Quantum Mechanical Expression for the Rotational g Tensor

The derivation of the quantum mechanical expression for the rotational g tensor requires the derivation of quantmn mechanical expressions for the rigid and induced contribution to the rotational magnetic moment. An expression for the first is most easily derived in analogy to the electric dipole moment in Section 4.3 by translating the classical expression, Eq. (6.2), to quantum mechanics. Before doing so, however, we want to make use of Lagrange s formula for a vector triple product [see Exercise 6.11 

2 This definition is also given in the last column of Table B.3 of Appendix B. 

Comparison with Eq. (6.7) allows us to identify a component of the rigid contribution to the rotational g tensor as 

In a molecule the charge distribution p f) consists of the discrete nuclear charges located at the points Rx and the continuous charge distribution of the electrons. A quantum mechanical expression for the latter can be obtained again from Eq. (2.23). 

The derivation of the induced contribution, on the other hand, is very similar to the derivation for the magnetizability. We could start from the definition of the rotational g tensor as first derivative of the rotational magnetic moment, Eq. (6.8), which would then be the induced contribution to it, and use the response theory formalism of Section 3.11. Using Eq. (3.116) we could express the derivatives of the induced rotational magnetic moment in terms of a polarization propagator and ground-state expectation value. Here we will, however, make use of the definition as second 

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In the derivation of quantum mechanical expressions for the rotational g tensor e nuclei are usually treated as classical rotating point charges, Z e, located at Rk- Their contribution to the g tensor is then given as... 

The derivation of the quantum mechanical expressions for the spin rotation tensor is completely analogous to the one for the rotational g tensor. We will therefore just discuss the final expressions. The rigid contribution again consists of a nuclear and an electronic term... 

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