What can we learn from the adiabatic connection formalism about local hybrid functionals?

Area of Science:

• Quantum Chemistry
• Computational Materials Science

Background:

• Local hybrid functionals offer a promising approach for accurate electronic structure calculations.
• Local mixing functions (LMFs) control the position-dependent exact-exchange admixture in these functionals.
• Current LMFs are often empirically derived, lacking a strong theoretical foundation.

Purpose of the Study:

• To investigate the formal basis of local hybrid functionals using adiabatic connection theory.
• To derive first-principles local mixing functions (LMFs) a priori.
• To assess the performance of these new LMFs in predicting chemical properties.

Main Methods:

• Application of adiabatic connection formalism to derive LMFs.
• Development of AC-LSDA, AC-PW91, and AC-PBE LMFs.
• Testing LMFs in local hybrid functionals for calculating atomization energies and reaction barriers.

Main Results:

• First-principles LMFs derived from adiabatic connection theory (AC-LSDA, AC-PW91, AC-PBE) showed reduced performance.
• Performance was inferior compared to previously used semiempirical LMFs for key chemical properties.
• Limited flexibility of first-principles LMFs and adiabatic connection formalism limitations were identified.

Conclusions:

• While first-principles LMFs derived via adiabatic connection theory show promise, they currently underperform empirical approaches.
• Further development is needed to enhance the flexibility and applicability of a priori LMFs.
• The study provides valuable insights into the physical underpinnings of local hybrid functionals.