Quenching of orbital angular momentum

The paramagnetism of transition metal ions is mainly attributed to the magnetic moment due to the electron spin as for free radicals and triplet state molecules. The contribution due to orbital angular momentum is to a large extent quenched . In other words the orbital angular momentum is locked by the crystal field and cannot reorient in a magnetic field. 

Quenching of Orbital Angular Momentum by the Crystal Field 

The reason that orbital angular momentum does not conhibute to the paramagnetism of transition metal ions can be explained by considering the electrostatic field (crystal field) effect on the free ion. Assume that the SchrOdinger wave-function is a complex function q = y i - - i p2 and that the corresponding energy E is non-degenerate. Thus, 

Two wave-functions with the same energy are obtained, contradicting the assumption of a non-degenerate state. Thus, the wave-function can be taken real (cp2 = 0). The orbital angular momentum is also a real quantity. On the other hand, the corresponding quantum mechanical operator of e.g. the x-component. Lx = iHy i - z- ) is imaginary. Thus, the expectation value is zero, Lx l ) = 0. 

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For the lanthanoid elements, ligand field splittings are so small that quenching of orbital angular momentum is not important. This probability also applies in the actinoid elements. 

In connection with the Jahn-Teller effect the role of A may be well defined. It has been shown that if a dynamic Jahn-Teller effect is operative, very substantial quenching of orbital angular momentum may take place — the Ham effect. In the case of T ground terms, if the dynamic Jahn-Teller frequencies bear the right relationship to spin-orbit coupling and temperature, A may be reduced to values well below 0.5.113119... 

Chemical binding is promoted by the lowering of valence-electron kinetic energy and hence by the quenching of orbital angular momentum. 

The explanation of quenching of orbital angular momentum on the basis of crystal field theory ... 

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