Related papers: A Mathematical Aspect of Hohenberg-Kohn Theorem
Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned.…
In this paper, we present a completely rigorous formulation of Kohn-Sham density functional theory for spinless fermions living in one dimensional space. More precisely, we consider Schr\"odinger operators of the form $H_N(v,w) = -\Delta +…
The molecular density functional theory of fluids provides an exact theory for computing solvation free energies in implicit solvents. One of the reasons it has not received nearly as much attention as quantum density functional theory for…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
We discuss the validity of generalized Debye-H\"uckel (GDH) equation proposed by Fisher {\itshape et al.} from the functional integral point of view. The GDH theory considers fluctuations around prescribed densities of positive and negative…
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such…
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…
We model the Hartree-exchange-correlation potential of Kohn-Sham density-functional theory adopting a novel strategy inspired by the strictly-correlated-electrons limit and relying on the exact decomposition of the potential based on the…
The variational argument is presented to establish the attainability of homogeneity of degree one in the number of particles for any functional $F[n, f]$ that depends on both the state variable $f$ and the particle count $n$. Euler's…
Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to…
We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial…
The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of…
The one-particle Green function of a many-electron system is traditionally formulated within the self-energy picture. A different formalism was recently proposed, in which the self-energy is replaced by a dynamical exchange-correlation…
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the…
An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density…
In this work we study in a formal way the density dependent hadron field theory at finite temperature for nuclear matter. The thermodynamical potential and related quantities, as energy density and pressure are derived in two different…