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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...

Fermi Level Dynamics

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...

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.

Graphing the Wave Function

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

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Related Experiment Video

Updated: Jan 5, 2026

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

Wannier90 as a community code: new features and applications.

Giovanni Pizzi¹, Valerio Vitale, Ryotaro Arita

¹Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|October 29, 2019

Summary

Wannier90 v3.0 now offers advanced features for calculating maximally-localised Wannier functions (MLWFs) and new material properties. This open-source program enhances electronic structure calculations with improved performance and usability.

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Published on: May 27, 2020

Area of Science:

Condensed matter physics
Computational materials science

Background:

Wannier90 is a key tool for calculating maximally-localised Wannier functions (MLWFs).
Its development has shifted to a community-driven model, fostering new advancements.

Purpose of the Study:

To detail the new features and improvements in Wannier90 v3.0.
To highlight the expanded capabilities for material property calculations and code usability.

Main Methods:

Implementation of new wannierisation and disentanglement features.
Addition of new property calculations, including shift currents and Berry-curvature dipole.
Performance enhancements through parallelisation and improved interpolation methods.

Main Results:

Wannier90 v3.0 includes symmetry-adapted and selectively-localised Wannier functions.
New capabilities enable calculation of dielectric, electronic, magnetic, optical, topological, and transport properties.
Significant improvements in code performance, usability, and software engineering practices.

Conclusions:

Wannier90 v3.0 represents a major upgrade, expanding its applicability in materials science.
The community-driven development model ensures continued growth and broader scientific adoption.