ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Iterative methods for the calculation of the lowest eigenvalue and the corresponding eigenvector are derived from the partitioned Schrödinger equation in matrix form. While they have a formal similarity to the Brillouin-Wigner perturbation expansion, they converge for a much wider class of matrices. The double iteration methods (DIM and DIMA) lead to a series of upper and lower bounds to the desired lowest eigenvalue in accordance with Löwdin's bracketing theorem and can be used in a strategy which insures convergence to the solution for arbitrarily large perturbations. A much more efficient single iteration method (SIMA) produces the proper solution even for numerically very ill-conditioned matrices (large offdiagonal elements and small separation of the diagonal elements from the lowest). An important feature of the iterative methods is their insensitivity toward roundoff errors which makes them especially suited for very large matrices, where direct diagonalisation, for example by the Jacobi method, is impracticable.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560030510
