Quantum Mechanical Expression for the Spin Rotation Tensor

6 Quantum Mechanical Expression for the Spin Rotation Tensor 

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 

For the derivation of the induced contribution we will start from the definition as second derivative of the electronic energy, Eq. (6.47) in the presence of a nuclear magnetic moment and the molecular rotation. The corresponding vector potentials, Eqs. (5.55) and (6.5), lead to two first-order perturbation Hamiltonians, Eqs. (5.56) and (6.19), and a new second-order-order-perturbation Hamiltonian [see Exercise 6.4] 

As for the rotational g tensor this operator is very similar to the one for the diamagnetic contribution to the nuclear magnetic shielding tensor but with one of the electronic 

Exercise 6.4 Derive the second-order perturbation Hamiltonian for the induced contribution to the spin rotation tensor, Eq. (6.51), by inserting the vector potentials, (5.55) and (6.5), in the general expression of the molecular Hamiltonian, Eq. (2.101), retaining the bihnear second-order term. 

---