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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.
For an atom with electronic spin S and nuclear spin I, there are (2S + 1)(2I + 1) spin states. For example, neutral Na atoms, which have S = 1/2 , were passed through a series of inhomogeneous magnetic fields that selected one of the two electronic spin states and separated the nuclear spin states, from which four beams were observed.
A pair of electrons in a spin singlet state has S = 0, and a pair in the triplet state has S = 1, with m S = −1, 0, or +1. Nuclear-spin quantum numbers are conventionally written I for spin, and m I or M I for the z-axis component. The name "spin" comes from a geometrical spinning of the electron about an axis, as proposed by Uhlenbeck and ...
Examples of atoms in singlet, doublet, and triplet states. In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
In the ground state of dioxygen, this energy level is occupied by two electrons of the same spin, as shown in the molecular orbital diagram. The molecule, therefore, has two unpaired electrons and is in a triplet state. In contrast, the first and second excited states of dioxygen are both states of singlet oxygen. Each has two electrons of ...
The factor of two arises because the number of allowed states doubles with each successive shell due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin + 1 ⁄ 2 (usually denoted by an up-arrow) and one with a spin of − 1 ⁄ 2 (with a down-arrow).
One of these electrons must have, (for some chosen direction z) m s = 1 ⁄ 2, and the other must have m s = − 1 ⁄ 2. Hund's first rule states that the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open subshell. The orbitals of the subshell are each occupied singly with ...
A high multiplicity state is therefore the same as a high-spin state. The lowest-energy state with maximum multiplicity usually has unpaired electrons all with parallel spin. Since the spin of each electron is 1/2, the total spin is one-half the number of unpaired electrons, and the multiplicity is the number of unpaired electrons + 1.