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 the 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 the total energy is substantially greater than in the low-correlation case. Hence, we propose 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 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 approximate energy functionals valid for the Wigner regime.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 the 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 the total energy is substantially greater than in the low-correlation case. Hence, we propose 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 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 approximate energy functionals valid for the Wigner regime.

Jan 1, 20150 citations

Dynamical Correlation of Electrons in Two-Dimensions

Sadhana R. Sharma

Jan 1, 19820 citations

Electron Correlations in Two Dimensions

K. W. Becker, Peter Fulde

Physics of Low-Dimensional SystemsJul 1, 19890 citations

Wigner high-electron-correlation regime of nonuniform density systems: A quantal-density-functional-theory study

Douglas Achan, Lou Massa, Viraht Sahni

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, we propose 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.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, we propose 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.

Physical Review AAug 8, 201417 citations

Correlation Energy in Solids

Norman Henry March

Springer eBooksJan 1, 19781 citation

Effect of core-valence electron correlation in low-energy electron scattering with Ca atoms

Jianmin Yuan, C. D. Lin

$R$ -matrix calculations have been carried out to investigate the effect of core-valence electron correlation on the scattering of electrons with Ca atoms at low energies. While the major feature of the $d$ -wave shape resonance with a peak near 1.3 eV in the total cross section can be reproduced by including only the correlation among the valence electrons, we show that the existence of a low-energy peak near 0.15 eV, which has also been observed experimentally, can be obtained only if the correlations between the valence and core electrons are considered. This low-energy peak is shown not caused by a shape resonance, but rather due to the rapid decrease of the $s$ - and $p$ -wave phase shifts with collision energies. The present result also indirectly supports the previous conclusion that core-valence electron correlation is responsible for bringing the electron affinity of ${\mathrm{Ca}}^{\ensuremath{-}}$ from 72 to 15 meV, i.e., to a value which is much closer to the experiment.$R$-matrix calculations have been carried out to investigate the effect of core-valence electron correlation on the scattering of electrons with Ca atoms at low energies. While the major feature of the $d$-wave shape resonance with a peak near 1.3 eV in the total cross section can be reproduced by including only the correlation among the valence electrons, we show that the existence of a low-energy peak near 0.15 eV, which has also been observed experimentally, can be obtained only if the correlations between the valence and core electrons are considered. This low-energy peak is shown not caused by a shape resonance, but rather due to the rapid decrease of the $s$- and $p$-wave phase shifts with collision energies. The present result also indirectly supports the previous conclusion that core-valence electron correlation is responsible for bringing the electron affinity of ${\mathrm{Ca}}^{\ensuremath{-}}$ from 72 to 15 meV, i.e., to a value which is much closer to the experiment.

Physical Review AOct 1, 199814 citations

R

-matrix calculations have been carried out to investigate the effect of core-valence electron correlation on the scattering of electrons with Ca atoms at low energies. While the major feature of the

d

-wave shape resonance with a peak near 1.3 eV in the total cross section can be reproduced by including only the correlation among the valence electrons, we show that the existence of a low-energy peak near 0.15 eV, which has also been observed experimentally, can be obtained only if the correlations between the valence and core electrons are considered. This low-energy peak is shown not caused by a shape resonance, but rather due to the rapid decrease of the

s

- and

p

-wave phase shifts with collision energies. The present result also indirectly supports the previous conclusion that core-valence electron correlation is responsible for bringing the electron affinity of ${\mathrm{Ca}}^{\ensuremath{-}}$ from 72 to 15 meV, i.e., to a value which is much closer to the experiment.