Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms.

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Theoretical Chemistry

Background:

• Double-hybrid (DH) density functionals are crucial in computational chemistry.
• Existing DH functionals often rely on second-order Görling-Levy (GL2) perturbation theory.
• There is a need for more accurate and versatile DH functional constructions.

Purpose of the Study:

• To establish connections between Görling-Levy perturbation theory and DH density functional parameters.
• To present a generalized DH density functional theory incorporating higher-order perturbation terms (GL3, GL4).
• To explore the performance of these advanced DH functionals.

Main Methods:

• Utilizing the adiabatic connection formalism to link GL perturbation theory and DH functionals.
• Developing a generalized DH density functional theory framework.
• Assessing performance using higher-order and long-range corrected DH functionals based on PBE and GL2 correlation energy.

Main Results:

• Established formal connections between GL perturbation theory and DH functional parameters.
• Presented a generalized DH functional theory allowing for higher-order GL terms.
• Demonstrated that a class of DH functionals, including prior ones, can be constructed via this formalism.
• Evaluated the performance of higher-order and long-range corrected DH functionals.

Conclusions:

• The proposed generalized DH functional theory offers a physically appealing framework for developing non-local functionals.
• Incorporating higher-order perturbation terms enhances the sophistication and accuracy of DH functionals.
• This approach facilitates the use of more accurate semilocal functionals within DH constructions.