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Related Concept Videos

Energy Diagrams - I01:14

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
Energy Diagrams - II01:10

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The slope...
Introduction to Enzyme Kinetics01:19

Introduction to Enzyme Kinetics

Enzyme kinetics studies the rates of biochemical reactions. Scientists monitor the reaction rates for a particular enzymatic reaction at various substrate concentrations. Additional trials with inhibitors or other molecules that affect the reaction rate may also be performed.
The experimenter can then plot the initial reaction rate or velocity (Vo) of a given trial against the substrate concentration ([S]) to obtain a graph of the reaction properties. For many enzymatic reactions involving a...
Energy Diagrams, Transition States, and Intermediates02:13

Energy Diagrams, Transition States, and Intermediates

Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products.  Peaks on the energy diagram represent stable structures with measurable lifetimes, while other...
Arrhenius Plots02:34

Arrhenius Plots

The Arrhenius equation relates the activation energy and the rate constant, k, for chemical reactions. In the Arrhenius equation, k = Ae−Ea/RT, R is the ideal gas constant, which has a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules.
The Arrhenius equation can be used to...
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...

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Related Experiment Video

Updated: Jun 18, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

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

Published on: July 19, 2019

Graph-based analysis of kinetics on multidimensional potential-energy surfaces.

T Okushima1, T Niiyama, K S Ikeda

  • 1Department of Physics, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu 525-8577, Japan. okushima@ike-dyn.ritsumei.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a novel saddle connectivity graph method for analyzing potential-energy landscapes and system kinetics. This approach efficiently identifies dominant transition pathways and reveals self-similar structures in atomic clusters.

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Area of Science:

  • Computational chemistry
  • Chemical physics
  • Materials science

Background:

  • Analyzing complex potential-energy landscapes is crucial for understanding chemical kinetics.
  • Existing methods often struggle with the high dimensionality and complexity of these landscapes.

Purpose of the Study:

  • To introduce and describe the saddle connectivity graph (SCG) method for analyzing potential-energy landscapes.
  • To demonstrate the application of SCG for studying the kinetics of realistic systems.
  • To explore the dynamical properties and topographical features of potential-energy landscapes.

Main Methods:

  • Development of an alternative graph-based analysis method: saddle connectivity graph (SCG).
  • Application of a Dijkstra-type shortest path algorithm to identify dynamically dominant transition pathways using kinetic costs.
  • Implementation of a coarse-graining procedure tailored for SCGs to analyze atomic clusters.

Main Results:

  • The SCG method successfully analyzes global topography and dynamical properties of potential-energy landscapes.
  • Dynamically dominant transition pathways were extracted using a shortest path algorithm.
  • Kinetic properties of Lennard-Jones clusters (13 and 38 atoms) were obtained using SCG coarse-graining.
  • A self-similar hierarchical structure was revealed in these clusters through iterative coarse-graining.

Conclusions:

  • The saddle connectivity graph method provides a powerful tool for analyzing complex potential-energy landscapes and chemical kinetics.
  • The coarse-graining procedure effectively reduces graph complexity and reveals hierarchical structures in atomic clusters.
  • Self-similarity is proposed as a common characteristic in many-atom Lennard-Jones clusters, suggesting broader applicability of the findings.