Levy-Perdew-Sahni equation and its application to perform atomic calculations

Area of Science:

• Quantum Chemistry
• Computational Physics
• Atomic Physics

Background:

• The Levy-Perdew-Sahni (LPS) equation connects electron density decay to ionization potential in many-electron systems.
• The original LPS derivation utilized an effective potential derived from the system's wavefunction.

Purpose of the Study:

• To explore solving the LPS equation with approximate wavefunctions.
• To establish a method for obtaining accurate ground-state properties of two-electron systems.
• To demonstrate the effectiveness of this approach for closed-shell atoms.

Main Methods:

• Variational derivation of the LPS equation.
• Development of a self-consistent cycle using a modified Le Sech wavefunction.
• Utilizing approximate wavefunctions to derive accurate effective potentials.

Main Results:

• Demonstrated that approximate wavefunctions yield accurate effective potentials for the LPS equation.
• Showed that using the LPS equation with these wavefunctions leads to accurate electron densities.
• Successfully performed calculations for closed-shell atoms, validating the method.

Conclusions:

• The proposed method provides an efficient route to accurate electron densities for many-electron systems.
• This approach simplifies calculations by employing approximate wavefunctions within the LPS framework.
• The findings are applicable to understanding and predicting properties of atomic systems.