#### Date of Award

1981

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Abstract

The correlation energy of an unpolarized relativistic electron gas is numerically calculated by summing ring diagrams due to both the longitudinal and transverse photon contributions. From this a local relativistic correlation potential is deduced which appears in the density functional theory of inhomogeneous systems where relativistic effects make important contributions. The non-relativistic gas results are found to be significant underestimates. A fitted form of the correlation energy and potential were used in a self-consistent calculation of energies of atoms of large Z. Trends of the correlation contribution across the periodic table are evaluated and discussed. Correlation contributions to the K(alpha)(,1) and K(alpha)(,2) lines are compared to the differences between accurate computations, without correlation, and experimental values. The role of the Breit interaction in a local approximation is evaluated through self-consistent atomic calculations. It is found that the full transverse interaction is underestimated by about an atomic unit in the systems investigated. Comparison with previous non-local Dirac-Fock calculations indicate that non-local effects may be important. The problem of the relativistic spin polarized electron gas is considered. The Green function is deduced and used to calculate the particle density, magnetization, exchange energy and potentials. In the ultrarelativistic limit the magnetization is found to be one-third its non-relativistic value. States of uniform magnetization do not appear as ground states in the Hartree-Fock approximation. The exchange energy is found to change sign over a range of values of the relativistic parameter (beta)(=(H/2PI)k(,F)/mc) and magnetization. Effective one particle equations for the inhomogeneous polarized gas are given. The effective one particle potentials that appear in this equation are calculated in a local density scheme and their significance discussed.

#### Recommended Citation

Ramana, Munagala Venkata, "Inhomogeneous Relativistic Electron Systems: a Density Functional Formalism." (1981). *LSU Historical Dissertations and Theses*. 3652.

https://digitalcommons.lsu.edu/gradschool_disstheses/3652

#### Pages

144

#### DOI

10.31390/gradschool_disstheses.3652