Quadrupole Interactions and Line-Narrowing Methods

For nuclei with 7 1, the nuclear electric quadrupole moment interacts with the electric field gradient in a nonsymmetric environment of electrons around the nucleus. The electric field gradient is described by a tensor that can be expressed in diagonal form (components Vx, VY, and IQ) in a principal axis system fixed in the molecule. By Laplace s equation the sum of the three components is zero, so there are two independent parameters, usually taken as the largest of the three components, V7 = d2V/dz2, and the asymmetry parameter tj = (Vx — IQ)/ Vz, with the convention that VZ VX. The electrical interaction leads to 

When the Zeeman interaction is much larger than the quadrupole interaction, nonsecular terms may be discarded to give a relatively simple expression for the quadrupole Hamiltonian  

FIGURE 7.10 2H (D) NMR spectrum of polycrystalline alanine-d3 at three temperatures. The line shape variation results from reorientation of the CD3 group, (a) At 123 K the powder pattern represents a nearly static CD3. (b) At 177 K, the line shape is distorted by motional averaging, (c) At 293 K, motion is fast enough to produce an undistorted axially symmetric averaged powder pattern. Spectra courtesy of Dennis A.Torchia (National Institutes of Health). 

FIGURE 7.11 Variation of energy levels for / = 1 with angle 6 and illustration of the constant energy separation for the Am = 2 transition. 

---