Molecular Rotation as Source for Magnetic Moments

When a molecule rotates around its centre of nuclear masses Rcm-, there are rotating charges, which give rise to an additional current density y (r. This current density can be expressed in terms of the angular momentum of the rotation J and the moment 

In this expression, we have assumed that the charges rotate rigidly and therefore added the superscript rig . This means in particular that the electrons move rigidly with the nuclear frame and do not lag behind. However, in a real molecule the electronic charge distribution will not rotate rigidly, but will be influenced by the fact that the nuclei rotate with angular momentum J. This coupling between nuclear rotational motion and the motion of the electrons 

In complete analogy to Eq. (5.30) this magnetic induction leads to an induced magnetic moment in addition to the magnetic moment of the rigidly 

Contrary to the definition of the properties in the previous chapters here one combines traditionally the rigid and induced or Born ppenheimer breakdown contribution in one property and defines only one property, the rotational g tensor 5j, as the proportionality tensor between the rotational magnetic moment m ( J) and the rotational angular momentum J 

From the expansion in Eq. (6.7) we can define the components of the rotational g tensor as first derivatives of the rotational magnetic moment with respect to a component of the rotational angular momentum J of the nuclei 

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