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

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal Density01:19

Crystal Density

The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

You might also read

Related Articles

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

Sort by
Same author

Role of real-world evidence from patient registries for psoriasis in decision-making: a systematic review.

BMJ open quality·2026
Same author

Deucravacitinib in Patients with Plaque Psoriasis Who Screened Positive for Psoriatic Arthritis: Improvements in Joint Pain and the Impact of Musculoskeletal Symptoms.

Dermatology and therapy·2025
Same author

Economic and humanistic burden of HPV-related disease in Indonesia: A qualitative analysis.

Global public health·2023
Same author

Health Impact and Cost-Effectiveness of Implementing Gender-Neutral Vaccination With the 9-Valent Human Papillomavirus Vaccine in Belgium.

Frontiers in pharmacology·2021
Same author

The status of human papillomavirus vaccination recommendation, funding, and coverage in WHO Europe countries (2018-2019).

Expert review of vaccines·2020
Same author

Healthcare utilization and associated costs following initiation of perampanel in patients with epilepsy.

Epilepsy & behavior : E&B·2020

Related Experiment Video

Updated: Jul 11, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Grid-free density functional calculations on periodic systems.

Stefan Varga1

  • 1Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia. stefan.varga@savba.sk

The Journal of Chemical Physics
|September 25, 2007
PubMed
Summary

A new density fitting scheme efficiently calculates the exchange part of the Kohn-Sham potential for infinite systems. This method reduces computational demands, matching the scaling of the Coulomb part for improved performance in electronic structure calculations.

More Related Videos

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

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

Related Experiment Videos

Last Updated: Jul 11, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

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

Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Accurate calculation of electronic structure in infinite systems is computationally demanding.
  • The exchange part of the Kohn-Sham potential presents a significant computational bottleneck.
  • Existing methods often struggle with scaling for large, periodic systems.

Purpose of the Study:

  • To develop and apply a grid-free density fitting scheme for the exchange potential in infinite systems.
  • To analyze the computational scaling of this new approach.
  • To demonstrate the efficiency and robustness of the scheme on a model system.

Main Methods:

  • Application of a density fitting scheme to the exchange part of the Kohn-Sham potential.
  • Utilizing a grid-free local density approximation for systems with translational periodicity.
  • Testing various auxiliary basis set expansion coefficients with Coulomb and overlap metrics.

Main Results:

  • The computational demands for the exchange part scale comparably to the Coulomb part.
  • The efficiency of the density fitting scheme is demonstrated on an infinite polymer chain model.
  • Effectiveness is discussed concerning robustness and norm preservation across different coefficient choices.

Conclusions:

  • The proposed density fitting scheme offers an efficient and scalable method for calculating the exchange potential in infinite systems.
  • This approach significantly reduces computational costs, making complex electronic structure calculations more feasible.
  • The method shows promise for applications in condensed matter physics and materials science.