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

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

Distribution of Molecular Speeds

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

Thermodynamic Potentials

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

Adiabatic Processes for an Ideal Gas

Adiabatic Processes for an Ideal Gas

When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...

Absorption of Radiation

Absorption of Radiation

The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:

You might also read

Related Articles

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

Sort by

Same author

Integrating Charge Equilibration with Equivariant Machine-Learning Interatomic Potentials.

Journal of chemical theory and computation·2026

Same author

Erasing dielectric breakdown artifacts to machine-learn charged Pt-water interfaces.

The Journal of chemical physics·2026

Same author

Kinetic restructuring of catalyst active sites: a MACE-APE study of fluxional Pd<sub><i>n</i></sub>/MgO (<i>n</i> = 3-11) clusters.

Faraday discussions·2026

Same author

DSKO: Dancing through DFTB Parametrization.

Journal of chemical theory and computation·2026

Same author

Simulating quadrupolar NMR dynamics in solid electrolyte Li10GeP2S12.

The Journal of chemical physics·2026

Same author

Interplay between shape and composition in bimetallic nanoparticles revealed by an efficient optimal-exchange optimization algorithm.

The Journal of chemical physics·2026

Search research articles

Related Experiment Video

Updated: Jan 17, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

On Boltzmann averaging in ab initio thermodynamics.

Hendrik H Heenen¹, Karsten Reuter¹

¹Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.

The Journal of Chemical Physics

|September 15, 2025

Summary

This study introduces Boltzmann averaging to account for higher-energy surface configurations in ab initio thermodynamics. This approach provides a more accurate prediction of surface stability by considering thermal accessibility beyond just the lowest energy state.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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

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

Published on: December 4, 2017

Related Experiment Videos

Last Updated: Jan 17, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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

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

Published on: December 4, 2017

Area of Science:

Computational materials science
Surface science
Physical chemistry

Background:

Ab initio thermodynamics predicts surface stability using computationally efficient methods.
Current methods often equate stability with the lowest surface free energy structure.
This overlooks the potential contribution of higher-energy configurations.

Purpose of the Study:

To investigate the inclusion of thermally accessible, higher-energy surface configurations in thermodynamic predictions.
To develop a robust method for calculating ensemble averages of surface properties.
To provide a more accurate understanding of surface behavior under varying conditions.

Main Methods:

Analytical derivation of Boltzmann averaging for extended surface configurations.
Computation of surface energetics within periodic boundary condition supercells.
Exhaustive sampling within a surface unit-cell exceeding the system's correlation length.
Application to a lattice-gas Hamiltonian model for oxygen adsorption on Pd(100).

Main Results:

Demonstrated that Boltzmann averaging can accurately capture the thermal accessibility of competing surface configurations.
Showed that converged averages require a candidate pool from exhaustive sampling beyond the correlation length.
Highlighted that averaging over small, ad hoc pools is generally ill-defined.
Illustrated the practical application using oxygen adsorption on Pd(100).

Conclusions:

Boltzmann averaging offers a more complete picture of surface thermodynamics than relying solely on the lowest energy state.
Accurate ensemble averages necessitate comprehensive sampling strategies.
The findings are crucial for precise predictions in surface science and catalysis.