Efficient Methods for Dynamic Correlation in Atoms

An algorithm for large-scale correlated calculations on atoms is presented that significantly reduces the scaling of these calculations with the number of single-particle functions used to construct the N-particle states. The reduction is provided in the stage in which the Hamiltonian matrix is contracted with the coefficients or amplitudes of the basis states in an iterative procedure such as the Davidson method. The algorithm relies on the representation of the radial one-particle functions on a grid, and it makes use of the multipole expansion of the electron–electron interaction in a sequence of transformations on the spinors, coefficients, and potentials. It also uses prototyping for the angular integrals and evaluation of recoupling coefficients for the configuration state functions (CSFs) separately rather than for pairs of CSFs. The scaling is verified with calculations on two-electron atoms and analyzed in terms of the number of operations required for each stage of both the proposed algorithm and the conventional methods.