BioPHYSICAL chemistry

These energies can be expressed in terms of the

Larmor frequency,νL, by:

(16.5)

For a nucleus with a spin of 1/2, this interaction with

the magnetic field will result in a splitting of the ener-

gies for the two spin states (Figure 16.1). For a spin

1/2 system, there is only one transition between the

spin down and up states. If the spin is larger there

are more states and more transitions. For spin 1 there

are three states (+1, 0, −1) and two possible transi-

tions of equal energy with Δml=1. In general there

are 2I+1 states for a given spin.

The experimental system needed to measure

an NMR signal is in principle very simple, with

just a radiofrequency transmitter coupled to the sample, in a loop in a

magnet followed by a receiver (Figure 16.2). Although signals can be

measured by simple systems, accurate measurements require very pre-

cise equipment. The magnetic field must be uniform throughout the

sample, which is often rotated. The most resolved signals make use of

very high field magnets. Whereas routine studies of the products of a

synthesis reaction can be performed on a system

of 300 MHz, for proteins spectrometers operat-

ing at higher frequencies of 600 MHz and above

are required to obtain separation of closely lying

peaks. Such spectrometers operate with a field

strength requiring magnetic fields of at least

12 T, which is generated using a superconduct-

ing magnet. Superconductors are materials that

change their properties dramatically at very

low temperatures, typically at liquid helium

temperatures or 1–10 K. For these materials, the

resistance normally encountered by the electrons

in the material is not present at temperatures

of a few degrees Kelvin. The superconducting

material can maintain electrical current forever

and so superconducting magnets can produce

extremely homogeneous fields. For many proteins,

the spectra are complex and difficult to interpret,

so many NMR experiments are now performed

on systems that operate at 900 MHz to maximize

the resolution of the spectra.

Emh v

B

mIL LI=− ν =

γ

π

or

2

346 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

B  0 B  0

ΔE  γhB

mi   (^12)
mi   (^12)
Figure 16.1The nuclear-spin energy
levels in the presence of a magnetic field.
Radiofrequency
generator
Sample in tube
RF out RF in
Superconducting
magnet
Detector
amplifier
Signal
converter
Print
Figure 16.2A simple scheme of an NMR
spectrometer.