# Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory

## Related Articles

- Tight constraints on the exchange-correlation potentials of degenerate states. Ayers, Paul W.; Levy, Mel // Journal of Chemical Physics;5/14/2014, Vol. 140 Issue 18, p18A537-1
Identities for the difference of exchange-correlation potentials and energies in degenerate and nondegenerate ground states are derived. The constraints are strong for degenerate ground states, and suggest that local and semilocal approximations to the exchange-correlation energy functional are...

- Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations. Kraisler, Eli; Kronik, Leeor // Journal of Chemical Physics;5/14/2014, Vol. 140 Issue 18, p18A540-1
The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt...

- Differentiable but exact formulation of density-functional theory. Kvaal, Simen; Ekström, Ulf; Teale, Andrew M.; Helgaker, Trygve // Journal of Chemical Physics;5/14/2014, Vol. 140 Issue 18, p18A518-1
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the densityâ€”in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a...

- The problem of the universal density functional and the density matrix functional theory. Bobrov, V.; Trigger, S. // Journal of Experimental & Theoretical Physics;Apr2013, Vol. 116 Issue 4, p635
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the...

- Ground-state densities from the Rayleigh-Ritz variation principle and from density-functional theory. Kvaal, Simen; Helgaker, Trygve // Journal of Chemical Physics;2015, Vol. 143 Issue 18, p1
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of...

- Variational principle, Hohenberg-Kohn theorem, and density function origin shifts. Carbó-Dorca, Ramon // Journal of Mathematical Chemistry;May2013, Vol. 51 Issue 5, p1397
Origin shifts performed on the density functions (DF) permit to express the Hohenberg-Kohn theorem (HKT) as a consequence of the variational principle. Upon ordering the expectation values of Hermitian operators, an extended variational principle can be described using origin shifted DF. Under...

- Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number. Levy, Mel; Anderson, James S. M.; Zadeh, Farnaz Heidar; Ayers, Paul W. // Journal of Chemical Physics;5/14/2014, Vol. 140 Issue 18, p18A538-1
Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to...

- The education of Walter Kohn and the creation of density functional theory. Zangwill, Andrew // Archive for History of Exact Sciences;Nov2014, Vol. 68 Issue 6, p775
The theoretical solid-state physicist Walter Kohn was awarded one-half of the 1998 Nobel Prize in Chemistry for his mid-1960s creation of an approach to the many-particle problem in quantum mechanics called density functional theory (DFT). In its exact form, DFT establishes that the total charge...

- A variational method for density functional theory calculations on metallic systems with thousands of atoms. Ruiz-Serrano, Álvaro; Skylaris, Chris-Kriton // Journal of Chemical Physics;Aug2013, Vol. 139 Issue 5, p054107
A new method for finite-temperature density functional theory calculations which significantly increases the number of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic...