Leading Correction to the Local Density Approximation for Exchange in Large-Z Atoms

Area of Science:

• Atomic Physics
• Quantum Chemistry
• Computational Physics

Background:

• The local density approximation (LDA) in density functional theory (DFT) requires corrections for accurate atomic energy calculations.
• The large-Z asymptotic expansion provides a framework for understanding these corrections, particularly for heavy atoms.

Purpose of the Study:

• To determine the coefficient of the leading ZlnZ term in the exchange-energy correction for large-Z atoms.
• To compare this coefficient with that from the gradient expansion approximation (GEA).
• To develop an analytic expression for the exchange-energy correction.

Main Methods:

• Numerical determination of the ZlnZ term coefficient.
• Analytic calculations in the limit of vanishing interaction (Bohr atom model).
• Comparison with existing gradient expansion approximation results.

Main Results:

• The exchange-energy correction is well-approximated by a leading ZlnZ term.
• The coefficient for this term was found numerically.
• Analytic results suggest the coefficient is 2.7 times larger than its GEA counterpart.

Conclusions:

• An analytic expression for the exchange-energy correction was derived.
• This expression achieves approximately 5% accuracy for all Z.
• The findings offer insights into improving DFT approximations for atomic energies.