## Dissertations, Theses, and Capstone Projects

#### Date of Degree

2-2015

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Program

Chemistry

#### Advisor

Louis J. Massa

#### Advisor

Viraht Sahni

#### Subject Categories

Physical Chemistry | Physics

#### Keywords

correlation-kinetic effects, correlation-kinetic energy, nonuniform density systems, quantal density functional theory, spectral methods, Wigner high electron correlation regime

#### Abstract

The Wigner regime of a system of electrons in an external ﬁeld is characterized by a low electron density and a high electron-interaction energy relative to the kinetic energy. The low correlation regime is in turn described by a high electron density and an electron-interaction energy smaller than the kinetic energy. The Wigner regime of a nonuniform electron density system is investigated via quantal density functional theory (QDFT). Within QDFT, the contributions of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic eﬀects are separately delineated and explicitly deﬁned. The nonuniform electron density system studied is that of Hooke's atom in the Wigner regime for which the exact wave function is derived. As such the results of the QDFT analysis are exact. It is observed that in comparison to the low correlation case, not only is the electron-interaction energy greater than the kinetic energy as a fraction of the total energy, but so are its individual Hartree, Pauli, and Coulomb components. The ionization potential as a fraction of the total energy too is greater. But most signiﬁcantly, in the Wigner regime, the correlation-kinetic energy as a fraction of both the electron-interaction and total energy is substantially greater than in the low correlation case. Hence, it is proposed that the Wigner regime now also be characterized by a high correlation-kinetic energy. The kinetic energy as a fraction of the total energy, however, is less than in the low correlation case. This fact and the high correlation-kinetic energy value in the Wigner regime is explained by the new concept of 'quantal compression' of the kinetic energy density derived from QDFT. The corresponding results for the low correlation case are in turn a consequence of a 'quantal decompression' of the kinetic energy density. From the QDFT analysis, the exact values for the Kohn-Sham theory 'exchange-correlation' and 'correlation' energy functionals of the density, and their respective functional derivatives are also obtained. These results ought to be of value in the construction and testing of new approximate energy functionals valid for the Wigner regime.

#### Recommended Citation

Achan, Douglas Mortimer, "Wigner High-Electron-Correlation Regime Of Non-Uniform Density Systems: A Quantal-Density-Functional-Theory Study" (2015). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/514