Self-consistent convolutional density functional approximations: Application to adsorption at metal surfaces

TL;DR

This paper introduces a novel approach to constructing exchange-correlation functionals in density functional theory using convolutions of kernels with electron density, enabling spatially adaptive functionals beyond traditional Jacob's ladder.

Contribution

It develops a new class of XC functionals based on convolutional inputs, derives their variational derivatives, and demonstrates a proof-of-concept functional, PBEq, that adapts locally while satisfying PBE constraints.

Findings

PBEq generalizes PBEα with spatially-resolved density features.

The approach allows different GGAs at different spatial points.

Results show potential for multi-property optimization.

Abstract

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals is available, but nearly all are based on the hierarchy of inputs commonly referred to as "Jacob's ladder." This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBE$\alpha$ framework where $\alpha$ is a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.