Density functionals based on the mathematical structure of the strong‐interaction limit of DFT

Abstract

While in principle exact, Kohn-Sham density functional theory-the workhorse of computational chemistry-must rely on approximations for the exchange-correlation functional. Despite staggering successes, present-day approximations still struggle when the effects of electron-electron correlation play a prominent role. The limit in which the electronic Coulomb repulsion completely dominates the exchange-correlation functional offers a well-defined mathematical framework that provides insight for new approximations able to deal with strong correlation. In particular, the mathematical structure of this limit, which is now well-established thanks to its reformulation as an optimal transport problem, points to the use of very different ingredients (or features) with respect to the traditional ones used in present approximations. We focus on strategies to use these new ingredients to build approximations for computational chemistry and highlight future promising directions.

Toward routine Kohn-Sham inversion using the "Lieb-response" approach

“…This manuscript considers basis sets, such as GTOs, in which real-valued orbitals and potentials, (8) are expanded in terms of compact sets of real-valued basis functions {φ p } and {v P } that are optimized to be small and therefore efficient, yet to also yield useful energies. In a finite basis, eq.…”

“…More recently, machine learning has helped to create DFAs that can solve problems that were previously believed to be intractable for DFAs. 5 Future major advances in DFT are likely to come from a combination of human learning and machine learning, as done in DM21, 5 where fundamental physical constraints [6][7][8][9] are combined with data-driven optimization. Standard data-driven optimization uses total energy differences (reaction energies) as an ingredient, which has proved to be very effective.…”

Nonlocal functionals inspired by the strongly interacting limit of DFT: exact constraints and implementation

“…Despite the tremendous successes of DFT, the description of strong correlation electronic effects remains the major challenge in the development of new XC approximations. [5][6][7][8][9] One can argue that the insufficient accuracy and not uncommon qualitative failures of the standard DFT for strong correlations 1,6,7 can be traced back to the limited number of building blocks that standard DFT uses for XC approximations. 8,9 These building blocks (or features) form the so-called "Jacob's Ladder" as formulated by Perdew.…”

“…[5][6][7][8][9] One can argue that the insufficient accuracy and not uncommon qualitative failures of the standard DFT for strong correlations 1,6,7 can be traced back to the limited number of building blocks that standard DFT uses for XC approximations. 8,9 These building blocks (or features) form the so-called "Jacob's Ladder" as formulated by Perdew. 10,11 The complexity and cost of the features increase as we climb up the Jacob's ladder, where at the bottom rung we find the density; then the density gradient, its Laplacian (or kinetic energy density) in the middle rungs; and the KS occupied and unoccupied orbitals in the top rungs.…”

“…containing information about the electronic density everywhere). 8,9 Then the question arises: what is the form of the fully nonlocal features that can be used? While some very recent ML XC models attempted to make use of different nonlocal features [17][18][19][20][21] , the strongly interacting limit (SIL) of DFT provides a natural and theoretically firm ground for the development and utilization of the fully nonlocal features.…”