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

Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

556
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
556
Curvilinear Motion: Normal and Tangential Components01:27

Curvilinear Motion: Normal and Tangential Components

446
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
446
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

434
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...
434
Equation of Rotational Dynamics01:08

Equation of Rotational Dynamics

8.8K
Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
8.8K
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

1.1K
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
1.1K
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

1.5K
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
1.5K

You might also read

Related Articles

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

Sort by
Same author

Multilevel Fragmentation and Boundary Corrections for Accurate Vibrational Spectra of Large Molecules.

Journal of chemical theory and computation·2026
Same author

Mode-Selective Dual-Level Vibrational Perturbation Theory Assisted by Machine Learning for Rotational and Vibrational Spectra of Benzoic Acid and Aspirin.

The journal of physical chemistry. A·2026
Same author

Exploring the Origin of Molecular Chirality: A Standalone Suite of Tools to Visualize and Analyze Transition Current Density.

Journal of chemical theory and computation·2026
Same author

From Localized to Delocalized OH···O Hydrogen Bonds: Benchmark of Hierarchical Quantum Chemical Methods against Rotational Spectroscopy.

Journal of chemical theory and computation·2026
Same author

WMS-Rot: From quantum-chemical predictions to rotational spectral assignment and refinement.

The Journal of chemical physics·2026
Same author

Tensor structure and transport of centrifugal distortion constants: A representation-independent framework connecting spectroscopy and quantum chemistry beyond the linear regime.

The Journal of chemical physics·2026

Related Experiment Video

Updated: Aug 23, 2025

Direct Imaging of Laser-driven Ultrafast Molecular Rotation
10:52

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

9.8K

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates.

Marco Mendolicchio1, Julien Bloino2, Vincenzo Barone2

  • 1Scuola Superiore Meridionale, Largo S. Marcellino 10, Napoli I-80138, Italy.

Journal of Chemical Theory and Computation
|November 2, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new computational method for analyzing molecular vibrations using curvilinear coordinates. This approach enhances accuracy for complex molecules by reducing coupling effects, improving theoretical predictions.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K
Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.7K

Related Experiment Videos

Last Updated: Aug 23, 2025

Direct Imaging of Laser-driven Ultrafast Molecular Rotation
10:52

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

9.8K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K
Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

5.7K

Area of Science:

  • Computational Chemistry
  • Theoretical Chemistry
  • Molecular Spectroscopy

Background:

  • Anharmonic vibrations are crucial for understanding molecular behavior.
  • Traditional Cartesian coordinate methods face limitations with strong inter-mode couplings.
  • Accurate vibrational analysis is essential for predicting molecular properties.

Purpose of the Study:

  • To implement and validate a second-order perturbative approach for anharmonic vibrations using curvilinear internal coordinates.
  • To develop a more robust method for treating strong vibrational couplings, including Fermi resonances.
  • To demonstrate the advantages of curvilinear coordinates over Cartesian ones in vibrational analysis.

Main Methods:

  • A second-order perturbative approach combined with a variational treatment of strong couplings (GVPT2).
  • Utilized curvilinear internal coordinates, requiring expansion of the kinetic energy operator.
  • Tested the method on numerous cases, focusing on Fermi resonances.

Main Results:

  • The implementation successfully validates the GVPT2 approach in curvilinear coordinates.
  • Curvilinear coordinates significantly reduce inter-mode couplings compared to Cartesian methods.
  • Fermi resonances were effectively treated, confirming the method's reliability.

Conclusions:

  • The curvilinear coordinate-based GVPT2 method offers a significant simplification and improved accuracy.
  • This approach enhances the reliability of perturbative treatments for semi-rigid and flexible molecules.
  • It enables better decoupling of small- and large-amplitude motions for advanced theoretical studies.