Jan Linderberg

Electronic correlation energy in 3- and 4-electron atoms☆

The electronic correlation energy in 3- and 4-electron atomic systems is compared to previously well established correlation energies in 2-electron atoms. It is shown that the distribution of correlation energy in the K shell of these atoms between radial and angular correlation parallels that of the 2-electron system very closely. It is found, however, that the correlation in the L shell of the Be ground state is almost purely angular correlation energy. There is negligible correlation energy associated with K-L interaction. Analysis of the Z dependence of the correlation energy of 4 electron atoms shows a term linear in Z. It is suggested that this term arises from degeneracies existing in the limit of infinite Z, and a tabulation of states expected to have this property is given. The analysis suggests a convenient scheme for constructing a semiempirical method for estimating atomic energies rather accurately. It is pointed out that a similar analysis for molecules in terms of the internuclear parameters suggests there may be inherent difficulties in constructing such a scheme for the molecular case. (auth)

Approximate Natural Orbitals for Four‐Electron Systems

Approximate natural orbitals for four‐electron wavefunctions for Be as calculated by Boys, Matsen, Watson, and Weiss and LiH as calculated by Ebbing are obtained by diagonalization of the appropriate first‐order reduced density matrices. The formalism for carrying out the process is extended to the case of a nonorthogonal basis. Occupation numbers are presented and compared for the functions reported. In addition, truncated natural expansions reproducing the original functions are tabulated. Natural‐orbital functions are tabulated. Natural‐orbital occupation numbers, the orbitals themselves, and the natural expansions are shown to have considerable value in comparing these functions. The nature of the approximations used in the individual functions is clarified by the analysis, and considerable insight is afforded to the nature of the physical system.

Correlation effects in the band structure of graphite

Abstract Dynamical electronic correlation is investigated for graphite layers in a tight-binding model suggested by Hubbard. Changes in the density of states are small but the damping of quasi-particle states is considerable.

Doubly excited states and natural orbitals in the study of atoms by perturbation theory

Abstract Calculations have been carried out on K -shell second-order energy shifts in perturbation theory by means of a natural orbital expansion method. Results show that rapidly convergent expansions are obtained, where each additional term accounts for at least 75% of remaining energy error.