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Related Concept Videos

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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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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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.
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sp3d and sp3d 2 Hybridization
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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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Quantum Numbers02:43

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The GW-Method for Quantum Chemistry Applications: Theory and Implementation.

M J van Setten1, F Weigend1,2, F Evers1,3

  • 1Institute of Nanotechnology, Karlsruhe Institute of Technology , P.O. Box 3640, D-76021 Karlsruhe, Germany.

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|November 22, 2015
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The GW method significantly improves electronic structure calculations by correcting density functional theory (DFT) artifacts. This approach reduces errors in predicting ionization potentials and electron affinities, enhancing computational chemistry accuracy.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Density Functional Theory (DFT) relies on approximations for exchange-correlation (XC) functionals, leading to inaccuracies.
  • Kohn-Sham (KS) single-particle energies and states in DFT are susceptible to these XC functional artifacts.

Purpose of the Study:

  • To present the formalism and implementation of the GW method, adapted for standard quantum chemistry packages.
  • To evaluate the accuracy of the GW method in correcting KS-DFT electronic structure calculations.

Main Methods:

  • The study implements the GW approximation, a many-body perturbation theory method.
  • Calculations were performed on a typical set of molecules to test the GW implementation.

Main Results:

  • The G0W0 approximation (first iteration of GW self-consistency) significantly reduces deviations in quasi-particle energies.
  • Quasi-particle energies calculated with G0W0 show an order of magnitude improvement compared to KS-DFT for ionization potentials and electron affinities.
  • The G0W0 results exhibit diminished dependency on the underlying XC functional of DFT.

Conclusions:

  • The GW method effectively corrects KS-DFT artifacts, leading to more accurate predictions of electronic properties.
  • The G0W0 approach offers a computationally feasible way to achieve substantial accuracy improvements in electronic structure calculations.