BASIC THEORY OF NMR SHIELDING

The basic equations for the NMR shielding were developed by Ramsey (1950), using quantum mechanical sum-over-states perturbation theory. The total shielding, a, defined by the equation  

In a more modem formulation the shielding is usually represented as the second derivative of the total molecular energy with respect to components of the magnetic field and the magnetic moment of the nucleus N  

It is still important in this formulation to deal correctly with the gauge-origin problem. The perturbation Hamiltonian contains terms involving the A vector of the magnetic field, related to the field B by  

The working equation for the shielding within the GIAO method is  

Although absolute shielding scales are available for many elements, e.g.. Si (Jameson and Jameson 1988), it is common to define a NMR shift, 5 scale, in which the shielding for the atom in a compound is compared with that in a reference  

---