In the introductory section, we compare the total, kinetic, nuclearแelectron, Coulomb, exchange, and correlation energies of ground-state atoms.
ลฝ . From the analyses of the data, one can conclude that the HartreeแFock HF model is notably good and might require only a small perturbation 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 perturbation on the kinetic, the nuclearแelectron, or the Coulomb HF operators. The perturbations are expressed as very simple functions of products of orbital probability density. The three perturbations yield very equivalent results and the computed ground-state energies are reasonably near to the accurate nonrelativistic energies recently provided by E. Davidson and his collaborators for the 2แ18 electron systems and the estimates by Clementi and his collaborators for the 19แ54 electron systems. The first ionization potentials from He to Cs, the second ionization potentials from Li to Zn, and excitation energies for np n , 3d n , and 4 s 1 3d n configurations are used as additional verification and validation. The above three effective Hamiltonians are then combined in order to redistribute the correlation energy correction in a way which exactly satisfies the virial theorem and maintains the HF energy ratios between kinetic, nuclearแelectron, and electronแelectron interaction energies; the resulting effective Hamiltonian, named '' virial constrained,'' yields good quality data comparable to those obtained from the three independent effective operators. Concerning excitation energies, these effective Hamiltonians yield values only in modest agreement with experimental data, even if definitively superior to HF computations. To further improve the computed excitation energies, we applied an empirical scaling in the vector coupling coefficient; this correction yields very reasonable excitations for all the configurations that we have considered. We conclude that the use of effective potentials to introduce small perturbations density-dependent onto the HF model constitutes a broad class of practical and reliable semiempirical solutions to atomic many-electron problems, can provide an alternative to popular proposals from density functional theory, and should prepare the ground for ''generalized HF models. '' แฎ 1997