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

Electron Orbital Model01:18

Electron Orbital Model

68.2K
Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
68.2K
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

1.3K
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's...
1.3K
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

27.1K
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...
27.1K
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

548
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
548
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.7K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.7K
The Bohr Model02:18

The Bohr Model

59.6K
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...
59.6K

You might also read

Related Articles

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

Sort by
Same author

Long-Range Configuration Interaction with an <i>Ab Initio</i> Short-Range Correction and an Asymptotic Lower Bound†.

The journal of physical chemistry. A·2024
Same author

Modified Expression for the Hamiltonian Expectation Value Exploiting the Short-Range Behavior of the Wave Function.

The journal of physical chemistry. A·2024
Same author

Exploring the role of mean-field potentials and short-range wave function behavior in the adiabatic connection.

Journal of computational chemistry·2024
Same author

Second-order adiabatic connection: The theory and application to two electrons in a parabolic confinement.

The Journal of chemical physics·2023
Same author

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

Physical chemistry chemical physics : PCCP·2022
Same author

The effect of uncertainty on building blocks in molecules.

The Journal of chemical physics·2022
Same journal

Kinetic and Mechanistic Insights into H-Abstraction and Subsequent Isomerization and Decomposition of Monoglyme and Key Combustion Intermediates.

The journal of physical chemistry. A·2026
Same journal

First-Principles Analysis of Protonation-Induced Electronic Effects in Tetrakis(<i>p</i>-aminophenyl)porphyrin (TAPP).

The journal of physical chemistry. A·2026
Same journal

Exploring the Reactivity of the CH Radical toward Nitrous Oxide in the Context of the Interstellar Medium.

The journal of physical chemistry. A·2026
Same journal

Infrared Photodissociation Spectroscopy of Benzene-V<sup>+</sup>(CO)<sub>n</sub> "Piano Stool" Cations.

The journal of physical chemistry. A·2026
Same journal

Correction to "Solvent-Dependent Ultrafast Photochemical Dynamics of <i>N</i>-Methyl Oxindole Overcrowded Alkene Molecular Motors".

The journal of physical chemistry. A·2026
Same journal

Accelerating the Discovery of Superhalogens via Physics-Informed Graph Neural Networks.

The journal of physical chemistry. A·2026
See all related articles

Related Experiment Video

Updated: Aug 12, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Correcting Models with Long-Range Electron Interaction Using Generalized Cusp Conditions.

Andreas Savin1, Jacek Karwowski2

  • 1Laboratoire de Chimie Théorique, CNRS and Sorbonne University4 Place Jussieu, 75252Paris cedex 05, France.

The Journal of Physical Chemistry. A
|January 31, 2023
PubMed
Summary
This summary is machine-generated.

This study improves energy calculations by refining approximations for Coulomb interactions. Using generalized cusp conditions significantly enhances accuracy for electronic systems.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Author Spotlight: Exploring Cellular Processes by Modeling Ligands in Cryo-EM Maps
09:30

Author Spotlight: Exploring Cellular Processes by Modeling Ligands in Cryo-EM Maps

Published on: July 19, 2024

1.5K

Related Experiment Videos

Last Updated: Aug 12, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Author Spotlight: Exploring Cellular Processes by Modeling Ligands in Cryo-EM Maps
09:30

Author Spotlight: Exploring Cellular Processes by Modeling Ligands in Cryo-EM Maps

Published on: July 19, 2024

1.5K

Area of Science:

  • Quantum chemistry
  • Computational physics
  • Theoretical chemistry

Background:

  • The Coulomb interaction is fundamental in electronic structure calculations.
  • Approximations for the Coulomb interaction can introduce energy errors.
  • Accurate representation of the wave function at small inter-electron distances is crucial.

Purpose of the Study:

  • To explore energy errors arising from the erfc(μr)/r approximation of the Coulomb interaction.
  • To improve the accuracy of electronic energy calculations.
  • To extend the range of parameters yielding chemically accurate results.

Main Methods:

  • Utilizing generalized cusp conditions to represent the wave function at small inter-electron distances (small r).
  • Applying the erfc(μr)/r approximation for the Coulomb interaction.
  • Performing numerical calculations for two-electron harmonium systems.

Main Results:

  • Demonstrated significant improvement in energy calculation results.
  • Extended the range of the parameter μ that provides energies within chemical accuracy.
  • Identified the effectiveness of generalized cusp conditions in mitigating approximation errors.

Conclusions:

  • Generalized cusp conditions are vital for accurate electronic structure calculations using approximate Coulomb interactions.
  • The erfc(μr)/r approximation, when combined with cusp conditions, offers a viable path to achieving chemical accuracy.
  • This approach provides a robust method for studying model systems like two-electron harmonium.