Question

Give and describe the relevant terms in the Hamiltonian that apply to NMR (skip chemical shift anisotropy, direct polar copling, and quadrupolar coupling.

predict 19F NMR for SF4 (19F:N = abundance = 100%. I= 1/2)

predict 1H NMR of GeH4 and label the coupling

Answer 1

The nuclear spin Hamiltonian can be written as a sum of internal and external parts:

H = Hint + Hext

With this separation, the e?ects intrinsic to the spin system are included in the Hint Hamiltonian while Hext contains terms due to the experimental setup. It can be further subdivided into the basic interactions resulting from the environment of the nucleus:

HCS + HJ + HD + HQ

where HCS is the chemical shielding (or chemical shift), HJ is the indirect spin-spin coupling (or J coupling), HD is the direct dipole-dipole coupling (or dipolar coupling), and HQ is the quadrupolar coupling. Each of these interactions is intrinsic to the spin system and the hamiltonians primarily depends upon the chemical environment of the nucleus. E?ects that are a result of actions performed on the spin system are included in the external Hamiltonian, and they can usually be separated into Zeeman and radio frequency (RF) contributions:

Hext = HZ + HRF

It is through the Hamiltonian that the experimenter is able to interact with the spins, and this has been the focus of much of the ?eld of NMR. With a thorough knowledge of the information that is intrinsically available from
the internal Hamiltonian, we can tailor our Hext to extract the desired information.

The basic NMR interaction Hamiltonians can be described as the product of vectors. In addition to expressing spin interactions in terms of Cartesian tensors, they may also be written using spherical tensors. This is often times more convenient when calculating the e?ects of rotations or other unitary transformations.