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Density00:56

Density

14.6K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
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Theory of Metallic Conduction01:17

Theory of Metallic Conduction

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The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
1.3K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.4K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.4K
Van der Waals Equation01:10

Van der Waals Equation

4.0K
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...
4.0K
Van der Waals Interactions01:24

Van der Waals Interactions

63.7K
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.
63.7K
Current Density01:21

Current Density

3.9K
The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net...
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Related Experiment Video

Updated: Jun 16, 2025

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Small basis set density functional theory method for cost-efficient, large-scale condensed matter simulations.

Elisabeth Keller1,2, Jack Morgenstein3, Karsten Reuter1

  • 1Fritz Haber Institute of the Max Planck Society, Berlin, Germany.

The Journal of Chemical Physics
|August 15, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient computational method for predicting solid material structures. A corrected density functional theory approach improves accuracy for bond lengths across the Periodic Table.

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Area of Science:

  • Computational Materials Science
  • Solid-State Physics
  • Quantum Chemistry

Background:

  • Predicting solid material structures is crucial for materials discovery.
  • First-principles methods offer high accuracy but often demand significant computational resources.
  • Small basis sets in density functional theory (DFT) reduce costs but introduce systematic errors in bond lengths.

Purpose of the Study:

  • To develop an efficient and reliable first-principles method for predicting solid material structures.
  • To address systematic errors in bond lengths caused by using a compact basis set.
  • To demonstrate the accuracy and transferability of the corrected method across the Periodic Table.

Main Methods:

  • Utilized a density functional theory (DFT) baseline with a compact, near-minimal min+s basis set.
  • Developed a linear pairwise correction for chemical bond lengths, parameterized for elements Z=1-86 (excluding lanthanides).
  • Employed the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional.
  • Validated the corrected approach using geometry optimizations and molecular dynamics simulations.

Main Results:

  • The corrected DFT approach demonstrates reliable predictions of equilibrium volumes for materials across the Periodic Table.
  • The method shows good transferability to various coordination environments and multi-elemental crystal structures.
  • Evaluated relative energies, forces, and stresses, confirming the approach's robustness.

Conclusions:

  • The presented efficient first-principles method, with a linear pairwise correction, reliably predicts solid material structures.
  • This approach offers a balance between computational efficiency and accuracy for materials prediction.
  • The correction is broadly applicable for elements up to Z=86, excluding lanthanides.