The RPA Atomization Energy Puzzle.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• The random phase approximation (RPA) is a density functional that includes full exact exchange and correlation via unoccupied Kohn-Sham orbitals.
• Corrections to RPA, such as LSDA and GGA, are typically short-ranged and effective for simple systems.
• Previous nonempirical functionals (RPA+) improved RPA for atoms but showed minimal impact on molecular atomization energies.

Purpose of the Study:

• To develop a fully nonlocal density functional (RPA++) for RPA correlation corrections.
• To investigate the puzzling underestimation of molecular atomization energies by RPA.
• To improve the accuracy of density functional theory for predicting molecular properties.

Main Methods:

• Construction of the RPA++ functional using the van der Waals density functional (vdW-DF) framework.
• Evaluation of RPA, RPA+, and RPA++ on total and ionization energies of free atoms.
• Testing a hybrid functional combining 50% Perdew-Burke-Ernzerhof (GGA) with 50% RPA+ for molecular atomization energies.

Main Results:

• RPA++ provided helpful corrections to RPA total and ionization energies for free atoms.
• RPA++ yielded only minor corrections (approx. 1 kcal/mol) to RPA atomization energies of molecules.
• The 50% GGA + 50% RPA+ hybrid functional significantly improved molecular atomization energy accuracy compared to individual components.

Conclusions:

• The underestimation of molecular atomization energies by RPA is attributed to the spreading of the correlation hole in polyatomic systems.
• This delocalization effect, which partially cancels the exchange hole spread, is not fully captured by RPA, RPA+, or vdW-DF.
• A hybrid functional incorporating nonlocalities from both GGA and RPA+ is necessary to accurately describe the exchange-correlation hole in molecules.