Related papers: Spherical Density Functional Theory
Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…
Spherical density functional theory (DFT) is a reformulation of the classic theorems of DFT, in which the role of the total density of a many-electron system is replaced by a set of sphericalized densities, constructed by…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial…
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…
A new potential is presented for spherical galaxies. The technique of the construction of our model is similar to that given by An and Evans. In a special case, its mass density becomes a special one of the Hernquist model. Another special…
The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high resolution cosmological N-body simulations by…
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for…
The atomization energies of molecules from first-principles density functional approximations improve from the local spin-density approximation (LSDA) to the Perdew-Burke-Ernzerhof (PBE)) generalized gradient approximation (GGA) to the…
A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been…