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Related Concept Videos

Force and Potential Energy in Three Dimensions01:04

Force and Potential Energy in Three Dimensions

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Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
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The Quantum-Mechanical Model of an Atom02:45

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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.
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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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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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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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Force and Potential Energy in One Dimension01:13

Force and Potential Energy in One Dimension

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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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Hellmann-Feynman forces within the DFT + U in Wannier functions basis.

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This study introduces a new method for calculating atomic forces in strongly correlated materials using Wannier functions within the DFT+U framework. This advancement improves the accuracy of simulations for complex electronic structures.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Chemistry

Background:

  • Localized electronic states in strongly correlated materials are generally described using Wannier functions.
  • The Density Functional Theory combined with the Hubbard U (DFT+U) method is widely used for such systems.

Purpose of the Study:

  • To extend the capabilities of the DFT+U method by incorporating Wannier functions.
  • To develop and implement a novel technique for calculating the Hubbard contribution to atomic forces.

Main Methods:

  • Utilized Wannier functions as a basis set within the DFT+U framework.
  • Developed a new computational technique for atomic force calculations.
  • Implemented the technique in the plane-wave pseudopotential code Quantum-ESPRESSO.

Main Results:

  • Successfully implemented and tested a technique to compute Hubbard forces.
  • Validated the method on a charge transfer insulator (NiO) and a correlated metal (SrVO3).

Conclusions:

  • The developed technique enhances the DFT+U method for accurate simulations of strongly correlated materials.
  • This provides a more robust tool for studying the properties of materials with localized electronic states.