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

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.

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...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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...

Electron Orbital Model

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

You might also read

Related Articles

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

Sort by

Same author

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

Journal of chemical theory and computation·2026

Same author

Mutasynthesis and Antibiotic Activity of Mupirocin Analogues.

Chembiochem : a European journal of chemical biology·2026

Same author

Connection between <i>GW</i> and Extended Coupled Cluster.

Journal of chemical theory and computation·2026

Same author

Scalar machine learning of tensorial quantities-Born effective charges from monopole models.

The Journal of chemical physics·2026

Same author

Drop-on-fixed-target reaction initiation approach for serial and time-resolved crystallography.

IUCrJ·2026

Same author

Standardized numbering and alignment of the KPC family of β-lactamases.

Antimicrobial agents and chemotherapy·2026

Search research articles

Related Experiment Video

Updated: Mar 29, 2026

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

Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set.

Andreas Grüneis¹, George H Booth², Martijn Marsman¹

¹Faculty of Physics and Center for Computational Materials Science, University Vienna , Sensengasse 8/12, A-1090 Vienna, Austria.

Journal of Chemical Theory and Computation

|November 26, 2015

Summary

Natural orbitals significantly reduce computational costs for quantum chemistry calculations using plane wave basis sets. This method, evaluated with Møller-Plesset perturbation theory (MP2), enables efficient correlated calculations for atoms and molecules.

More Related Videos

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

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: Mar 29, 2026

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

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

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 Chemistry
Quantum Mechanics
Materials Science

Background:

Correlated calculations in quantum chemistry are computationally intensive.
Plane wave basis sets under periodic boundary conditions are common for condensed matter systems.
Reducing computational cost is crucial for studying larger systems.

Purpose of the Study:

To demonstrate the efficiency of natural orbitals in reducing computational cost for wave function based correlated calculations.
To apply natural orbitals in conjunction with plane wave basis sets and periodic boundary conditions.
To test the implementation using various quantum chemistry methods.

Main Methods:

Evaluation of natural orbitals using second-order Møller-Plesset perturbation theory (MP2).
Development of an approximation to reduce computational scaling from O(N^5) to O(N^4).
Application to coupled-cluster singles and doubles (CCSD) and Quantum Monte Carlo calculations for H2.
Calculation of atomization energies for LiH molecule and solid.

Main Results:

Natural orbitals effectively reduce the computational cost of correlated calculations.
An O(N^4) scaling approximation provides significant reduction in virtual orbitals.
MP2 and CCSD calculations on H2 and LiH demonstrate the method's applicability.
Accurate atomization energies were obtained for LiH.

Conclusions:

Natural orbitals are a powerful tool for accelerating correlated electronic structure calculations.
The developed approximation offers a practical way to further enhance computational efficiency.
This approach is beneficial for studying extended systems and complex molecules.