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

Gravitational Potential Energy for Extended Objects01:07

Gravitational Potential Energy for Extended Objects

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...
Direction Cosines of a Vector01:29

Direction Cosines of a Vector

Direction cosines, which help describe the orientation of a vector with respect to the coordinate axes, are an essential concept in the field of vector calculus. Consider vector A that is expressed in terms of the Cartesian vector form using i, j, and k unit vectors. The magnitude of vector A is defined as the square root of the sum of the squares of its components. The direction of this vector with respect to the x, y, and z axes is defined by the coordinate direction angles α, β, and γ,...
Two-Dimensional Force System01:20

Two-Dimensional Force System

A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
Orthogonal Trajectories01:26

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
Polar Equations of Conics01:29

Polar Equations of Conics

A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can describe any conic...

You might also read

Related Articles

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

Sort by
Same author

Non-adiabatic quantum interference and complex formation in ultracold collisions of Rb with KRb.

Physical chemistry chemical physics : PCCP·2026
Same author

Mixed Quantum/Classical Theory Approach to Rotationally Inelastic Molecular Collisions Implemented on a Quantum Computer.

Journal of chemical theory and computation·2025
Same author

Low duty cycle pulsed UV technique for spectroscopy of aluminum monochloride.

Optics express·2024
Same author

Correction: The Li + CaF → Ca + LiF chemical reaction under cold conditions.

Physical chemistry chemical physics : PCCP·2023
Same author

The Li + CaF → Ca + LiF chemical reaction under cold conditions.

Physical chemistry chemical physics : PCCP·2023
Same author

Signatures of Non-universal Quantum Dynamics of Ultracold Chemical Reactions of Polar Alkali Dimer Molecules with Alkali Metal Atoms: Li(<sup>2</sup>S) + NaLi(<i>a</i><sup>3</sup>Σ<sup>+</sup>) → Na(<sup>2</sup>S) + Li<sub>2</sub>(<i>a</i><sup>3</sup>Σ<sub></sub><sup>+</sup>).

The journal of physical chemistry letters·2023

Related Experiment Video

Updated: Jun 4, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials.

Xuan Li1, Daniel A Brue, Brian K Kendrick

  • 1Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA. li@nhn.ou.edu

The Journal of Chemical Physics
|February 17, 2011
PubMed
Summary

This study introduces a new method for treating collinear conical intersections in triatomic systems using a geometric phase angle approach. This advances the understanding and calculation of quantum mechanical effects in molecular systems.

More Related Videos

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Related Experiment Videos

Last Updated: Jun 4, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Molecular Physics

Background:

  • Collinear conical intersections are crucial in molecular dynamics and quantum chemistry.
  • Geometric phase effects significantly influence the behavior of molecular systems near these intersections.
  • Accurate treatment of these phenomena is essential for predicting molecular properties and reactions.

Purpose of the Study:

  • To present a novel method for treating collinear conical intersections in triatomic systems.
  • To incorporate geometric phase effects using a general vector potential approach.
  • To develop an introductory phase angle method for these calculations.

Main Methods:

  • Utilizing a general vector potential (gauge theory) approach.
  • Employing hyperspherical coordinates for the system.
  • Deriving the geometric phase angle (η) in terms of internal coordinates.
  • Applying the method to a spin-aligned quartet lithium triatomic system.

Main Results:

  • An analytical form for the vector potentials associated with collinear conical intersections was derived.
  • The geometric phase angle (η) was explicitly calculated for the lithium system.
  • The methodology was demonstrated for a specific triatomic A(3) system.

Conclusions:

  • The presented phase angle method offers a viable approach for treating collinear conical intersections.
  • The derived analytical forms and calculated phase angles provide valuable data for theoretical studies.
  • The methodology is extendable to other molecular systems like AB(2) and ABC.