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

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.

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 I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

You might also read

Related Articles

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

Sort by

Same author

First-Principles Analysis of Protonation-Induced Electronic Effects in Tetrakis(<i>p</i>-aminophenyl)porphyrin (TAPP).

The journal of physical chemistry. A·2026

Same author

Probing the Ultrafast Photodynamics of Dihydroazulene with In Silico Time-Resolved Photoelectron Spectroscopy and Ultrafast Electron Diffraction.

The journal of physical chemistry. A·2026

Same author

Complete Active Space Self-Consistent Field with GPU-Accelerated Density Fitting.

Journal of chemical theory and computation·2026

Same author

Shadow excited state molecular dynamics with the ΔSCF method.

The Journal of chemical physics·2026

Same author

Accelerating CCSD(T) on Graphical Processing Units (GPUs).

The journal of physical chemistry. A·2026

Same author

Robust and Automated Force Field Parameterization Using Validation Sets and Active Learning.

Journal of chemical theory and computation·2026

Search research articles

Related Experiment Video

Updated: Apr 10, 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

An atomic orbital-based formulation of the complete active space self-consistent field method on graphical processing

Edward G Hohenstein¹, Nathan Luehr¹, Ivan S Ufimtsev¹

¹Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA.

The Journal of Chemical Physics

|June 15, 2015

Summary

This summary is machine-generated.

We developed a new algorithm for complete active space self-consistent field (CASSCF) computations, leveraging sparsity and GPUs. This enables larger molecular system calculations and analytic gradient computations for advanced computational chemistry.

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: Apr 10, 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 Chemistry
Materials Science

Background:

Complete active space self-consistent field (CASSCF) methods are crucial for accurately describing electron correlation in complex molecular systems.
Existing CASSCF algorithms face scalability challenges, limiting their application to smaller systems compared to single-reference methods.

Purpose of the Study:

To develop and implement an efficient algorithm for CASSCF orbital optimization.
To enhance the applicability of CASSCF to larger molecular systems.
To enable the computation of analytic gradients for CASSCF energies.

Main Methods:

Developed a novel CASSCF orbital optimization algorithm utilizing sparsity in the atomic orbital (AO) basis.
Implemented the algorithm on graphical processing units (GPUs) for accelerated computation.
Integrated analytic gradient calculations, also benefiting from GPU acceleration and AO sparsity.

Main Results:

The new algorithm significantly increases the applicability of CASSCF, enabling calculations on systems with over one thousand atoms.
GPU acceleration and AO sparsity lead to substantial performance improvements in CASSCF computations.
Analytic gradients for CASSCF energies are now efficiently computable for large systems.

Conclusions:

The developed GPU-accelerated, sparsity-aware CASSCF algorithm overcomes previous scalability limitations.
This advancement opens new possibilities for accurate electronic structure calculations in large and complex molecular systems.
The ability to compute analytic gradients further enhances the utility of CASSCF for geometry optimization and vibrational analysis.