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The Van der Waals Equation

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,...

Van der Waals Equation

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...

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

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 Interactions

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.

Valence Bond Theory and Hybridized Orbitals

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

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...

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Related Experiment Video

Updated: May 21, 2026

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

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

Published on: April 12, 2019

A simplified implementation of van der Waals density functionals for first-principles molecular dynamics

Jun Wu¹, François Gygi

¹Graduate Group in Applied Science, University of California Davis, Davis, California 95616, USA.

The Journal of Chemical Physics

|June 21, 2012

Summary

We present a simplified, numerically stable implementation of non-local van der Waals density functionals. This method accurately computes interaction energies and crystal structures, including those with hydrogen bonding.

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Last Updated: May 21, 2026

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

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Published on: April 12, 2019

New Features in Visual Dynamics 3.0

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

Computational Chemistry
Condensed Matter Physics
Quantum Chemistry

Background:

Accurate description of van der Waals interactions is crucial for predicting material properties.
Existing non-local van der Waals functionals can be computationally intensive and numerically challenging.
A simplified and robust implementation is needed for broader applicability.

Purpose of the Study:

To present a simplified numerical implementation of the non-local van der Waals correlation functional.
To provide complete expressions for the self-consistent correlation potential and stress tensor.
To implement and test five versions of van der Waals density functionals.

Main Methods:

Simplified implementation of the non-local van der Waals correlation functional, removing the logarithmic singularity.
Combination with various exchange functionals to create five distinct van der Waals density functionals.
Application to benchmark systems: benzene-water complex interaction energy and benzene crystal parameters.

Main Results:

Successful computation of interaction energy for the benzene-water complex.
Accurate prediction of equilibrium cell parameters for benzene crystal.
Calculation of equilibrium structures for aspirin polymorphs, considering hydrogen bonding and dispersion.

Conclusions:

The simplified implementation offers a numerically stable and efficient approach to van der Waals density functionals.
The method accurately captures both non-covalent interactions and structural properties of molecular crystals.
This work provides a valuable tool for materials science and computational chemistry research.