NOTE ON THE ATOMIC CORRELATION-ENERGY

In the introductory section, we compare the total, kinetic, nuclear-el ectron, Coulomb, exchange, and correlation energies of ground-state at oms. From the analyses of the data, one can conclude that the Hartree- Fock (HF) model is notably good and might require only a small perturb ation to become essentially an ''accurate'' model. For this reason and considering past literature, we present a semiempirical extension of the HF model. We start with a calibration of three independent models, each one with an effective Hamiltonian, which introduces a small pert urbation on the kinetic, the nuclear-electron, or the Coulomb HF opera tors. The perturbations are expressed as very simple functions of prod ucts of orbital probability density. The three perturbations yield ver y equivalent results and the computed ground-state energies are reason ably near to the accurate nonrelativistic energies recently provided b y E. Davidson and his collaborators for the 2-18 electron systems and the estimates by Clementi and his collaborators for the 19-54 electron systems. The first ionization potentials from He to Cs, the second io nization potentials from Li to Zn, and excitation energies for np(n), 3d(n), and 4s(1)3d(n) configurations are used as additional verificati on and validation. The above three effective Hamiltonians are then com bined in order to redistribute the correlation energy correction in a way which exactly satisfies the virial theorem and maintains the HF en ergy ratios between kinetic, nuclear-electron, and electron-electron i nteraction energies; the resulting effective Hamiltonian, named ''viri al constrained,'' yields good quality data comparable to those obtaine d from the three independent effective operators. Concerning excitatio n energies, these effective Hamiltonians yield values only in modest a greement with experimental data, even if definitively superior to HF c omputations. To further improve the computed excitation energies, we a pplied an empirical scaling in the vector coupling coefficient; this c orrection yields very reasonable excitations for all the configuration s that we have considered. We conclude that the use of effective poten tials to introduce small perturbations density-dependent onto the HF m odel constitutes a broad class of practical and reliable semiempirical solutions to atomic many-electron problems, can provide an alternativ e to popular proposals from density functional theory, and should prep are the ground for ''generalized HF models.'' (C) 1997 John Wiley & So ns, Inc.