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Related Concept Videos

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Thermodynamic Potentials01:26

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...
Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
Deviation from Ideal Behaviour01:23

Deviation from Ideal Behaviour

Real gases do not perfectly obey the ideal gas laws, especially at high pressures and low temperatures or when they are about to condense to a liquid. These deviations occur due to intermolecular forces between gas molecules. Repulsive forces aid expansion and are significant when molecules are very close together, typically at high pressure. Attractive forces assist compression and have a longer range, being effective over several molecular diameters. They become significant when molecules are...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Constant pressure ab initio molecular dynamics with discrete variable representation basis sets.

Zhonghua Ma1, Mark Tuckerman

  • 1Department of Chemistry, New York University, New York, New York 10003, USA. zhma@nyu.edu

The Journal of Chemical Physics
|November 16, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a method for ab initio molecular dynamics using discrete variable representation (DVR) basis sets. This enables accurate simulations in the isothermal-isobaric ensemble with flexible boxes, crucial for condensed matter physics.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Last Updated: Jun 6, 2026

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Computational Chemistry
  • Condensed Matter Physics
  • Materials Science

Background:

  • Ab initio molecular dynamics (AIMD) is essential for simulating material properties.
  • Accurate forces are critical for converged AIMD simulations.
  • Discrete Variable Representation (DVR) basis sets offer advantages in computational efficiency and accuracy.

Purpose of the Study:

  • To extend the DVR basis set framework to isothermal-isobaric (NPT) ensemble AIMD.
  • To develop and validate a DVR-based pressure tensor expression for NPT AIMD.
  • To demonstrate the application of this method for flexible simulation boxes.

Main Methods:

  • Implementation of DVR basis sets within AIMD.
  • Derivation of a DVR-based pressure tensor expression using Kohn-Sham density functional theory.
  • Coupling with Martyna-Tobias-Klein and Car-Parrinello algorithms.
  • Testing with a 64-atom silicon system in a flexible box.

Main Results:

  • Successful application of DVR basis sets for NPT AIMD with flexible boxes.
  • Validated DVR-based pressure tensor expression shows convergence with basis set size.
  • Demonstrated the feasibility and accuracy of the developed approach.

Conclusions:

  • The DVR basis set approach is effective for NPT AIMD with flexible simulation boxes.
  • This method provides converged energies and forces, enhancing simulation reliability.
  • The developed framework is a valuable tool for studying condensed matter systems.