This article is about the quantum mechanical probability density of an electron. For the number density of electrons in a plasma, also called "electron density", see Plasma (physics).
Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either or . The density is determined, through definition, by the normalised -electron wavefunction which itself depends upon variables ( spatial and spin coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of density functional theory.
According to quantum mechanics, due to the uncertainty principle on an atomic scale the exact location of an electron cannot be predicted, only the probability of its being at a given position; therefore electrons in atoms and molecules act as if they are "smeared out" in space. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction.
Electrondensity or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding...
the case of DFT, these are functionals of the spatially dependent electrondensity. DFT is among the most popular and versatile methods available in condensed-matter...
chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs...
lattice if the electrondensity is less than a critical value. This is because the potential energy dominates the kinetic energy at low densities, so the detailed...
topological analysis of the electrondensity of molecules. Such quantum chemical topology (QCT) methods include the electron localization function (ELF)...
The electron ( e− or β− ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton...
proposed. While electrondensity ρ(r) itself generally does not provide useful guidance in this regard, the Laplacian of the electrondensity is revealing...
is proportional to the charge density of the electron at any point. In atoms and molecules the charge of the electrons is distributed in clouds called...
sometimes called the electron heat capacity, is the specific heat of an electron gas. Heat is transported by phonons and by free electrons in solids. For pure...
Langmuir waves (after Irving Langmuir), are rapid oscillations of the electrondensity in conducting media such as plasmas or metals in the ultraviolet region...
^{2}}{5m_{\text{e}}}}{\rho _{\text{e}}}^{5/3},} where ρe is the free electrondensity (the number of free electrons per unit volume). For the case of a metal, one can prove...
fixed and it depends upon the electrondensity of the ionosphere. Critical frequency can be computed with the electrondensity given by: f c = 9 N max {\displaystyle...
conduction band for electrons, integrating over the valence band for holes). If the total number of charge carriers is known, the carrier density can be found...
the quantization (i.e. the Hall plateau) as the electrondensity is varied. Since the electrondensity remains constant when the Fermi level is in a clean...
reaction. An electron withdrawing group (EWG) will have the opposite effect on the nucleophilicity of the ring. The EWG removes electrondensity from a π...
are now mostly made using density functional theory (DFT), which directly calculates the electrondensity. This electrondensity is then analyzed using the...
this overlap occurs laterally. Each of these atomic orbitals has an electrondensity of zero at a shared nodal plane that passes through the two bonded...
measurement of electrondensity, ion temperature and electron temperatures, ion composition and plasma velocity. If there is a greater amount of electrons present...
sensitive to a variety of factors including: 1) metal identity and electrondensity; 2) sterics; 3) participating ligands; 4) coordination number; 5) geometry;...
electrondensity at the aryl carbon bonded to the carbonyl carbon (10c, 11d). Phenyl groups have low migratory aptitude, but higher electrondensity at...
effect in a molecule is a local change in the electrondensity due to electron-withdrawing or electron-donating groups elsewhere in the molecule, resulting...
variation of the electrondensity from bottom of the ionosphere to the altitude of maximum density than in describing the total electron content (TEC)....
bonded electrons—the molecular orbitals—as linear combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional...
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