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Van der Waals Equation01:10

Van der Waals Equation

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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...
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Van der Waals Interactions01:24

Van der Waals Interactions

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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.
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The Van der Waals Equation01:26

The Van der Waals Equation

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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,...
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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

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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.
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Molecular Geometry and Dipole Moments02:36

Molecular Geometry and Dipole Moments

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The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:
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Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Related Experiment Video

Updated: Apr 12, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

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

Published on: October 12, 2019

8.5K

Linear-Scaling and Memory-Efficient Implementation of van-der-Waals Interaction (DFT-D3) for Large Systems.

Han-Zhi Luo1, Cheng Shang1, Zhi-Pan Liu1,2

  • 1State Key Laboratory of Porous Materials for Separation and Conversion, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Key Laboratory of Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China.

Journal of Chemical Theory and Computation
|April 10, 2026
PubMed
Summary
This summary is machine-generated.

We developed LASP-D3, a fast GPU implementation for van der Waals (vdW) interactions in large atomic simulations. This method accelerates calculations for materials like LiTaCl6, crucial for understanding ion diffusion and conductivity.

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Area of Science:

  • Computational materials science
  • Condensed matter physics
  • Physical chemistry

Background:

  • Van der Waals (vdW) interactions are fundamental to material properties but computationally intensive for large systems.
  • Accurate atomic simulations require efficient methods to include long-range vdW forces.

Purpose of the Study:

  • To develop a highly efficient GPU implementation of the DFT-D3 method for vdW corrections in large-scale atomic simulations.
  • To enable fast vdW calculations compatible with machine-learning potentials.

Main Methods:

  • Implemented the DFT-D3 method using CUDA for GPU acceleration (LASP-D3).
  • Achieved linear-scaling time complexity O(N) for periodic systems.
  • Combined LASP-D3 with a generalized global neural network potential.

Main Results:

  • LASP-D3 offers up to 100x speedup for systems >100,000 atoms compared to existing methods.
  • Significantly reduced GPU memory consumption.
  • Accurately reproduced experimental conductivity of the solid electrolyte LiTaCl6, highlighting the role of vdW interactions in Li-ion diffusion.

Conclusions:

  • LASP-D3 provides a computationally efficient approach for large-scale atomic simulations incorporating vdW interactions.
  • The method facilitates accurate modeling of material properties, such as ionic conductivity in solid electrolytes.
  • This work enables faster discovery and design of advanced materials.