Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Hybridization of Atomic Orbitals I

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...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Atomic Orbitals

Atomic Orbitals

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.

Valence Bond Theory and Hybridized Orbitals

Valence Bond Theory and Hybridized Orbitals

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...

You might also read

Related Articles

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

Sort by

Same author

Beyond Content Delivery: A Systematic Review of Video-Based SRL Interventions and Gaps in Explicit Motivational and Resource-Management Instruction.

Journal of Intelligence·2026

Same author

Transient Dynamical Phase Diagram of the Spin-Boson Model.

Physical review letters·2025

Same author

SARS-CoV-2 CoCoPUTs: analyzing GISAID and NCBI data to obtain codon statistics, mutations, and free energy over a multiyear period.

Virus evolution·2025

Same author

Large exciton binding energy in a bulk van der Waals magnet from quasi-1D electronic localization.

Nature communications·2025

Same author

Nonequilibrium steady state full counting statistics in the noncrossing approximation.

The Journal of chemical physics·2024

Same author

Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions.

Reports on progress in physics. Physical Society (Great Britain)·2024

Search research articles

Related Experiment Video

Updated: Dec 19, 2025

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations.

Eitan Eidelstein^1,2, Emanuel Gull^3,4, Guy Cohen²

¹Department of Physics, NRCN, P.O. Box 9001, Beer Sheva 84190, Israel.

Physical Review Letters

|June 6, 2020

Summary

This summary is machine-generated.

A new inchworm Monte Carlo method precisely solves complex quantum impurity problems. This numerical technique overcomes the sign problem, enabling more accurate simulations in condensed matter physics.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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

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

Published on: May 27, 2020

Related Experiment Videos

Last Updated: Dec 19, 2025

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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

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

Published on: May 27, 2020

Area of Science:

Computational Physics
Quantum Many-Body Theory
Condensed Matter Physics

Background:

Quantum impurity models are crucial for understanding strongly correlated electron systems.
Existing methods like continuous-time hybridization expansion face limitations due to the sign problem, especially at finite temperatures.
Approximations are often required in ab initio embedding theories, limiting simulation accuracy.

Purpose of the Study:

To introduce a numerically exact inchworm Monte Carlo method for multiorbital quantum impurity problems.
To demonstrate the method's capability to overcome the sign problem in equilibrium quantum impurity models.
To provide a more accurate simulation tool for ab initio embedding problems without approximations.

Main Methods:

Development of a numerically exact inchworm Monte Carlo algorithm.
Application to equilibrium multiorbital quantum impurity models with general interactions and hybridizations.
Comparison with the continuous-time hybridization expansion method.

Main Results:

The inchworm Monte Carlo method successfully overcomes the sign problem as a function of temperature.
The method provides accurate results in cases where the continuous-time hybridization expansion fails.
It eliminates the need for approximations in simulating impurity problems within embedding theories.

Conclusions:

The inchworm Monte Carlo method is a powerful and accurate tool for quantum impurity problems.
This advancement removes a significant bottleneck in ab initio embedding calculations.
It enables more reliable simulations of complex condensed matter phenomena.