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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...

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 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.

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.

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Van der Waals coefficients beyond the classical shell model.

Jianmin Tao¹, Yuan Fang², Pan Hao²

¹Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA.

The Journal of Chemical Physics

|January 17, 2015

Summary

This summary is machine-generated.

A new hollow-sphere model accurately calculates van der Waals (vdW) coefficients using dynamic multipole polarizability. This model, especially its single-frequency approximation, is efficient and reliable for various systems, including nanoclusters and fullerenes.

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Area of Science:

Computational chemistry
Atomic and molecular physics
Materials science

Background:

Van der Waals (vdW) coefficients are crucial for understanding intermolecular interactions.
Accurate calculation of vdW coefficients relies on modeling dynamic multipole polarizability.
Static polarizabilities are foundational for accurate dynamic polarizabilities and vdW coefficients.

Purpose of the Study:

To present and analyze a hollow-sphere model for dynamic multipole polarizability.
To simulate vdW coefficients for inhomogeneous systems with cavities.
To assess the accuracy and efficiency of the model and its approximations.

Main Methods:

Utilizing a hollow-sphere model for dynamic multipole polarizability.
Employing accurate static multipole polarizabilities and electron density as inputs.
Implementing a single-frequency approximation (SFA) for simplification.
Comparing results with time-dependent density functional calculations.

Main Results:

The hollow-sphere model, particularly in its SFA, accurately predicts vdW coefficients for nanoclusters and cage molecules.
SFA provides results comparable to expensive time-dependent density functional calculations.
The classical shell model (CSM) is accurate for higher-order vdW coefficients only for large interacting objects.
Strong non-additivity of long-range vdW interactions was observed in nanoclusters.

Conclusions:

The hollow-sphere model and its SFA offer an accurate and efficient method for calculating vdW coefficients.
The model is suitable for inhomogeneous systems and various molecular structures.
Higher-order vdW terms can be significant, and non-additivity is important in nanocluster interactions.