Nuclear Magnetic Resonance Spectroscopy JAMES N. SHOOLERY Varian Associates, Palo Alto, Calif.
Fundamental concepts of nuclear magnetic resonance are discussed and the basic equation relating magnetic field and radio-frequency is derived. The types of apparatus in general use are described. Applications which can be accomplished using fields of moderate homogeneity are quantitative determinations of the number of nuclei of a given type, illustrated by the measurement of moisture. Nuclear magnetic resonance spectroscopy in extremely homogeneous fields is taken up and the various effects which are encountered are explained. Applications to research are found in molecular electron distribution, structure determination, organic group identification, and in general studies of the structural features of organic compounds, fluorocarbons, silicones, boranes, and compounds of phosphorus. High resolution spectra illustrate some of these applications.
T
HE fundamental concept of nuclear magnetic resonance is
that an alternating magnetic field can induce transitions between the Zeeman levels of a nucleus placed in a fixed magnetic field. The experiment differs from other spectroscopic techniques in two ways: 1. The separation of the energy levels and consequently the frequency of the absorbed energy can be varied by changing the value of the field. The absolute value of the frequency is not a property of either the nucleus or the molecule being studied, but must satisfy the relation w =
-,H
(1)
2. The alternating magnetic field is generated by an oscillating current in a coil and is coherent in time, as contrasted with the incoherent oscillating fields of much higher frequency, associated with the electric or magnetic component of electromagnetic radiation. Equation 1 can be derived very simply by the following method. The energy of interaction of the nucleus with a magnetic field is given by
Now the nucleus has a spin angular momentum, Z, associated with i t which points along the same axis as p . Only 21 1 orientations in the magnetic field are allowed by quantum theory. These are characterized by the quantum number m, running from m = -Z...O...+Z. Now &
,,. H
&
A
= p~
COS^ =
m I
+
(3)
Only transitions for which Am = A1 give detectable absorption, and the oscillating field must therefore be at right angles to the fixed field. Then
A W E w- h= - p H 2ir
z
(4)
have treated the fundanic~ntal equations of nuclear iii:rgiictic resonance in great detail. y differs niarkedly and i n :in uiiplctlic:tahle manner froni one nucleus to anothrr. Some nurli,i, for which I = 0, havc ncitlier spin nor magnetic. moment and cannot be detected. The signal voltage obtained from an ciiwnblr of nuclei depends upon -,1114; thcrefoi,r, the signals from some nuclei are very much dronger than others. Light hydrogen, Auorinc-10, phosphorus-31, alunlinum-27, and lithium-7 are in thi.4 r.nttgoq-, d o n g with qcveral i~;iwibotopc?. -5-
TEST TUBE WITH WATER S A M P L E
I
7
-3-
-4-
RECEIVER
TRANSM - T E R
1 -1-
MAGNET
-1
MAGNEl POLE
11-
m l
r
H
I I
TRANSMITTER
I Figure 1.
“DICAToR
I
Block Diagram of Nuclear Induction Spectrometer
The relation w = -?H applies to the field a t the nucleus, not the applied field. The applied field is altered inside a sample of material, owing to the bulk magnetic susceptibility. The field inside the electron shell of each atom is altered further by the contribution of the orbital motions of the electrons. Both of these effects result in small shifts, which are very significant. In an actual physical system, transitions are equally probable in both directions-from higher to lower energy and from lower energy to higher energy. Only the fact that the lower levels are more populated according to a Boltzman distribution gives us a net signal different from zero. Since AW
