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Systematic study of selected diagonalization methods for configuration interaction matrices
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DOI：10.1002/jcc.1111.abs.png)
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Abstract
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Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (Cl) computations. The combination of a generalized Davidson method, a periodic two-vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large-scale CI matrices by eliminating the need to ever store more than three expansion vectors (b(i)) and associated matrix-vector products (sigma (i)), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal-storage, single-vector method of Olsen is found to be a reasonable alternative for obtaining energies of well-behaved systems to within muE(h) accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10(-10) E-h) for very large CI problems. Several approximations to the diagonal elements of the Cl Hamiltonian matrix are found to allow simple on-the-fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant-based wave function, and to preserve the convergence characteristics of the diagonalization procedure. (C) 2001 John Wiley & Sons, Inc.
Keywords:
configuration interaction
diagonalization methods
Davidson method
ab inito methods
symmetric eigenvalue problem
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