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

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Molecular Models

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.

π Molecular Orbitals of 1,3-Butadiene

π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...

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...

Structure of Benzene: Molecular Orbital Model

Structure of Benzene: Molecular Orbital Model

According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).

MO Theory and Covalent Bonding

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

You might also read

Related Articles

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

Sort by

Same author

Random phase approximation-based local natural orbital coupled cluster theory.

The Journal of chemical physics·2026

Same author

Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method.

Journal of chemical theory and computation·2026

Same author

How to Use Quantum Computers for Biomolecular Free Energies.

Journal of chemical theory and computation·2026

Same author

Ab initio many-body quantum embedding and local correlation in crystalline materials using interpolative separable density fitting.

The Journal of chemical physics·2026

Same author

Thermal and vibronic effects on the absorption spectra of II-VI quantum dots: Atomistic origins of the Urbach tail.

The Journal of chemical physics·2026

Same author

Unphysical solutions in coupled-cluster-based random phase approximation and how to avoid them.

The Journal of chemical physics·2025

Same journal

Nuclear Gradients from Auxiliary-Field Quantum Monte Carlo and Their Applications in ML-Driven Geometry Optimization and Transition State Search.

Journal of chemical theory and computation·2026

Same journal

Correction to "Cluster-in-Molecule Local Correlation Method with an Accurate Distant Pair Correction for Large Systems".

Journal of chemical theory and computation·2026

Same journal

Machine-Learned Force Fields for Lattice Dynamics at Coupled-Cluster Level Accuracy.

Journal of chemical theory and computation·2026

Same journal

Systematic Molecularity-Dependent Entropy Errors in Continuum/RRHO Solution Thermochemistry: Origin and Correction.

Journal of chemical theory and computation·2026

Same journal

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

Journal of chemical theory and computation·2026

Same journal

Sample-Based Quantum Diagonalization Methods for Modeling the Photochemistry of Diazirine and Diazo Compounds.

Journal of chemical theory and computation·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 5, 2025

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

Bootstrap Embedding for Molecules in Extended Basis Sets.

Henry K Tran¹, Leah P Weisburn¹, Minsik Cho¹

¹Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.

Journal of Chemical Theory and Computation

|December 9, 2024

Summary

This summary is machine-generated.

Quantum embedding methods now work with extended basis sets. Bootstrap embedding combined with intrinsic atomic orbitals accurately captures electron correlation energy for larger systems.

More Related Videos

Interactive Molecular Model Assembly with 3D Printing

Interactive Molecular Model Assembly with 3D Printing

Published on: August 13, 2020

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Related Experiment Videos

Last Updated: Jun 5, 2025

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

Interactive Molecular Model Assembly with 3D Printing

Interactive Molecular Model Assembly with 3D Printing

Published on: August 13, 2020

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

Quantum Chemistry
Computational Chemistry
Electronic Structure Theory

Background:

Quantum embedding methods leverage electron correlation locality.
Previous methods were limited to small basis sets, hindering application to larger systems.
Extended basis sets pose challenges in defining localized orbitals.

Purpose of the Study:

To adapt bootstrap embedding (BE) for use with extended basis sets.
To address the challenge of localized orbitals in larger basis sets.
To improve the accuracy of quantum embedding for dynamic correlation.

Main Methods:

Modified bootstrap embedding (BE) for extended basis sets.
Utilized intrinsic atomic orbital (IAO) localization schemes.
Tested convergence of correlation energy across multiple basis sets (3-21G, 6-311G, cc-pVDZ).

Main Results:

The modified BE method with IAO localization achieved ~99.7% of the coupled cluster singles and doubles (CCSD) correlation energy.
High accuracy was maintained across different extended basis sets.
The approach proved effective for reasonably sized molecular fragments.

Conclusions:

Bootstrap embedding is successfully extended to handle extended basis sets.
This work enables more accurate studies of dynamic correlation in larger quantum systems.
The combination of BE and IAO localization is a significant step forward for quantum embedding methods.