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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...

Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

The Quantum-Mechanical Model of an Atom

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

Energy Associated With a Charge Distribution

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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.

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,...

Thermodynamic Potentials

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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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Empirical correction of nondynamical correlation energy for density functionals.

Wanyi Jiang¹, Chris C Jeffrey, Angela K Wilson

¹Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, Denton, Texas 76203-5017, USA.

The Journal of Physical Chemistry. A

|September 20, 2012

Summary

This study introduces an empirical correction to improve hybrid density functionals for accurately calculating nondynamical correlation. This method enhances predictions for chemical reactions involving strong electron correlation.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Chemistry

Background:

Nondynamical correlation is crucial for accurately describing chemical bonds and reactions.
Standard hybrid density functionals often struggle with systems exhibiting significant nondynamical correlation.

Purpose of the Study:

To develop an efficient empirical correction for single and double hybrid density functionals.
To improve the accuracy of these functionals in regions of moderate to high nondynamical correlation.

Main Methods:

Formulation of an empirical correction using specific Kohn-Sham orbitals.
Application of the correction to hybrid BLYP and B2K-PLYP functionals.
Validation against ab initio multireference methods and established datasets (DBH24, BH76).

Main Results:

The corrected hybrid BLYP accurately predicted potential energy curves for ethylene torsional rotation and cyclobutadiene automerization.
Empirical corrections reduced errors in B2K-PLYP for reaction barrier heights.
The method demonstrated efficiency in handling nondynamical correlation.

Conclusions:

The proposed empirical correction effectively enhances the performance of hybrid density functionals.
This approach provides a computationally efficient way to address nondynamical correlation in quantum chemistry.
The correction broadens the applicability of density functional theory to complex chemical systems.