Nonlocal Wigner-like correlation energy density functional: parametrization and tests on two-electron systems

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Wigner's correlation energy density functional requires specific reparametrization for different systems.
• Helium and Hooke's atom isoelectronic sequences necessitate distinct functional adjustments.

Purpose of the Study:

• To develop a universal density functional parametrization.
• To avoid reparametrization for different one-body potentials.
• To improve the nonlocal dependence of density functionals.

Main Methods:

• Proposed a novel parametrization for correlation energy density functional.
• Utilized scale-invariant combinations of expectation values of local one-body operators.
• Tested on two-electron systems with potentials r(zeta), where zeta ranges from -1/2 to 2.

Main Results:

• The new parametrization closely fits correlation energies for the helium isoelectronic sequence.
• A different parametrization was needed for Hooke's atom isoelectronic sequence with the original functional.
• Encouraging results were obtained for two-electron systems across a range of potentials.

Conclusions:

• The proposed parametrization offers a potentially more effective way to incorporate nonlocal density dependence.
• This method provides an alternative to the density-gradient paradigm.
• The approach shows promise for systems with varying one-body potentials.