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 interaction (CI) 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 (bi) and associated matrix-vector products (σ 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 μEh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10−10 Eh) for very large CI problems. Several approximations to the diagonal elements of the CI 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. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574–1589, 2001