Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Density-Functional Theory

Background:

• The exchange-correlation (XC) hole is essential for developing accurate density-functional approximations.
• Calculating accurate XC holes requires complex computations of reduced density matrices over a coupling-constant range.
• Coupled-cluster singles and doubles (CCSD) can be exact for two-electron systems but struggles with the electron-electron cusp in finite basis sets.

Purpose of the Study:

• To investigate the impact of the electron-electron cusp error on XC hole calculations using CCSD.
• To evaluate the accuracy of XC hole models by comparing them against benchmark calculations.
• To analyze the relative contributions of basis set incompleteness and cusp errors in XC hole calculations.

Main Methods:

• Utilized coupled-cluster singles and doubles (CCSD) method for a two-electron Hooke's atom model.
• Calculated the Lieb functional across various coupling constants (λ) to determine the λ-integrated XC hole.
• Computed system-, angle-, and coupling-constant-averaged XC holes for benchmarking.

Main Results:

• The electron-electron cusp error in CCSD calculations with Gaussian basis sets was found to be negligible for Hooke's atom.
• Basis set incompleteness error was identified as the dominant source of error in the XC hole calculations.
• The calculated XC holes served as a benchmark for assessing the Perdew-Burke-Ernzerhof and local density approximation models.

Conclusions:

• For two-electron systems like Hooke's atom, basis set incompleteness is a more critical factor than the electron-electron cusp error in CCSD-based XC hole calculations.
• Accurate XC hole calculations are vital for advancing density-functional theory approximations.
• The study provides valuable benchmark data for evaluating approximate XC hole models.