The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory*

Approximations to the density functional for the exchange-correlation energy of Kohn-Sham theory can be constructed by fitting to data sets for bonded systems, or by satisfying exact mathematical constraints on the functional and appropriate norms (such as the uniform electron gas), or both. Fitting is interpolative, and can predict accurately for systems similar to those in the data sets, while satisfying exact constraints makes a functional more widely predictive over the immense space of possible molecules and materials. For example, the SCAN (strongly constrained and appropriately normed) functional [1] satisfies all 17 exact constraints that a computationally-efficient meta-generalized gradient approximation can, and has been remarkably successful for some complex materials (like liquid water [2]) and some strongly-correlated materials (like the cuprate high-temperature superconducting materials [3,4]). Prospects for an improved SCAN and for the correction of its residual self-interaction error will also be discussed.
[1] J. Sun, A. Ruzsinszky, and J.P. Perdew, Strongly Constrained and Appropriately Normed Semi-local Density Functional, Physical Review Letters 115, 036402 (2015).
[2] M. Chen et al., Ab Initio Theory and Modeling of Water, Proceedings of the National Academy of Sciences (USA) 114, 10846-10851 (2017).
[3] J.W. Furness et al., An Accurate First-Principles Treatment of Doping-Dependent Electronic Structure of High-TemperatureSuperconductors, Nature Communications Physics, 1, 11 (2018).
[4] Y. Zhang, C. Lane, J.W. Furness, B. Barbiellini, J.P. Perdew, R.S. Markiewicz, A. Bansil, and J. Sun, Competing Stripe and Magnetic Phases in the Cuprates from First Principles, submitted.