MODIFICATION OF THE DIIS METHOD FOR DIAGONALIZING LARGE MATRICES

The existing 'residual minimization/direct inversion in the iterative subspace' (DIIS) method for the iterative calculation of low-lying eig enstates of a large matrix is further developed and modified. The DIIs method, which uses the residual minimization criterion, may fail to p rovide correct low-lying eigenspectra in the case of ill-formed matric es, e.g. the momentum-space representation of Hamiltonian matrices of systems containing transition metal, rare earth, or first-row elements . We suggest the inclusion of another criterion-the vanishing of the o verlap integral of an iterative eigenvector with already obtained low- lying eigenvectors in order to prevent the eigenvector from collapsing to lower states. Two numerical examples of the success of our modifie d DIIS method in contrast to the failure of the conventional DIIs meth od are presented.