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Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that ( a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and ( b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.
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The exact exchange–correlation potential in time-dependent density functional theory: Choreographing electrons with steps and peaks
The time-dependent exchange–correlation potential has the unusual task of directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for its structure, especially in the non-perturbative regime, leading to step and peak features that cannot be captured by bootstrapping any ground-state functional approximation. We review what has been learned about these features in the exact exchange–correlation potential of time-dependent density functional theory in the past decade or so and implications for the performance of simulations when electrons are driven far from any ground state.
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- Award ID(s):
- 1940333
- PAR ID:
- 10439844
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Chemical Physics Reviews
- Volume:
- 3
- Issue:
- 3
- ISSN:
- 2688-4070
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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