Related upper and lower bounds to atomic binding energies

The method proposed by Singh for the calculations of lower bounds to atomic binding energies has been generalized to encompass upper bounds as well. The result is a pair of related matrix eigenvalue problems, constructed from similar sets of basic matrix elements, with the solution of one yielding the tower bound, and of the other, the upper bound. The upper bounds are identical to those calculated by the Rayleigh–Ritz method, which can be useful when the inversion of the normalization matrix is ill‐conditioned. The lower bounds are comparable with the best available in the literature. © 1993 John Wiley & Sons, Inc.