Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...

Centroid of a Body: Problem Solving

Centroid of a Body: Problem Solving

The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance point, and even its design. In this context, consider a thin wire bent in the form of a quarter circular arc. Polar coordinates are used to calculate the centroid. The wire is first divided into small differential elements of a length equal to the radius multiplied by the differential angle.
The x-coordinates and y-coordinates of each element's...

Kinetic Energy for a Rigid Body

Kinetic Energy for a Rigid Body

Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.

Central-Force Motion

Central-Force Motion

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 radial distance...

Centroid for the Paraboloid of Revolution

Centroid for the Paraboloid of Revolution

The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...

Applications of Integration to Find Centers of Mass

Applications of Integration to Find Centers of Mass

Rotational equilibrium provides a natural framework for defining the center of mass of a system. For a plank balanced on a pivot with two unequal masses, equilibrium is achieved when the net torque about the pivot is zero. Torque is defined as the product of a force and its perpendicular distance from the pivot. When the torques due to all forces cancel, the pivot coincides with the center of mass of the system.For a system composed of several discrete point masses, the center of mass lies at...

You might also read

Related Articles

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

Sort by

Same author

Proton Tautomerism for Anhydrous Superprotonic Conduction in 1,2,3-Triazolium Dihydrogen Phosphate Crystal.

Angewandte Chemie (International ed. in English)·2026

Same author

Computation of the heat capacity of water from first principles.

The Journal of chemical physics·2025

Same author

Structural and Energetic Analysis of the CmABCB1 Substrate Transport.

Journal of chemical theory and computation·2025

Same author

<i>Ab initio</i>path-integral simulations of hydrogen-isotope diffusion in face-centred cubic metals.

Journal of physics. Condensed matter : an Institute of Physics journal·2025

Same author

Self-learning path integral hybrid Monte Carlo with mixed ab initio and machine learning potentials for modeling nuclear quantum effects in water.

The Journal of chemical physics·2024

Same author

High-Temperature Atomic Diffusion and Specific Heat in Quasicrystals.

Physical review letters·2024

Search research articles

Related Experiment Video

Updated: May 22, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates.

Motoyuki Shiga¹, Hiroshi Fujisaki

¹Center for Computational Science and E-systems, Japan Atomic Energy Agency, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8587, Japan.

The Journal of Chemical Physics

|May 16, 2012

Summary

We introduce the "centroid IRC," a new reaction coordinate for quantum systems. It reveals that quantum effects significantly lower energy barriers in proton transfer reactions for molecules like NH3 and N2H5(-).

Related Experiment Videos

Last Updated: May 22, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Area of Science:

Quantum Chemistry
Theoretical Chemistry
Chemical Dynamics

Background:

The Intrinsic Reaction Coordinate (IRC) is crucial for understanding chemical reaction pathways.
Classical approximations often neglect significant nuclear quantum effects in chemical reactions.
Path integral simulations are essential for accurately describing quantum many-body systems.

Purpose of the Study:

To generalize the IRC concept for quantum many-body systems using imaginary-time path integral theory.
To introduce and compute the 'centroid IRC' as a measure of minimum free energy pathways.
To investigate the impact of nuclear quantum effects on proton transfer reactions.

Main Methods:

Development of the centroid IRC based on mass-weighted ring polymer centroids.
Implementation of a numerical procedure combining ab initio path integral simulations with the string method.
Application to the intramolecular proton transfer in NH(3) and intermolecular proton transfer in N(2)H(5)(-), including deuterated isotopomers.

Main Results:

For NH(3) intramolecular proton transfer, the centroid IRC shows a ~20% reduction in the free energy barrier compared to classical calculations at room temperature.
The centroid IRC for N(2)H(5)(-) intermolecular proton transfer significantly deviates from the classical IRC.
Nuclear quantum effects drastically reduce the free energy barrier in the intermolecular proton transfer of N(2)H(5)(-).

Conclusions:

The centroid IRC provides a more accurate description of reaction pathways in quantum systems.
Nuclear quantum effects play a critical role in determining reaction barriers, particularly in proton transfer reactions.
This generalized IRC method offers a powerful tool for studying quantum dynamics in complex chemical systems.