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Molecular oxygen is a good example. Even in the frozen solid it contains di-radical molecules resulting in paramagnetic behavior. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the overlap is limited to the one neighbor in the O 2 molecules. The distances to other oxygen atoms in the lattice remain too large to ...
Paramagnetism diminishes the resolution of an NMR spectrum to the extent that coupling is rarely resolved. Nonetheless spectra of paramagnetic compounds provide insight into the bonding and structure of the sample. For example, the broadening of signals is compensated in part by the wide chemical shift range (often 200 ppm in 1 H NMR).
Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μ eff. For first-row transition metals the magnitude of μ eff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula.
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field, assuming some simplifying assumptions (such as the sample system being ellipsoidal), one can derive a few compact thermodynamic relations. [4]
The Hamiltonian for an electron in a static homogeneous magnetic field in an atom is usually composed of three terms = + (+) + where is the vacuum permeability, is the Bohr magneton, is the g-factor, is the elementary charge, is the electron mass, is the orbital angular momentum operator, the spin and is the component of the position operator orthogonal to the magnetic field.
It only holds for high temperatures and weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures and strong fields. If the Curie constant is null, other magnetic effects dominate, like Langevin diamagnetism or Van Vleck paramagnetism.
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This arrangement results in a bond order of 2 and an excess of one electron spin, giving rise to the molecule's paramagnetism: both observations are in agreement with molecular orbital theory treatments of the molecule. In effect, the LDQ structure is equivalent to the combination of a two-centre one-electron bond (purple spin set) and a two ...