Micro view of NMR

Quantum transitions in nuclei

NMR is an instrumental technique that uses photons of radio frequency energy to cause a transition, or change in state, in an atom. Radio is used because transitions at the atomic level are quantized, and the amount of energy needed to cause these transitions happens to fall in the radio region of the electromagnetic spectrum. Quantized energy means there has to be the right amount of energy to cause a change of state, too much or too little and no change occurs.

There are many transitions in atoms, and the ones of interest in NMR are quantum spin transitions of protons and neutrons. Quantum spin in protons and neutrons has two states, which are normally equivalent, but when placed in a magnetic field they become non-equivalent, so adding the appropriate sized photon of energy can cause a transition from one to the other. This works fine for single protons and neutrons, but when these are combined into a nucleus the situation gets more complex and we have to rely on a net nuclear spin, called I.

Across the entire periodic table, net nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found. Protons and neutrons each have net spins of ½, but this derives from the elementary quarks and gluons of which they are composed. As a result of this complexity, no simple formula exists to predict I based on the number of protons and neutrons within an atom.

The formula for the number of states = 2I+1, thus a spin 1/2 nucleus such as a single hydrogen atom will have 2 states and 1 transition (when placed in a static magnetic field). For I greater than 1 there are more than two states and thus many transitions. The focus in NMR is on spin 1/2 nuclei since two states with one transition gives good, clean spectra that are easily interpretable. A lot of information about the environment of a nucleus can thus be obtained, making 1H NMR the most useful analytical technique in science.

From here on, the focus will be on spin 1/2 nuclei, specifically ¹H. This nucleus is referred to as "proton" in the NMR literature, but other spin 1/2 nuclei will behave the same. Nuclei with spins other than 1/2 will have more than one transition and give much more complicated spectra, so these will be explored in another section.

To obtain a spectrum, a spin 1/2 atom must first be placed into a static magnetic field (B₀) to cause separation of the two states. The amount of separation depends on the gyromagnetic ratio for that atom (a constant) and the intensity of the static magnetic field according to the equation:

v₀=γ*B₀

The atom is then pulsed with a composite radio wave that includes the frequency v₀, called the Larmor Frequency. The atom absorbs just the v₀ part of the radio wave (since it is a quantum transition), and a detector in the same axis as the radio wave (usually the same antenna) is then turned on to receive any emitted energy.

Making this happen in an instrument is thus mainly an engineering problem.

Spectra

From the equation above, since γ is a constant and B₀ is a constant, there is just one frequency for that proton, which makes sense since there is just one transition, thus there is just one peak expected in the spectrum. In reality though, an atom never exists in isolation, thus it never experiences the pure B₀. The actual frequency v is thus slightly different for atoms of a particular γ based on the actual magnetic field around the atom. These slight differences in frequency are what gives a spectrum of peaks for a molecule rather than a single peak. There is still just one transition for that atom type (if that type is spin 1/2, such as ¹H), but the transition energy is different for each ¹H that is in a different magnetic environment.

If the ¹H is part of a molecule then ¹H atoms in the molecule in similar magnetic environments can be grouped and can be expected to give one peak per group.

To see examples, the view will be increased beyond a single ¹H atom and into a collection of ¹H atoms as part of molecules, such as a solution of one compound in a solvent.

For a solution of ethanol (CH₃CH₂OH) dissolved in water, we first have to list the spin 1/2 groups in the mixture: ¹H and ¹³C

• Fortunately, the γ for ¹H and ¹³C are very different, which means that the radio frequencies needed to cause spin transitions are also different. If a narrow band of radio is used both to transmit and receive, it is possible to "see" ¹H and ¹³C separately. In other words, when looking at ¹H, the 13C will not be excited because the quantum energy is not correct. The ¹³C are invisible in ¹H spectra, and the ¹H are invisible in ¹³C spectra.

Next is a listing of ¹H groups in the mixture:

A group for the protons in water

A group for the protons in the CH₃ of ethanol

A group for the protons in the CH₂ of ethanol

A group for the OH of ethanol.

Thus four peaks are expected in the ¹H spectrum of this mixture.

• Another spin 1/2 nucleus in this sample is carbon, specifically the ¹³C isotope. Based on the isotope abundance table, ¹³C is only 1.11% of the total carbon atoms in a sample. The other carbon atoms have spin 0 and are not visible in NMR, so, if the instrument is sensitive enough, it can detect the 1.1% of carbons in a sample that are spin 1/2.

A list of possible ¹³C carbons in the mixture:

A group for the CH₃ of ethanol

A group for the CH₂ of ethanol.

There are no other carbon sources in this sample so there should be just 2 peaks in the spectrum.

Radio pulse power

How powerful should the radio pulse be to get a good signal? Each transition requires one photon, so enough photons are needed in a pulse to cause transitions in all the nuclei in a sample. The total number of photons in a pulse of radio is the power of the pulse times the length of time that the pulse is turned on, where power is given in watts (W) and time in microseconds (µ). It is then a simple matter of running multiple experiments at difference power and time values until the maximum signal is achieved. The ideal numbers are actually determined by technical problems such as transmitter parameters and timing capabilities.

Peak Intensity

So far there has been no discussion of how big the peaks are.

List of topics in this section

• Gyromagnetic ratio
• Spins of nuclei
• Net nuclear spin
• Isotope abundance