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The spin of a charged particle is associated with a magnetic dipole moment with a g-factor that differs from 1. (In the classical context, this would imply the internal charge and mass distributions differing for a rotating object. [4]) The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative ...
This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total orbital angular momentum, which is also 1 as indicated by the letter P.
Spin network diagram, after Penrose In physics , a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics . From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups .
The (total) spin quantum number has only one value for every elementary particle. Some introductory chemistry textbooks describe m s as the spin quantum number, [6] [7] and s is not mentioned since its value 1 / 2 is a fixed property of the electron; some even use the variable s in place of m s. [5]
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number M S for a given spin S. J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S ...
Another more-general definition of a density is the "linear-response density". [11] [12] This is the density that when contracted with any spin-free, one-electron operator yields the associated property defined as the derivative of the energy. For example, a dipole moment is the derivative of the energy with respect to an external magnetic ...
Low-spin [Fe(NO 2) 6] 3− crystal field diagram. The Δ splitting of the d orbitals plays an important role in the electron spin state of a coordination complex. Three factors affect Δ: the period (row in periodic table) of the metal ion, the charge of the metal ion, and the field strength of the complex's ligands as described by the spectrochemical series.
A and B can also be the same metal with different valences, as is the case with magnetite, Fe 3 O 4 (as Fe 2+ Fe 3+ 2 O 2− 4), which is the most abundant member of the spinel group. [3] Spinels are grouped in series by the B cation. The group is named for spinel (MgAl 2 O 4), which was once known as "spinel ruby". [4] (Today the term ruby is ...