Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.2K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
7.2K
Density00:56

Density

13.5K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
13.5K
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

800
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
800
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

1.4K
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the...
1.4K
Density and Archimedes' Principle01:05

Density and Archimedes' Principle

6.4K
When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The...
6.4K
Energy Carried By Electromagnetic Waves01:22

Energy Carried By Electromagnetic Waves

2.8K
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...
2.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions.

Entropy (Basel, Switzerland)·2026
Same author

Fisher Information Density Functional Theory.

Journal of computational chemistry·2025
Same author

Density functional theory from spherically symmetric densities: Ground and excited states of Coulomb systems.

The Journal of chemical physics·2024
Same author

Spherical densities and potentials in exactly solvable model molecules.

The Journal of chemical physics·2023
Same author

Spherical Density Functional Theory and Atoms in Molecules.

The journal of physical chemistry. A·2019
Same author

Time-dependent pair density from the principle of minimum Fisher information.

Journal of molecular modeling·2018

Related Experiment Video

Updated: May 9, 2025

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

8.9K

Ensemble density functional theory with spherically symmetric densities.

Á Nagy1

  • 1Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary.

The Journal of Chemical Physics
|May 2, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces spherical ensemble theory for excited states, extending Hohenberg-Kohn theorems to spherically symmetric densities. This new framework allows for novel energy functional partitioning and analysis of molecular systems.

More Related Videos

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

12.6K
Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

10.6K

Related Experiment Videos

Last Updated: May 9, 2025

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

8.9K
Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

12.6K
Assembly and Characterization of Polyelectrolyte Complex Micelles
08:44

Assembly and Characterization of Polyelectrolyte Complex Micelles

Published on: March 2, 2020

10.6K

Area of Science:

  • Quantum Chemistry
  • Theoretical Physics
  • Condensed Matter Physics

Background:

  • The Hohenberg-Kohn theorems are foundational for density functional theory (DFT).
  • Excited states in quantum mechanics present challenges for standard DFT methods.
  • Ensemble DFT addresses some limitations but requires extensions for specific symmetries.

Purpose of the Study:

  • To develop a spherical ensemble theory for describing excited electronic states.
  • To extend the Hohenberg-Kohn theorems to ensembles with spherically symmetric densities.
  • To derive new Kohn-Sham-like equations within this spherical ensemble framework.

Main Methods:

  • Development of the spherical ensemble theory.
  • Extension of Hohenberg-Kohn theorems using constrained search.
  • Derivation of spherical ensemble Kohn-Sham-like equations.
  • Generalization of the spherical Hartree expression for ensembles.

Main Results:

  • The spherical ensemble theory provides a new approach to partitioning the energy functional.
  • The theory enables the application of different energy functional partitions.
  • An exactly soluble model of a harmonic two-electron molecule was analyzed using the developed theory.

Conclusions:

  • The spherical ensemble theory offers a viable method for studying excited states with spherical symmetry.
  • The derived equations and generalized Hartree expression are key outcomes.
  • The analysis of the soluble model validates the theoretical framework.