Model Atomic Hamiltonians

• Published in: The Journal of chemical physics 1968-01, Vol.48 (8), p.3740-3750
• Main Authors: Piech, Kenneth R., Wilson, Kenneth G.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.1669680

A model Hamiltonian for the n = 1 and n = 2 states of the first- and second-row atoms is developed. The model is easily soluble and represents total and ionization energies reasonably well. The model is constructed on a cubic lattice space and is defined by five postulates. They are: (1) Each electron is confined to seven lattice sites: the origin and its six nearest-neighbor sites; (2) The form of the Hamiltonian is taken from the finite difference approximation to the exact Hamiltonian; (3) The parameters in the Hamiltonian are determined phenomenologically; (4) The parameters scale as simple functions of Z. The fifth postulate allows one to distinguish s states from p states in the spectra of the models. A matrix diagonalization problem results which is easily solved by perturbation expansion. The model is applied to the atoms H to B, together with associated isoelectronic sequences. Ionization energies are given to approximately 25%, and total energies to approximately 2%. The eigenfunctions of the model are of nonproduct form and demonstrate correlation effects. A simple approximation to the ground-state energies of H–Ne is developed, which involves a calculation of the minimum-energy electron configuration on the seven-point lattice, and which is accurate to approximately 3%. The model results are compared to previous semiempirical Z− i expansions of ground-state atomic energies. Implications of the model for the problem of complex molecules are discussed.