Abstract: The field-dependent chemical shift caused by hetero-nuclear dipolar interactions is discussed by the averaging Hamiltonian theory, and compared with the results from the second-order perturbation, it was found that the effect of "A" term has been additionally involved. It is shown that the first-order averaging Hamiltonian is generally more precise than the second-order perturbation when the effects of non-secular terms are considered. The field-dependent chemical shifts produced by homo-nuclear dipolar interaction are also discussed.

Key words: Field-dependent Chemical Shifts, Effect of Non-secular Terms, Averaging Hamiltonian Theory