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

69.5K
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...
69.5K
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

50.4K
sp3d and sp3d 2 Hybridization
50.4K
Atomic Orbitals02:44

Atomic Orbitals

47.5K
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.
47.5K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

31.2K
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.
31.2K
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

33.2K
According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
33.2K
Graphing the Wave Function01:13

Graphing the Wave Function

3.4K
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
3.4K

You might also read

Related Articles

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

Sort by
Same author

Efficient Coupled-Cluster Python Frameworks for Next-Generation GPUs: A Comparative Study of CuPy and PyTorch on the Hopper and Grace Hopper Architecture.

Journal of chemical theory and computation·2026
Same author

After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective.

Journal of chemical theory and computation·2026
Same author

Analytic gradients and geometry optimization for orbital-optimized pair coupled cluster doubles.

The Journal of chemical physics·2026
Same author

A Flexible, Automated, and Basis-Set-Insensitive Domain-Based Charge-Transfer Decomposition for Correlated Wave Functions and Its Application to Inter- and Intramolecular Cases.

The journal of physical chemistry letters·2026
Same author

Neural Quantum States Based on Selected Configurations.

The journal of physical chemistry letters·2026
Same author

How to Use Quantum Computers for Biomolecular Free Energies.

Journal of chemical theory and computation·2026

Related Experiment Video

Updated: Apr 7, 2026

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

8.8K

Selection of active spaces for multiconfigurational wavefunctions.

Sebastian Keller1, Katharina Boguslawski1, Tomasz Janowski2

  • 1Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland.

The Journal of Chemical Physics
|July 3, 2015
PubMed
Summary
This summary is machine-generated.

The unrestricted natural orbital (UNO) criterion offers an efficient method for defining active spaces in strongly correlated systems. This approach, validated by Density Matrix Renormalization Group (DMRG) calculations, simplifies electronic structure calculations.

More Related Videos

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.9K
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

9.1K

Related Experiment Videos

Last Updated: Apr 7, 2026

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

8.8K
Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.9K
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

9.1K

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Electronic Structure Theory

Background:

  • Accurately describing electronic structure in strongly correlated systems remains a significant challenge.
  • Standard methods involve multiconfigurational wavefunctions (Complete Active Space, CAS) and adding dynamical correlation, but require careful active space selection.
  • Intuitive active space selection is often unreliable for complex molecules.

Purpose of the Study:

  • To rigorously test the validity of the unrestricted natural orbital (UNO) criterion for defining active spaces in electronic structure calculations.
  • To compare the UNO criterion's performance against established methods using advanced computational techniques.
  • To assess the UNO criterion's applicability across a diverse range of strongly correlated molecules.

Main Methods:

  • The study employed the unrestricted natural orbital (UNO) criterion to define active spaces, utilizing Unrestricted Hartree-Fock (UHF) orbitals.
  • Calculations involved the UNO-Complete Active Space (UNO-CAS) method, bypassing computationally expensive orbital optimization.
  • Comparisons were made against Density Matrix Renormalization Group (DMRG) calculations, which provide accurate approximations of highly correlated wavefunctions.

Main Results:

  • The UNO criterion demonstrated effectiveness in defining active spaces across various strongly correlated molecules, including those with electronegative atoms, polyenes, aromatics, radicals, and transition metal compounds.
  • UNO-CAS calculations showed good agreement with DMRG results, indicating the UNO criterion's reliability.
  • The study found that spatial symmetry breaking is generally not essential for correct active space generation, and suggested using average UHF density for multiple UHF solutions.

Conclusions:

  • The UNO criterion provides a reliable and computationally inexpensive method for selecting active spaces in strongly correlated systems.
  • The UNO-CAS method offers a practical alternative to traditional CASSCF, significantly reducing computational cost.
  • Further research is needed to address challenges such as finding UHF solutions, potential energy surface discontinuities, and incorporating dynamical correlation for excited states.