Orbital magnetic dipole moment

By Ampere s78 law,/ can be related to an orbital magnetic dipole moment p,/ ... 

Jab + aIP results from the electronic orbital magnetic dipole moments. 

The formal analogy of the most delocalized "real" orbitals and to the spin functions and quantized with respect to the X axis, and of the most delocalized complex orbitals and to the spin functions and quantized along the y axis, is obvious from Table 1 and is emphasized by the notation chosen. The orbitals, B have the same complex phase in all space and can therefore be referred to as "real" we use quotation marks to indicate the distinction. An electron in such an orbital generates no current nor orbital magnetic dipole moment. The orbitals A, B are essentially complex and carry both a current and an orbital magnetic dipole moment. 

The operator for the orbital magnetic dipole moment is related to the angular momentum operator with respect to the origin of the coordinate system, that is. 

The orbital magnetic dipole moment induced in the n electrons of a molecule by an external magnetic field with flux density B is evaluated assuming linear response. 

There are two contributions to the magnetic dipole moment of an electron bound to an atomic nucleus, which, in semiclassical models, are attributed to orbital motion, represented by quantum number l, and spin, represented by quantum number, v. The orbital and spin components are linked, or coupled, on isolated atoms or ions to give an overall magnetic dipole moment for the atom. The total magnetic dipole moment of the atom is given by... 

Equation (S6.1) is applicable to the salts of lanthanide ions. These have a partly filled 4f shell, and the 4f orbitals are well shielded from any interaction with the surrounding atoms by filled 5.9, 5p, and 6.9 orbitals, so that, with the notable exceptions, Eu3+ and Sm3+, they behave like isolated ions. For the transition metals, especially those of the 3d series, interaction with the surroundings is considerable. Because of this, the 3d transition-metal ions often have magnetic dipole moments corresponding only to the electron spin contribution. The orbital moment is said to be quenched. In such materials Eq. (S6.1) can then be replaced by a spin-only formula ... 

This can be roughly seen by considering the classical view of the valence electron, where this electron describes a circular orbit of radius r around the nucleus. In this case, the magnitude of the magnetic dipole moment is proportional to the area of the circular orbit and u , a so that u ,(r) = Um(—r). 

Magnetic properties are due to the orbital and spin motions of electrons in atoms. The relation between the magnetic dipole moment p and the angular momentum J of an electron of charge e and mass m can be expressed as... 

Evaluate required integrals over the electric and magnetic dipole moment and spin-orbit coupling operators as well as GIAO contributions, if needed. 

Just as orbital angular momentum L gives rise to a magnetic dipole moment pL, spin angular momentum S gives rise to a spin magnetic dipole moment fis. Dirac s relativistic theory of the electron showed that... 

In quantum mechanics, the projection of the angular momentum l is mfi. We, therefore, expect the magnetic dipole moment due to the orbital motion of the electron to be given by... 

Both the orbital and the effective spinning motions of the electron have associated angular moments quantized in units of ii = 1.055 x 10-34 Js. It is an elementary exercise in physics to show that the relationship between the magnetic dipole moment /< and the angular momentum L for a moving particle of mass m and charge Q is... 

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