Nuclear magnetic resonance is analogous to other kinds of spectroscopy in that the transitions between two levels (we can call them ground and excited it we wish) are driven by electromagnetic radiation. However, there is one substantial difference in NMR, which is that the energy levels are created artificially by placing the sample in a large magnetic field. The magnetic field interacts with spins, which we can think of spin up and spin down, to create two energy levels. The splitting is much smaller than in any other kind of spectroscopy. We have seen that UV-vis transitinos are in the range from 10,000 - 100,000 cm-1, vibrations are in the range from 10-4,400 cm-1 and rotations are in the range from 0.1-60 cm-1. The frequency of the NMR transition is approximately indicated by the names we give to magnets, 500 MHz, 700 MHz etc. Keep in mind that 1 cm-1 is equal to 30 GHz. So 500 MHz is approximately 1/60 cm-1. Since the splitting of the magnetic field is very small and there are only two energy levels the populations of the two levels are nearly equal. There is approximately a 1/10,000 differece between the levels. This leads to a lack of sensitivity in NMR. Nonetheless, NMR spectroscopy is one of the most power methods known. It is also very useful to study NMR as an example of quantum mechanics in action.
Spin angular momentum is the physical phenomenon that gives rise to an energy splitting in a magnetic field. Nuclei can have spins quantum numbers ranging from 0 to 7/2, depending on the number of protons in the nucleus. Just as with electrons, the spins can cancel such that even numbered atomic numbers result in spin = 0. For this reason, rmany common elements have spin = 0 and are NMR silent. For example, 12C, 14N, and 16>O all have zero spin. However, the H atom nucleus consists of a proton and hence has a spin = 1/2. It turns out the 13C and 15N isotopes also have spin = 1/2. This is fortuitous since spin = 1/2 is the simplest case for theoretical treatments. Therefore, we can study proteins and nucleic acids using labeled samples. We can extract information by analyzing the manipulation of spin in a magnetic field.
The frequency of rotation of a nucleus in a spectrometer is referred to as the Larmor frequency. The Larmor freqeuncy is determined in part by the magnetic field strength, and in fact, we can consider the names of NMR spectrometers to gives us an approximate idea what the Larmor frequency of a H nucleus is. For example, 300 MHz, 400 MHz, etc. are the Larmor frequencies of a typical H nucleus. However, one of the important aspects of NMR spectroscopy is that each nuclear environment in a molecule has unique shift relative to a reference frequency. We usually use an internal reference, but this is not absolutely necessary. One common standard used in organic solvents is tetramethylsilane. The shifts in frequency of typical nuclei is quite small and is measured in parts per million. However, the resolution of the NMR experiment is sufficiently high to permit these various shifts to be easily detected. Thus, we can simultaneously observe many H atoms in many different environments.
Each nucleus in a molecule has a slightly different magnetic environment depending on the details of the structure and screening by electrons. Thus, the precise Larmor frequency of each nucleus is slightly different. For this reason we can observe multiple peaks from a given molecule, which gives information on the structure of a molecule. The shifts in frequency are sufficiently small that they are measured on a scale of parts per million relative to the reference freqeuncy. The units of ppm are units of chemical shift. The shielding is very good in the TMS standard and therefore the majority of chemical shifts are to lower freqeuncies. The scale for chemical shift is measured in ppm less than the refernce.
In an NMR experimental one creates an excited state by application of a magnetic field pulse. The pulse has a sufficient duration to cause the magnetization vector to rotate from the vertical orientation (z-axis) into the x,y plane. The magnetization vector then rotates in the x,y plane under the influence of the large magnetic field of the permanent magnet. As they rotate the spins lose coherence and relax back to the original population (associated with the z-orientation of the magnetization vector). This relaxation causes the signal to decrease exponentially. Thus, the form of the signal is that of a damped oscillation. Mathematically, that corresponds to a sinusoid times an exponential. This signal is known as the Free Induction Decay (FID). The Fourier Transform of the FID gives rise to the NMR spectrum. The FID is a correlation function and consequently NMR spectroscopy is an excellent example the application of the time correlator in spectroscopy. We have made the comparison known as the NMR analogy previously. The power of NMR spectroscopy is evident when we begin to observe various experiments to measure the relaxation times, T1 and T2 as well as the applications that permit us to observe spin interactions by scalar coupling and through-space coupling.
