Systematic study of selected diagonalization methods for configuration interaction matrices

Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interact ion (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 t he 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-vecto r products (sigma (i)), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal-storage, single-vector me thod of Olsen is found to be a reasonable alternative for obtaining energie s of well-behaved systems to within muE(h) accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yiel d high accuracy (ca. 10(-10) E-h) for very large CI problems. Several appro ximations to the diagonal elements of the Cl Hamiltonian matrix are found t o allow simple on-the-fly computation of the preconditioning matrix, to mai ntain the spin symmetry of the determinant-based wave function, and to pres erve the convergence characteristics of the diagonalization procedure. (C) 2001 John Wiley & Sons, Inc.