Self-Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Density functional theory (DFT) relies on exchange-correlation (XC) functionals to approximate multi-electron interactions.
• Existing XC functionals largely follow a hierarchical approach known as "Jacob's ladder."
• There is a need for new methods to construct XC functionals that can move beyond this established hierarchy.

Purpose of the Study:

• To introduce a novel approach for constructing XC functionals using convolutional kernels.
• To develop a method that transcends the limitations of the "Jacob's ladder" hierarchy.
• To present a proof-of-concept functional, PBEq, and demonstrate its capabilities.

Main Methods:

• Developed XC functionals based on convolutions of arbitrary kernels with the electron density.
• Derived variational derivatives for these new functionals, demonstrating consistency with Generalized Gradient Approximation (GGA).
• Implemented and tested a proof-of-concept functional, PBEq, which generalizes the PBE framework.

Main Results:

• The PBEq functional allows for spatially resolved application of different GGAs within a single system while adhering to PBE constraints.
• Analysis highlighted the significance of error cancellation and the XC potential in data-driven functional design.
• Testing on small molecules, bulk metals, and surface catalysts showed promising results for optimizing multiple properties.

Conclusions:

• The proposed convolutional kernel approach offers a viable route to construct XC functionals beyond "Jacob's ladder."
• This method enables the simultaneous optimization of diverse material properties.
• The findings underscore the potential of this approach for advancing DFT calculations and materials discovery.