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

Radius of Gyration of an Area01:12

Radius of Gyration of an Area

2.5K
The second moment of area, also known as the moment of inertia of area, is a crucial factor in understanding an object's resistance against bending deformation, or stiffness. To accurately estimate the second moment of area along any axis, one needs to concentrate all areas associated with that object into a thin strip, which should be placed parallel to that particular axis.
2.5K
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

19.3K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
19.3K
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

762
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
762
Spherical Coordinates01:23

Spherical Coordinates

14.4K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
14.4K
Central-Force Motion01:17

Central-Force Motion

683
The central force system operates by exerting a force on an object directed towards a fixed point, typically the origin, with the force magnitude determined by the object's distance from this fixed point. In the context of an object with mass 'm,' polar coordinates are employed to express the equation of motion. Notably, the azimuthal component of force is nonexistent in this system. A comprehensive rewrite and integration of this equation reveal that the product of the squared...
683
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

485
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
485

You might also read

Related Articles

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

Sort by
Same author

Methodological considerations for evaluating deep learning segmentation models in digital pathology whole-slide images.

Journal of medical imaging (Bellingham, Wash.)·2026
Same author

A fovea-centered retinal signature linked to plasma biomarkers in prodromal Alzheimer's disease.

Alzheimer's & dementia (Amsterdam, Netherlands)·2026
Same author

Reply: Hydrodissection for conduit harvesting: Catch the wave!

JTCVS open·2026
Same author

Experimental evaluation of eco-friendly exfoliation strategies for Tour-method graphene oxide.

Scientific reports·2026
Same author

Can riboflavin offer a novel personalised strategy for maintaining healthy blood pressure in pregnancy in populations globally?

BMJ nutrition, prevention & health·2026
Same author

Gpr75 Deletion in Adipocytes Protects From Diet-Induced Obesity: Changes in Glucose Homeostasis and Inflammatory Responses.

FASEB journal : official publication of the Federation of American Societies for Experimental Biology·2026

Related Experiment Video

Updated: Dec 31, 2025

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

13.1K

Software to obtain spatially localized functions from different radial functions.

Jesús Sánchez-Márquez1, Victor García1, David Zorrilla2

  • 1Departamento de Química-Física, Facultad de Ciencias, Campus Universitario Río San Pedro, Universidad de Cádiz, 11510, Puerto Real, Cádiz, Spain.

Journal of Computer-Aided Molecular Design
|January 4, 2020
PubMed
Summary

We developed an algorithm for simplified box orbital functions (SBOs) in quantum chemistry. This method optimizes coefficients and radii, simplifying calculations for large molecular systems and confined environments.

Keywords:
Basis set generationConfined systemsNon-standard basis-setSBOSpatially localized functions

More Related Videos

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.7K
A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:46

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

3

Related Experiment Videos

Last Updated: Dec 31, 2025

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
08:39

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles

Published on: October 16, 2017

13.1K
Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

4.7K
A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:46

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

3

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Simplified Box Orbital Functions (SBOs) are valuable in quantum chemistry.
  • SBOs offer spatial restriction and can be defined within specific intervals.
  • Their application in large chemical systems and confined environments is beneficial.

Purpose of the Study:

  • To develop an algorithm for obtaining SBOs with optimized coefficients.
  • To enable the determination of optimal radii and coefficients for SBOs.
  • To provide flexibility for users to define specific radii and calculate corresponding coefficients.

Main Methods:

  • An algorithm was developed for fitting functions to determine SBO coefficients.
  • The method allows for the optimization of the radius parameter.
  • User-defined radii can be used to calculate SBO coefficients.

Main Results:

  • The algorithm successfully generates SBOs with optimized coefficients and radii.
  • SBOs demonstrate utility in calculating molecular properties.
  • The method reduces complexity in integral calculations for large systems like atomic clusters.

Conclusions:

  • The developed algorithm provides an efficient way to obtain SBOs.
  • SBOs are suitable for studying confined systems and large chemical systems.
  • SBO functions yield results comparable to standard basis sets for molecular reactivity calculations.