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

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

2.6K
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
2.6K
Atomic Orbitals02:44

Atomic Orbitals

42.3K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
42.3K
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

64.6K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
64.6K
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

47.1K
sp3d and sp3d 2 Hybridization
47.1K
π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

1.5K
An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
1.5K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

29.6K
In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
29.6K

You might also read

Related Articles

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

Sort by
Same author

Inverse Design of Anthraquinone-Mimicking COFs via Electronic Fingerprints for Sacrificial-Agent-Free Photocatalytic H<sub>2</sub>O<sub>2</sub> Production under Visible Light.

Journal of the American Chemical Society·2026
Same author

Theoretical Perspectives of Precision Chemistry.

Precision chemistry·2026
Same author

KSSOLV Toolbox: A MATLAB Graphical User Interface for Plane-Wave Density Functional Theory Calculations.

Journal of chemical theory and computation·2026
Same author

Linkage-Locking Cyclization Enables Hydrolysis-Resistant Imine COFs for Photocatalytic Water Splitting.

The journal of physical chemistry letters·2026
Same author

Proposed Strongly Correlated Excitonic Insulator in Nitrogen-Boron-Centered Triangulene Honeycomb Lattice.

The journal of physical chemistry letters·2026
Same author

Electromagnetic vs Chemical Interfacial Interactions at the Single-Molecule-Confined Sub-nanometer Molecule-Metal Gap: A Solution-Phase Chiroptical Study.

Nano letters·2026

Related Experiment Video

Updated: Dec 26, 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

8.9K

The Moving-Grid Effect in the Harmonic Vibrational Frequency Calculations with Numeric Atom-Centered Orbitals.

Honghui Shang1, Jinlong Yang2

  • 1State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China.

The Journal of Physical Chemistry. A
|March 18, 2020
PubMed
Summary

The moving-grid effect is crucial for calculating vibrational frequencies, unlike forces. This effect on force constants can be efficiently managed using translational symmetry in molecular and periodic systems.

More Related Videos

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.9K
Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.6K

Related Experiment Videos

Last Updated: Dec 26, 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

8.9K
Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.9K
Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.6K

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Atom-centered integration grids are commonly used in electronic structure calculations.
  • Displacing atoms causes their associated grid portions to move, known as the moving-grid effect.
  • This effect's impact on calculating molecular properties is an area of ongoing research.

Purpose of the Study:

  • To investigate the significance of the moving-grid effect on harmonic vibrational frequency calculations.
  • To analyze how this effect influences second-order derivatives in electronic structure computations.
  • To develop efficient methods for mitigating the moving-grid effect in vibrational frequency analysis.

Main Methods:

  • Utilizing all-electron, full-potential numeric atomic-centered orbitals as the basis set.
  • Calculating harmonic vibrational frequencies and comparing results with and without considering the moving-grid effect.
  • Analyzing the impact on force constant terms and employing translational symmetry to address the effect.

Main Results:

  • The moving-grid effect significantly impacts the calculation of second-order derivatives (vibrational frequencies), unlike first-order derivatives (forces).
  • Predominantly diagonal force constant terms are affected by the moving-grid effect.
  • The proposed method effectively bypasses the moving-grid effect by invoking translational symmetry.

Conclusions:

  • The moving-grid effect is essential for accurate vibrational frequency calculations using numeric atomic-centered orbitals.
  • Translational symmetry provides an efficient way to handle the moving-grid effect in force constant calculations.
  • The developed approaches are applicable to both finite molecular systems and extended periodic systems.