Shielding of Nuclei in Atoms and Molecules

The Larmor frequency of a free nuclear spin is given by the Larmor equation  

In atoms and molecules, a nucleus i is shielded by electrons. It does not experience the static field B0 applied but an individual field Bt, arising from superposition of the B0 field and an additional field flindi induced by the shielding electrons  

The strength of Bind t induced by the electrons is proportional to the strength of the applied field B0. 

The factor rr [9] is called the magnetic shielding constant for the nucleus i, and characterizes the chemical environment of that nucleus. The effective field experienced by the nucleus i follows from eqs. (1.38, 1.39)  

8 c) tells us that nuclei having different chemical environments precess at different Larmor frequencies. The shift of Larmor frequencies due to chemical nonequivalence of nuclei in molecules is called the chemical shift. 

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