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Density00:56

Density

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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...
19.4K
Current Density01:21

Current Density

5.1K
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...
5.1K
Bulk Density of Aggregate01:22

Bulk Density of Aggregate

1.1K
Bulk density refers to the mass of aggregate particles that would fill a unit volume. The concept of bulk density originates from the inability to pack aggregate particles in a manner that completely eliminates void spaces. Hence, the term bulk refers to the volume that encompasses both the aggregates and the voids. This measurement is crucial when aggregates are batched by volume and is used to convert quantities by mass to volume.
Most natural mineral aggregates, like sand and gravel,...
1.1K
Strain-Energy Density01:20

Strain-Energy Density

883
Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
883
Density and Archimedes' Principle01:05

Density and Archimedes' Principle

8.8K
When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The...
8.8K
Applications of the Ideal Gas Law: Molar Mass, Density, and Volume03:43

Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

63.3K
The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT,  suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature. At standard temperature and pressure, or STP (273.15 K and 1 atm), one mole of an ideal gas (regardless of its identity) has a volume of about 22.4 L — this is referred to as the standard molar volume.
63.3K

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Related Experiment Video

Updated: Jan 25, 2026

Nanosponge Tunability in Size and Crosslinking Density
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Nanosponge Tunability in Size and Crosslinking Density

Published on: August 4, 2017

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Multicomponent density functional theory with density fitting.

Daniel Mejía-Rodríguez1, Aurélien de la Lande1

  • 1Laboratoire de Chimie Physique, Université Paris Sud/CNRS, Université Paris Saclay, 15 Avenue Jean Perrin, 91405 Orsay, France.

The Journal of Chemical Physics
|May 10, 2019
PubMed
Summary
This summary is machine-generated.

Multicomponent Density Functional Theory (MDFT) efficiently simulates quantum particles using auxiliary densities. This implementation in deMon2k offers computational advantages for systems with electrons and quantum protons.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Multicomponent Density Functional Theory (MDFT) enables the inclusion of nuclear quantum effects and simulation of diverse particles.
  • Standard DFT implementations face challenges in achieving optimal efficiency.
  • Developing efficient MDFT methods is crucial for accurate simulations of quantum systems.

Purpose of the Study:

  • To introduce an efficient Multicomponent Density Functional Theory implementation using auxiliary DFT.
  • To focus on molecular systems containing both electrons and quantum protons.
  • To evaluate the performance of various electron-proton correlation functionals.

Main Methods:

  • Implementation of MDFT within the auxiliary DFT framework in the deMon2k code.
  • Utilizing a dual variational procedure to determine auxiliary electron and proton densities.
  • Employing fitted densities for classical Coulomb interactions and exchange-correlation potentials, including electron-proton correlation (EPC).

Main Results:

  • Auxiliary densities are suitable for classical Coulomb interactions and EPC, with considerations for the electronic auxiliary basis set flexibility.
  • Testing of various EPC functionals on proton affinities demonstrated their applicability.
  • The density fitting approach in MDFT provides significant computational advantages and scales well with system size.

Conclusions:

  • The auxiliary DFT approach offers an efficient pathway for MDFT calculations involving electrons and quantum protons.
  • Density fitting in MDFT significantly reduces computational cost while maintaining accuracy.
  • This implementation facilitates more accessible and scalable simulations of quantum mechanical systems.