Bur. Stand., 45, 255 (1950) |
| [7] | Liu, B., Numerical Algorithms in Chemistry: Algebraic Methods, (Moler, C.; Shavitt, I., LBL-8158 (1978), Lawrence Berkeley Laboratory: Lawrence Berkeley Laboratory Livermore, CA) |
| [8] | Butscher, W.; Kammer, W. J.E., J. Comput. Phys., 20, 13 (1976) |
| [9] | van Lenthe, J. H.; Pulay, P., J. Comput. Chem., 11, 1164 (1990) |
| [10] | Hestenes, M. R.; Stiefel, E., J. Res. Nat. Bur. Stand., 49, 498 (1952) |
| [11] | Wormer, P. E.S.; Visser, F.; Paldus, J., J. Comput. Phys., 48, 23 (1982) · Zbl 0492.65019 |
| [12] | Feler, M. G., J. Comput. Phys., 14, 341 (1974) · Zbl 0285.65026 |
| [13] | Wood, D. M.; Zunger, A., J. Phys. A, 18, 1343 (1985) · Zbl 0615.65043 |
| [14] | Ahlrichs, R.; Scharf, P., (Lawley, K. P., Ab Initio Methods in Quantum Chemistry I (1987), Wiley: Wiley Chichester) |
| [15] | Ahlrichs, R., Comput. Phys. Commun., 17, 31 (1979) |
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