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 I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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

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.

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

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.

You might also read

Related Articles

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

Sort by

Same author

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 author

Impact of therapeutic oral health education program in individuals with systemic sclerosis: A prospective study.

Journal of education and health promotion·2026

Same author

Pd-Decorated Ag-CeO<sub>2</sub>/PANI Nanocomposite: Fabrication, Application in the Synthesis of 2,3-Dihydroquinazolin-4(1<i>H</i>)-ones and Tetrahydrobenzo[<i>b</i>]pyrans, Antimicrobial Activity Evaluation, and Computational Study.

ACS applied bio materials·2026

Same author

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

The Journal of chemical physics·2026

Same author

Impact of oral health education program in children suffering from attention deficit hyperactivity disorder: A cross-sectional study.

Journal of education and health promotion·2026

Same author

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

Journal of chemical theory and computation·2026

Search research articles

Related Experiment Video

Updated: Jul 8, 2025

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

Toward Linear Scaling Auxiliary-Field Quantum Monte Carlo with Local Natural Orbitals.

Jo S Kurian¹, Hong-Zhou Ye², Ankit Mahajan^1,2

¹Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States.

Journal of Chemical Theory and Computation

|December 19, 2023

Summary

We developed a new method, local natural orbital-auxiliary-field quantum Monte Carlo (LNO-AFQMC), for faster quantum chemistry calculations. This approach achieves linear scaling, significantly reducing computational costs for complex molecular systems.

More Related Videos

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

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

Related Experiment Videos

Last Updated: Jul 8, 2025

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

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

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

Area of Science:

Computational chemistry
Quantum mechanics
Materials science

Background:

Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for electronic structure calculations.
Traditional AFQMC methods face challenges with computational scaling for larger systems.
Developing efficient and scalable quantum chemistry methods is crucial for advancing scientific discovery.

Purpose of the Study:

To develop a linear-scaling variant of AFQMC.
To reduce the computational cost of electronic structure calculations.
To enable accurate calculations for larger and more complex molecular systems.

Main Methods:

Introduction of local natural orbitals (LNOs) into the AFQMC framework.
Performing independent AFQMC calculations for each localized occupied orbital.
Utilizing a truncated set of tailored orbitals for each calculation.

Main Results:

The proposed LNO-AFQMC method exhibits linear scaling with system size.
Demonstrated significant cost reductions for molecular problems with hundreds to thousands of orbitals.
Observed faster convergence of energy differences compared to total energies.
LNO-AFQMC proved more cost-effective than canonical AFQMC even for small systems.

Conclusions:

LNO-AFQMC offers a computationally efficient approach for quantum chemistry.
The method is well-suited for applications in chemistry and material science due to rapid energy difference convergence.
This work enables linear-scaling AFQMC calculations for strongly correlated systems, potentially transforming ab initio quantum chemistry.