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Exact conditions on the temperature dependence of density functionals
Kieron Burke, Justin C. Smith, Paul E. Grabowski +1
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free e…
Accurate atomic quantum defects from particle-particle random phase approximation
Yang Yang, Kieron Burke, Weitao Yang
The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defe…
Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation
Justin C Smith, Aurora Pribram-Jones, Kieron Burke
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the si…
Thermal density functional theory: Time-dependent linear response and approximate functionals from the fluctuation-dissipation theorem
Aurora Pribram-Jones, Paul E. Grabowski, Kieron Burke
The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of…
Connection formulas for thermal density functional theory
Aurora Pribram-Jones, Kieron Burke
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and…
One Dimensional Mimicking of Electronic Structure: The Case for Exponentials
Thomas E. Baker, E. Miles Stoudenmire, Lucas O. Wagner +2
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more…
Density functional description of Coulomb blockade: Adiabatic or dynamic exchange-correlation?
Zhenfei Liu, Kieron Burke
Above the Kondo temperature, the Kohn-Sham zero-bias conductance of an Anderson junction has been shown to completely miss the Coulomb blockade. Within a standard model for the spe…
The Hubbard Dimer: A density functional case study of a many-body problem
Diego Carrascal, Jaime Ferrer, Justin C. Smith +1
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relation…
Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals
Kevin Vu, John Snyder, Li Li +5
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random samplin…