Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves  185

where

kB is the Boltzmann constant

T is the absolute temperature

For spin-​1/​2 nuclei, the only photon absorption transition is thus −1/​2 → +​1/​2 (which

involves spin-​flip in going from a spin-​down to a spin-​up orientation). For higher-​spin half-​

integer nuclei (e.g., ²³Na is a 3/​2-​spin nucleus), other transitions are possible; however, the

−1/​2 → +​1/​2 transition, called the central transition, is most likely, whereas other transitions,

known as satellite transitions, are less likely.

5.4.2  NMR CHEMICAL SHIFT

However, all atomic nuclei in a sample will not have exactly the same differences in spin

energy states because there is a small shielding effect from the surrounding electrons, which

causes subtle differences to the absolute level of the external magnetic field sensed in the

nucleus. These differences are related to the physical probability distribution of the local elec­

tron cloud, which in turn is a manifestation of the local chemical environment. In other

words, this shift in the resonance frequency, the chemical shift (δ), can be used to infer the

chemical structure of the sample. The resulting B-​field magnitude B′ at the nucleus can be

described in terms of a shielding constant σ:

(5.21)

′ =

−

(

)

B

B

1

σ

In practice, however, NMR measurements rarely refer to σ directly. Chemical shifts are typic­

ally in the range of a few parts per million (“ppm”) of the nonshifted resonance frequency (so

in absolute terms will correspond to a shift of ~1–​20 kHz):

(5.22)

δ

ν

ν

ν

=

−













10⁶

samples

references

references

An NMR spectrum consists of a plot of (radio frequency) electromagnetic radiation

absorption intensity in arbitrary units on the vertical axis as a function of δ in units of ppm

on the horizontal axis, thus generating a series of distinct peaks of differing amplitudes,

which correspond to a sample’s molecular fingerprint, often called the fine structure. The

most common form of NMR is performed on samples in the liquid state, and here, the

chemical shift is affected by the type of solvent, so is always referred to against a standard

reference.

For ¹H and ¹³C NMR, the reference solvent is often tetramethylsilane (TMS) of chemical

formula Si(CH3)4, though in specific NMR spectroscopy on protein samples, it is common

to use the solvent DSS (2,2-​dimethyl-​2-​silapentane-​5-​sulfonic acid). Thus, it is possible to

generate both negative (downfield shift) and positive (upfield shift) values of δ, depending

upon whether there is less or more nuclear screening, respectively, in the specific reference

solvent. It is also common to use deuterated solvent (i.e., solvents in which ¹H atoms have

been exchanged for ²H or deuterium, D, usually by exchanging ~99% of ¹H atoms, which

leaves sufficient remaining to generate a detectable proton NMR reference peak) since most

atomic nuclei in a solution actually belong to the solvent. The most common deuterated

solvent is deuterochloroform (CDCl3). This is a strongly hydrophobic solvent. For hydrophilic

samples, deuterated water (D2O) or dimethyl sulfoxide (DMSO), (CD3)2SO, are often used as

an alternative.

In principle, there is an orientation dependence on the chemical shift. The strength of the

shielding interaction varies in the same way as the magnetic dipolar coupling constant, which

has a (3cos² θ − 1) dependence where θ is the angle between the atomic nuclear magnetic

dipole axis and the external B-​field. However, in liquid-​state NMR, more commonly applied