Towards a potential-based conjugate gradient algorithm for order-N self-consistent total energy calculations

The determination of the total energy within density-functional theory can be formulated as a minimization problem in a space of trial self-consistent potentials. In order to apply a conjugate-gradient algorithm to this problem, a formula for the computation of the gradient of the energy with respect to the self-consistent potential is proposed. The second derivative of the energy with respect to potential changes is also analyzed, in order to obtain an efficient preconditioning operator. The wave functions do not appear explicitly in this approach, so that order-N algorithms could take advantage of it. The results of preliminary tests are reported. © 1996 The American Physical Society.