104 INSTRUMENTAL METHODS
affects each proton differently, causing larger separation of the resonances.
Both effects are useful in revealing more information about the structure of
the molecule. The effect of paramagnetic transition metals on NMR spectra
have been used to great advantage in the analysis of bioinorganic systems.
Normally, one speaks of “ chemical shifts ” rather than “ screening ” when
discussing NMR spectra. For two nuclei in different environments with screen-
ing constantsσ 1 and σ 2 , from equation 3.21 , the corresponding nuclear fre-
quencies will result in equation 3.22. Applying equation 3.22 to σ 2 , subtracting,
eliminatingB 0 , and setting σ 1 << 1, one fi nds equation 3.23 :
ν
γ
π
101 σ
2=( )B() 1 − (3.22)
νν
ν(^12) σσ
1
21
−
()=−() (3.23)
The quantity σ 2 – σ 1 is given the symbol δ and is called the chemical shift. Its
value is expressed in parts per million (ppm). It is normal to establish a chemi-
cal shift scale for a given nucleus choosing a standard and defi ning its chemical
shift arbitrarily at zero ppm. Tetramethylsilane, (CH 3 ) 4 Si, or TMS, is used as
the standard for the common nuclei,^1 H and^13 C. In recording spectra using
TMS, it is normal to depict the descreened (deshielded) nuclei to the left of
the standard. One calls the deshielded region “ low fi eld ” or “ high frequency. ”
A useful diagram detailing the terminology adapted from Figure 2.12 of refer-
ence 21 is shown in Figure 3.12.
3.4.3 Spin – Spin Coupling
A nucleus under study by nuclear magnetic resonance techniques is affected
by other nuclei in the same molecule. This phenomenon is known as spin – spin
coupling. The effect arises (in adjacent nuclei) from the two electrons joining
the nuclei in a covalent bond. Suppose the energy of states in which the elec-
trons in the bond have opposing spins is lower than the state in which the
electron spins are parallel. Then the ΔE between the two states (in this case a
negative number) is called the coupling constant, J , expressed in frequency
units, Hz. Internuclear spin – spin coupling constants may be either positive or
negative and depend on a number of factors:
- The number and bond order of bonds intervening between the nuclei as
well as the bond angles. Usually the interaction is observed only through
one to four bonds, and the effect is attenuated (the J value becomes
smaller) as the number of intervening bonds increases. - The magnetic moments of the two interacting nuclei. These are directly
proportional to the product of the magnetogyric ratios ( γAγB ) of the
interacting nuclei.