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Related Concept Videos

Conservative Forces01:14

Conservative Forces

According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of...
Force and Potential Energy in One Dimension01:13

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
Force and Potential Energy in Three Dimensions01:04

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
Conservative Forces01:03

Conservative Forces

Conservative forces are an essential concept in the field of mechanical engineering. Understanding the properties and characteristics of these forces is crucial to the design and analysis of mechanical systems.
Conservative forces are forces that are dependent only on the initial and final positions of an object and that are independent of the path that the object takes between these positions. These forces conserve energy, which means that the work done by the force is independent of the path...
Work-Energy Theorem for Motion Along a Curve01:09

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be considered a sum of many infinitesimal paths, each of which is a straight path. The force on the particle can be considered constant along any such infinitesimal path so that the work-energy theorem can be applied along it. So, it is also valid for the sum of these paths. The net work done is the integral of the work done along the infinitesimal...
Classical Mechanics01:12

Classical Mechanics

Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...

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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

From force fields to dynamics: classical and quantal paths.

D G Truhlar, M S Gordon

    Science (New York, N.Y.)
    |August 3, 1990
    PubMed
    Summary
    This summary is machine-generated.

    Reaction path methods bridge electronic structure and chemical dynamics. Quantal tunneling paths deviate from classical ones, especially with high barriers and hydrogenic motion, requiring broader force field mapping.

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    Area of Science:

    • Computational Chemistry
    • Chemical Dynamics
    • Quantum Mechanics

    Background:

    • Reaction path methods connect electronic structure calculations with chemical dynamics.
    • Classical paths often rely on minimum energy paths (MEP) and local force fields.
    • Quantum effects like tunneling become crucial for reactions with high energy barriers and significant hydrogenic motion.

    Purpose of the Study:

    • To explore the nuances of reaction path methods in chemical dynamics.
    • To investigate the deviation of quantal reaction paths from classical minimum energy paths.
    • To highlight the importance of reaction swath and advanced potential energy surface mapping.

    Main Methods:

    • Utilizing reaction path methods to analyze chemical reactions.
    • Considering quantum mechanical tunneling effects for specific reaction scenarios.
    • Mapping force fields over extended regions (reaction swath) beyond the MEP.
    • Employing global/semiglobal analytic functions or direct dynamics computations.

    Main Results:

    • Quantal reaction paths can significantly deviate from classical MEPs, particularly with increased MEP curvature in mass-scaled coordinates.
    • Tunneling paths tend to follow a 'corner-cutting' trajectory relative to the MEP.
    • Accurate modeling requires considering a broader 'reaction swath' of the potential energy surface.

    Conclusions:

    • Reaction path methods are essential for accurately describing chemical dynamics, especially when quantum effects are prominent.
    • The deviation of quantal paths necessitates a more comprehensive mapping of the force field.
    • These methods are applicable across various systems, from gas-phase reactions to solutions and interfaces.