Modified configuration-interaction method

A detailed presentation of the modified configuration-interaction (CI) method [S. P. Goldman, Phys. Rev. Lett. 73, 2541 (1994)] is given. The standard two-electron test case is used to introduce the concepts, as well as to show a sharp increase in the convergence of the calculations. Space-ordered radial coordinates and generalized angular functions involving the addition of large numbers of spherical harmonics are used. As a result, accuracies that exceed those of the usual CI method by several orders of magnitude are obtained with small basis sets. For example, in the case of helium, energies are obtained with relative errors of 2.6×{}10^-9, 1.4×{}10^-8, and 2.0×{}10^-10 for the 1¹S, 2¹S, and 2³S states with 420, 276, and 264 two-electron basis functions, respectively. A detailed discussion of the calculation of matrix elements and angular coefficients and of the extension to the many-electron case is presented.