Algebraic density functionals

A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are then obtained by standard elimination procedures of such degrees of freedom between the polynomials. Numerical examples illustrate the formalism.     

Symmetry and density functionals

The energies of different states belonging to an orbitally degenerate term are not consistent when evaluated with density functionals currently in use. This problem arises because the functionals do not transform according to the totally symmetric irreducible representation of the appropriate point group. A physically correct form can be obtained by projection.     

Development of electron-proton density functionals for multicomponent density functional theory

We present a strategy for the development of electron-proton density functionals in multicomponent density functional theory, treating electrons and selected nuclei quantum mechanically without the Born-Oppenheimer approximation. An electron-proton functional is derived using an explicitly correlated electron-proton pair density. This functional provides accurate hydrogen nuclear densities, thereby enabling reliable calculations of molecular properties. This approach is potentially applicable to relatively large molecular systems with key hydrogen nuclei treated quantum mechanically.     

Potential functionals: dual to density functionals and solution to the v-representability problem

A functional of external potentials and its variational principle for the ground-state energy is constructed. This potential functional formulation is dual to the density functional approach and provides a solution to the v-representability problem in the original Hohenberg-Kohn theory. A second potential functional for Kohn-Sham noninteracting systems establishes the foundation for the optimized effective potential approach and results in efficient approaches for ensemble Kohn-Sham calculations.     

Configuration interactions constrained by energy density functionals

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified model that reproduced the EDF binding-energy in the limit of single-Slater determinants, but can also be used for obtaining energy spectra and correlation energies with renormalized nucleon–nucleon interactions. The three-body and/or density-dependent terms that are necessary for good nuclear saturation properties are contained in the EDF. Applications to binding-energies and spectra of nuclei in the region above ²⁰⁸Pb are given.     

Nuclear energy density functionals constrained by low-energy QCD

A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional theory. Guided by two closely related features of QCD in the low-energy limit: a) in-medium changes of vacuum condensates, and b) spontaneous breaking of chiral symmetry; a relativistic energy density functional is developed and applied in studies of ground-state properties of spherical and deformed nuclei.     

Testing one-body density functionals on a solvable model

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent phase-space formalism, we thoroughly test some of the most popular of those functionals on a completely solvable model.     

Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.     

Semiclassical neutral atom as a reference system in density functional theory

We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.     

Concavity for nuclear bindings, thermodynamical functions and density functionals

Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential Ω(β,μ) for a mixture of nuclei at low or moderate temperatures T=β⁻¹ and at many chemical potentials μ. The average nucleon number A(β,μ) then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to the drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of A. Concavity, which always occurs for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.     

Microcanonical density functionals for critical systems: An exact one-dimensional example

Free-energy functionals suitable for describing realistic, nonuniform systems near criticality are discussed with emphasis on the advantages of a local formalism. It is proposed to investigatemicro canonical functionals in which both the usual order-parameter (or magnetization) density m(r)and the local energy density (r), which has independent critical fluctuations, are employed. This approach is tested by an exact calculation of the microcanonical functional [{m}, {}] in the continuum limit for a one-dimensional Ising model. Remarkably, the microcanonical functional is found to be local irrespective of the proximity to the critical point (located at zero temperature and zero field). Furthermore, its form relates closely to the scaling postulate advanced earlier by de Gennes and Fisher and displays features of conformal covariance.     

Semiclassical Symmetries

Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are considered. An infinitesimal analog of group relation is written. Sufficient conditions for reconstructing semiclassical group transformations (integrability of representation of Lie algebra) are discussed. The obtained results may be used for mathematical proof of Poincare invariance of semiclassical Hamiltonian field theory and for investigation of quantum anomalies.     

Effect of different density functionals on the core-level binding energies in some metals

Core level binding energies in metallic Mg, Al, Cd, In, Sn, Sb and Te have been calculated for various popular exchange correlation potentials. Calculations have been performed within the atom-in-jellium-vacancy mode using Slater's transition state theory. Theoretical results have been compared with the experiments.