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

Drawing Free-body Diagrams: Rules01:16

Drawing Free-body Diagrams: Rules

15.7K
The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams are useful in analyzing forces acting on an object or system, and are employed extensively in the study and application of Newton's laws of motion. The steps to draw a free-body diagram are listed below:
15.7K
Graphing the Wave Function01:13

Graphing the Wave Function

3.0K
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
3.0K
Exceptions to the Octet Rule02:55

Exceptions to the Octet Rule

37.2K
Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:
37.2K
Phase Transitions02:31

Phase Transitions

22.7K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
22.7K
Lewis Symbols and the Octet Rule02:36

Lewis Symbols and the Octet Rule

80.3K
Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a model called the Lewis model that simplified the depiction of chemical bond formation and provided straightforward explanations for the chemical bonds seen in most common compounds.
80.3K
The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

72.3K
To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the...
72.3K

You might also read

Related Articles

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

Sort by
Same author

A Fresh Look at Signatures of <i>s</i>-Wave Scattering: Symmetry and the Breakdown of the Born-Oppenheimer Approximation.

The journal of physical chemistry. A·2026
Same author

Collision-induced fragmentation of the EMI-BF4 propellant in electrospray thrusters: Ab initio molecular dynamics simulations.

The Journal of chemical physics·2026
Same author

Dynamic breaking of mirror symmetry in spin-dependent electron transport through chiral media causes enantiomeric excesses.

Science advances·2026
Same author

Optical Properties of New Donor-Acceptor Dyes for RNA Imaging: Insights from Ab Initio and Hückel's Model Calculations.

The journal of physical chemistry. B·2026
Same author

Equation-of-motion coupled-cluster methods for doubly ionized and doubly electron-attached states with single, double, and triple substitutions: Theory, implementation, and benchmarks.

The Journal of chemical physics·2026
Same author

Analytic gradients for EOM-DEA-CCSD and EOM-DIP-CCSD: Theory, implementation, and application to diradicals.

The Journal of chemical physics·2026

Related Experiment Video

Updated: Jan 21, 2026

Mammalian Cell Division in 3D Matrices via Quantitative Confocal Reflection Microscopy
10:22

Mammalian Cell Division in 3D Matrices via Quantitative Confocal Reflection Microscopy

Published on: November 29, 2017

9.6K

Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices.

Pavel Pokhilko1, Anna I Krylov1

  • 1Department of Chemistry , University of Southern California , Los Angeles , California 90089-0482 , United States.

The Journal of Physical Chemistry Letters
|August 7, 2019
PubMed
Summary
This summary is machine-generated.

This study extends molecular orbital theory to analyze tensor properties like spin-orbit couplings (SOCs) in complex molecules. The new method provides quantitative insights into electronic transitions and interstate properties, aiding in understanding chemical phenomena.

More Related Videos

A Reproducible Computerized Method for Quantitation of Capillary Density using Nailfold Capillaroscopy
05:17

A Reproducible Computerized Method for Quantitation of Capillary Density using Nailfold Capillaroscopy

Published on: October 27, 2015

9.4K
Infrared Degenerate Four-wave Mixing with Upconversion Detection for Quantitative Gas Sensing
10:42

Infrared Degenerate Four-wave Mixing with Upconversion Detection for Quantitative Gas Sensing

Published on: March 22, 2019

6.6K

Related Experiment Videos

Last Updated: Jan 21, 2026

Mammalian Cell Division in 3D Matrices via Quantitative Confocal Reflection Microscopy
10:22

Mammalian Cell Division in 3D Matrices via Quantitative Confocal Reflection Microscopy

Published on: November 29, 2017

9.6K
A Reproducible Computerized Method for Quantitation of Capillary Density using Nailfold Capillaroscopy
05:17

A Reproducible Computerized Method for Quantitation of Capillary Density using Nailfold Capillaroscopy

Published on: October 27, 2015

9.4K
Infrared Degenerate Four-wave Mixing with Upconversion Detection for Quantitative Gas Sensing
10:42

Infrared Degenerate Four-wave Mixing with Upconversion Detection for Quantitative Gas Sensing

Published on: March 22, 2019

6.6K

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Spectroscopy

Background:

  • One-particle transition density matrices and natural transition orbitals are crucial for describing electronic transitions and interstate properties in many-body systems.
  • Analyzing tensor properties, such as spin-orbit couplings (SOCs), requires methods that can handle states with different spin projections.

Purpose of the Study:

  • To extend the formalism of transition density matrices and natural transition orbitals to the analysis of tensor properties, specifically spin-orbit couplings (SOCs).
  • To develop a uniform approach for treating transitions between states with arbitrary spin projections using spinless density matrices and Wigner-Eckart's theorem.

Main Methods:

  • Utilized spinless density matrices and Wigner-Eckart's theorem to uniformly describe transitions between states with varying spin projections.
  • Applied the extended formalism to analyze equation-of-motion coupled-cluster (EOM-CC) calculations.
  • Investigated two transition metal complexes to illustrate the capabilities of the developed tool.

Main Results:

  • The extended formalism provides a quantitative description of electronic transitions and interstate properties, including SOCs.
  • The analysis yields quantitative contributions of hole-particle pairs to many-body matrix elements.
  • The method helps rationalize the magnitude of computed SOCs in relation to El-Sayed's rules.

Conclusions:

  • The developed approach offers a powerful new tool for the quantitative analysis of tensor properties and electronic transitions in complex molecular systems.
  • This method facilitates a deeper understanding of spin-orbit couplings and their role in chemical phenomena, particularly in transition metal complexes.
  • The formalism provides both pictorial and quantitative insights into electronic transitions and their underlying mechanisms.