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

Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
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...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

You might also read

Related Articles

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

Sort by
Same author

Transient disappearance of otoacoustic emissions after conventional hearing aid use in OTOF-related auditory neuropathy.

International journal of audiology·2026
Same author

Dimensions of wisdom perception across twelve countries on five continents.

Nature communications·2024
Same author

Predicting value for incomplete recovery in Bell's palsy of facial nerve ultrasound versus nerve conduction study.

Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology·2023
Same author

'Choroid bar': easy-to-seek marker of normal posterior fossa at 12-14 weeks' gestation.

Ultrasound in obstetrics & gynecology : the official journal of the International Society of Ultrasound in Obstetrics and Gynecology·2023
Same author

PENG block associated with dexmedetomidine sedation for intramedullary femoral fixation in high-risk elderly patients: a case series and review of the literature.

European review for medical and pharmacological sciences·2023
Same author

Neurosonographic and MRI diagnosis of fetal cerebral lesions heralding polymicrogyria.

Ultrasound in obstetrics & gynecology : the official journal of the International Society of Ultrasound in Obstetrics and Gynecology·2023
Same journal

A data-driven modeling study on the accurate identification of Doppler-free saturated absorption spectra in diatomic tellurium (130Te2).

The Journal of chemical physics·2026
Same journal

Anharmonic phonons via quantum thermal bath simulations.

The Journal of chemical physics·2026
Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026
Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026
Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026
Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026
See all related articles

Related Experiment Video

Updated: Jun 7, 2026

Enhancing Density Maps by Removing the Majority of Particles in Single Particle Cryogenic Electron Microscopy Final Stacks
06:41

Enhancing Density Maps by Removing the Majority of Particles in Single Particle Cryogenic Electron Microscopy Final Stacks

Published on: May 10, 2024

Frozen density embedding with hybrid functionals.

S Laricchia1, E Fabiano, F Della Sala

  • 1Center for Biomolecular Nanotechnologies of the Italian Institute of Technology, Via Barsanti, Arnesano, I-73100 Lecce, Italy.

The Journal of Chemical Physics
|November 2, 2010
PubMed
Summary
This summary is machine-generated.

We developed a new method to improve calculations of electronic properties using hybrid functionals. This approach accurately predicts system properties, outperforming standard methods for DNA base pairs and small molecules.

More Related Videos

Methods for Embedding Cell-Free Protein Synthesis Reactions in Macro-Scale Hydrogels
06:38

Methods for Embedding Cell-Free Protein Synthesis Reactions in Macro-Scale Hydrogels

Published on: June 23, 2023

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Related Experiment Videos

Last Updated: Jun 7, 2026

Enhancing Density Maps by Removing the Majority of Particles in Single Particle Cryogenic Electron Microscopy Final Stacks
06:41

Enhancing Density Maps by Removing the Majority of Particles in Single Particle Cryogenic Electron Microscopy Final Stacks

Published on: May 10, 2024

Methods for Embedding Cell-Free Protein Synthesis Reactions in Macro-Scale Hydrogels
06:38

Methods for Embedding Cell-Free Protein Synthesis Reactions in Macro-Scale Hydrogels

Published on: June 23, 2023

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Area of Science:

  • Quantum Chemistry
  • Computational Materials Science
  • Electronic Structure Theory

Background:

  • The Kohn-Sham equations are fundamental for electronic structure calculations.
  • Accurate treatment of exchange-correlation (XC) functionals is crucial for predicting material properties.
  • Existing methods struggle with nonlocal exact-exchange in subsystem calculations.

Purpose of the Study:

  • To extend Kohn-Sham equations with constrained electron density to hybrid XC functionals.
  • To develop a frozen density embedding generalized Kohn-Sham (FDE-GKS) scheme.
  • To enable accurate treatment of nonlocal exact-exchange within subsystems.

Main Methods:

  • Derivation of the FDE-GKS scheme for hybrid XC functionals.
  • Proposal of an approximated FDE-GKS with semilocal nonadditive exchange potential.
  • Application to ground-state electronic properties of small systems and DNA base pairs.
  • Comparison with coupled-cluster singles and doubles (CCSD) reference results.

Main Results:

  • Hybrid functionals significantly improve the description of ground-state electronic properties.
  • The semilocal FDE-GKS accurately reproduces dipole and electron density distribution.
  • Errors from the semilocal FDE-GKS are smaller than conventional semilocal XC functionals.
  • Calculations utilized BLYP/B3LYP/BHLYP and PBE/PBE0 XC functional hierarchies.

Conclusions:

  • The FDE-GKS scheme offers a robust method for electronic structure calculations with hybrid functionals.
  • The semilocal approximation provides a computationally efficient and accurate approach.
  • This method enhances the predictive power for molecular and material properties, including biomolecules.