Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Atomic Orbitals02:44

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 II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
Hybridization of Atomic Orbitals I03:24

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...
The Energies of Atomic Orbitals03:21

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.
Molecular Orbital Theory II03:51

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

Ceramic planar waveguide laser of non-aqueous tape casting fabricated YAG/Yb:YAG/YAG.

Scientific reports·2016
Same author

Influence of food groups on plasma total homocysteine for specific MTHFR C677T genotypes in Chinese population.

Molecular nutrition & food research·2016
Same author

NIR Light Propulsive Janus-like Nanohybrids for Enhanced Photothermal Tumor Therapy.

Small (Weinheim an der Bergstrasse, Germany)·2016
Same author

Smart Hydrogels with Inhomogeneous Structures Assembled Using Nanoclay-Cross-Linked Hydrogel Subunits as Building Blocks.

ACS applied materials & interfaces·2016
Same author

Synergy between von Hippel-Lindau and P53 contributes to chemosensitivity of clear cell renal cell carcinoma.

Molecular medicine reports·2016
Same author

Aerobic Degradation of Sulfadiazine by Arthrobacter spp.: Kinetics, Pathways, and Genomic Characterization.

Environmental science & technology·2016

Related Experiment Video

Updated: May 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion.

Lin Lin1, Mohan Chen, Chao Yang

  • 1Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 28, 2013
PubMed
Summary

The pole expansion and selected inversion (PEXSI) technique offers a computationally efficient alternative to matrix diagonalization for Kohn-Sham density functional theory (DFT) electronic structure calculations. This method achieves linear scaling for quasi-1D systems, enabling accurate calculations for large atomic systems.

More Related Videos

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization
05:37

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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: May 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization
05:37

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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 Chemistry
  • Materials Science

Background:

  • Kohn-Sham density functional theory (DFT) is a cornerstone for electronic structure calculations.
  • Traditional DFT methods often rely on matrix diagonalization, which becomes computationally prohibitive for large systems.
  • Atomic orbital discretization is a common approach in electronic structure calculations.

Purpose of the Study:

  • To present the application of the pole expansion and selected inversion (PEXSI) technique to atomic orbital-based Kohn-Sham DFT.
  • To derive analytic expressions for key physical quantities without relying on eigenvalues and eigenvectors.
  • To demonstrate the computational advantages and accuracy of PEXSI for large-scale electronic structure calculations.

Main Methods:

  • Application of the PEXSI technique to Kohn-Sham DFT with atomic orbital discretization.
  • Derivation of analytic expressions for charge density, total energy, Helmholtz free energy, and atomic forces (Hellmann-Feynman and Pulay).
  • Development of a method to update the chemical potential without Kohn-Sham eigenvalues.

Main Results:

  • PEXSI significantly reduces computational complexity compared to matrix diagonalization.
  • Linear scaling of PEXSI complexity with the number of atoms for quasi-1D systems (e.g., nanotubes).
  • Demonstrated feasibility of PEXSI for very large systems (10,000 atoms) with modest memory and wall clock time.
  • PEXSI maintains accuracy comparable to diagonalization for practical DFT calculations, as shown in geometry optimization of a 1024-atom nanotube.

Conclusions:

  • The PEXSI technique provides a highly efficient and accurate method for Kohn-Sham DFT electronic structure calculations.
  • PEXSI enables the study of significantly larger atomic systems than previously feasible.
  • The method is suitable for various materials, including insulating and metallic nanotubes, and maintains accuracy for complex tasks like geometry optimization.