The spectrometer is a radio receiver, and we change the frequency to "tune in" each nucleus at its characteristic frequency, just like the stations on your car radio. Because the resonant frequency is proportional to the external magnetic field strength, all of the resonant frequencies above would be increased by the same factor with a stronger magnetic field. The relative sensitivity is a direct result of the strength of the nuclear magnet, and the effective sensitivity is further reduced for those nuclei that occur at low natural abundance. For example, 13C at natural abundance is 5700 times less sensitive (1/(0.011 x 0.016)) than 1H when both factors are taken into consideration.

1.1.4 The Chemical Shift

The resonant frequency is not only a characteristic of the type of nucleus but also varies slightly depending on the position of that atom within a molecule (the "chemical environment"). This occurs because the bonding electrons create their own small magnetic field that modifies the external magnetic field in the vicinity of the nucleus. This subtle variation, on the order of one part in a million, is called the chemical shift and provides detailed information about the structure of molecules. Different atoms within a molecule can be identified by their chemical shift, based on molecular symmetry and the predictable effects of nearby electronegative atoms and unsaturated groups.

The chemical shift is measured in parts per million (ppm) and is designated by the Greek letter delta (5). The resonant frequency for a particular nucleus at a specific position within a molecule is then equal to the fundamental resonant frequency of that isotope (e.g., 50.000 MHz for 13 C) times a factor that is slightly greater than 1.0 due to the chemical shift:

Figure 1.3

For example, a 13C nucleus at the C-4 position of cycloheptanone (¿23.3 ppm) resonates at a frequency of

50.000 MHz (1.0 + 23.2 x 10-6) = 50.000(1.0000232) = 50,001,160 Hz

A graph of the resonant frequencies over a very narrow range of frequencies centered on the fundamental resonant frequency of the nucleus of interest (e.g., 13C at 50.000 MHz) is called a spectrum, and each peak in the spectrum represents a unique chemical environment within the molecule being studied. For example, cycloheptanone has four peaks due to the four unique carbon positions in the molecule (Fig. 1.3). Note that symmetry in a molecule can make the number of unique positions less than the total number of carbons.

1.1.5 Spin-Spin Splitting

Another valuable piece of information about molecular structure is obtained from the phenomenon of spin-spin splitting. Consider two protons (1 HaC-C1 Hb) with different chemical shifts on two adjacent carbon atoms in an organic molecule. The magnetic nucleus of Hb can be either aligned with ("up") or against ("down") the magnetic field of the spectrometer (Fig. 1.4). From the point of view of Ha, the Hb nucleus magnetic field perturbs the external magnetic field, adding a slight amount to it or subtracting a slight amount from it, depending on the orientation of the Hb nucleus ("up" or "down"). Because the resonant frequency is always proportional to the magnetic field experienced by the nucleus, this changes the Ha frequency so that it now resonates at one of two frequencies very close together. Because roughly 50% of the Hb nuclei are in the "up" state and roughly 50% are in the "down" state, the Ha resonance is "split" by Hb into a pair of resonance peaks of equal intensity (a "doublet") with a separation of J Hz, where J is called the coupling constant. The relationship is mutual so that Hb experiences the same splitting effect (separation of J Hz) from Ha. This effect is transmitted through bonds and operates only when the two nuclei are very close (three bonds or less) in the bonding network. If there is more than one "neighbor"

Figure 1.4

proton, more complicated splitting occurs so that the number of peaks is equal to one more than the number of neighboring protons doing the splitting. For example, if there are two neighboring protons (Ha C-CHb2), there are four possibilities for the Hb protons, just like the possible outcomes of flipping two coins: both "up," the first "up" and the second "down," the first "down" and the second "up," and both "down." If one is "up" and one "down" the effects cancel each other and the Ha proton absorbs at its normal chemical shift position (va). If both Hb spins are "up," the Ha resonance is shifted to the right by J Hz. If both are "down," the Ha resonance occurs J Hz to the left of va. Because there are two ways it can happen, the central resonance at va is twice as intense as the outer resonances, giving a "triplet" pattern with intensity ratio 1:2:1 (Fig. 1.5). Similar arguments for larger numbers of neighboring spins lead to the general case of n neighboring spins, which split the Ha resonance peak into n + 1 peaks with an intensity ratio determined by Pascal's triangle. This triangle of numbers is created by adding each adjacent pair of numbers to get the value below it in the triangle:

singlet doublet triplet quartet quintet sextet septet

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