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Related Concept Videos

Internal Energy02:00

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with initial internal energy, Uinitial, undergoes a change in energy (transfer of work or heat), and the final internal energy of the system is Ufinal. Change in internal energy equals the difference between Ufinal and Uinitial.
Internal Energy01:29

Internal Energy

The internal energy of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules or entities in the system. The kinetic energy of an individual molecule includes contributions due to its rotation and vibration, as well as its translational energy. The potential energy is associated only with the interactions between one molecule and the other molecules of the system. Neither the system's location nor its motion is of any consequence as far as the internal...
Induced Electric Dipoles01:28

Induced Electric Dipoles

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
The Molecular Nature of Internal Energy01:27

The Molecular Nature of Internal Energy

The internal energy of a molecule is determined by its degrees of freedom, including translational, rotational, and vibrational motions. In addition to these kinetic activities, the energy of molecules is also shaped by electronic energy, intermolecular forces, and the rest-mass energy of electrons and nuclei. These factors collectively influence the energy state of the molecules. The equipartition theorem of classical mechanics provides insight into this energy distribution. It posits that the...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

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Related Experiment Video

Updated: Jul 2, 2026

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

Coupled internal energy modes in DSMC.

Zakari S Eckert1, Michael A Gallis1

  • 1Sandia National Laboratories, Engineering Sciences Center, Albuquerque, New Mexico 87123, USA.

The Journal of Chemical Physics
|July 1, 2026
PubMed
Summary
This summary is machine-generated.

The Direct Simulation Monte Carlo (DSMC) method can accurately model gas vibrational energy relaxation, similar to the Landau-Teller model, by prohibiting multiple internal mode relaxations per collision. This ensures accurate simulations of gas dynamics.

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Last Updated: Jul 2, 2026

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Published on: July 19, 2019

Area of Science:

  • Chemical Physics
  • Computational Fluid Dynamics
  • Thermodynamics

Background:

  • The Landau-Teller model describes gas vibrational energy relaxation using first-order kinetics.
  • Direct Simulation Monte Carlo (DSMC) simulates collisions and tests internal energy modes for relaxation.
  • Reproducing Landau-Teller in DSMC requires prohibiting multiple internal mode relaxations per collision.

Purpose of the Study:

  • To analytically compare the Landau-Teller theory, vibrational master equation, and DSMC with and without multiple relaxation per collision.
  • To quantitatively examine the effect of allowing or prohibiting multiple relaxations in DSMC simulations.

Main Methods:

  • Analytical comparison of four models: Landau-Teller theory, vibrational master equation, and DSMC (allowing/prohibiting multiple relaxation).
  • Rigorous quantitative examination of DSMC's algorithmic choice on relaxation modeling.

Main Results:

  • Deviation from Landau-Teller in DSMC is minimal when allowing multiple relaxations, often less than statistical noise.
  • Neglecting direct coupling between internal modes in DSMC can lead to significant errors.

Conclusions:

  • DSMC can effectively model gas vibrational energy relaxation, aligning with the Landau-Teller model.
  • DSMC practitioners should carefully consider the impact of inter-modal coupling to avoid simulation inaccuracies.