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In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {\displaystyle \rho (\mathbf {r} )} can be written in terms of a sum of products of basis functions, φ:
This page shows the electron configurations of the neutral gaseous atoms in their ground states. For each atom the subshells are given first in concise form, then with all subshells written out, followed by the number of electrons per shell. For phosphorus (element 15) as an example, the concise form is [Ne] 3s 2 3p 3.
The number of valence electrons of an element can be determined by the periodic table group (vertical column) in which the element is categorized. In groups 1–12, the group number matches the number of valence electrons; in groups 13–18, the units digit of the group number matches the number of valence electrons. (Helium is the sole ...
Since metals can display multiple oxidation numbers, the exact definition of how many "valence electrons" an element should have in elemental form is somewhat arbitrary, but the following table lists the free electron densities given in Ashcroft and Mermin, which were calculated using the formula above based on reasonable assumptions about ...
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...
In the bond valence model, the valence of an atom, V, is defined as the number of electrons the atom uses for bonding. This is equal to the number of electrons in its valence shell if all the valence shell electrons are used for bonding. If they are not, the remainder will form non-bonding electron pairs, usually known as lone pairs.
Diagram of a helium atom, showing the electron probability density as shades of gray. The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various ...
Charge number (denoted z) is a quantized and dimensionless quantity derived from electric charge, with the quantum of electric charge being the elementary charge (e, constant). The charge number equals the electric charge ( q , in coulombs ) divided by the elementary charge: z = q / e .