4: Proton and carbon-13 NMR

NMR spectroscopy gives us information about the atoms in a molecule, how many there are, and how they are connected. NMR is amongst the most powerful techniques that chemists have at their disposal to figure out an organic molecule’s structure! 

Theory behind Nuclear Magnetic Resonance (NMR) spectroscopy

Just like the Earth spins on its axis, tiny nuclei of atoms spin on their axes. When an atom has an odd number of protons and neutrons in its nucleus, the nucleus has an “overall nuclear spin”. Since the nucleus is positively charged (because of its protons), the spinning motion induces a magnetic field - this causes the nuclei to act like tiny bar magnets. Atoms with nuclear spin which generate a magnetic field are NMR active. A ¹H atom is an example of an NMR active atom, because it has 1 proton, and 0 neutrons. 

Now imagine we apply an external magnetic field, which we will call B0. The ¹H nuclei – tiny magnets – will align such that their axes are parallel (same direction) or antiparallel (opposite direction) to the external magnetic field.

The ¹H atoms aligned parallel to the external field are in the ⍺ state, which is slightly lower in energy. The ¹H atoms aligned antiparallel to the external field and in the β state, which is slightly higher in energy.

Therefore, energy is required to excite the ¹H nuclei from the alpha state to the beta state. In an NMR instrument, this energy is supplied as radio waves. The lower energy ⍺ state ¹H nucleus absorbs the radio waves (1), and undergoes a “spin flip” (2) to the higher energy β state (3). After some time, the excited ¹H nucleus relaxes back down to the lower energy ⍺ state (4), emitting the energy it absorbed (5).

This emitted energy is detected and measured by the NMR instrument, allowing us to understand what atoms, connections, and environments we have in our sample. 

How? 

Well, the energy required to excite the nucleus from the low energy ⍺ state to the high energy β state changes depending on what other atoms it is connected to in the molecule. That is, the gap in energy between the two states changes, depending on the environment of the atom.

Remember that electrons are also charged, and also circulating. Therefore, the electron in a ¹H atom also generates its own magnetic field. The magnetic field generated by the electron acts to oppose the external magnetic field, B0, and stops the nucleus from feeling its full effect. This is called shielding. The electron shields the nucleus from the external magnetic field. This means a smaller energy gap between the ⍺ and β states.

If we are looking at a ¹H atom in a molecule that is next to an electronegative atom – such as an oxygen, O – what do you think will happen? The oxygen has a higher affinity for electrons, so the ¹H atom’s electron will spend more time closer to the oxygen. As a result, it is not able to shield the ¹H nuclei from the external field as well. The shielding on the ¹H nucleus is less. Less shielding is called deshielding, and means that the energy gap between the ⍺ and β states will be larger.

Reading an NMR spectrum

Now we have been introduced to the principles of NMR and hydrogen environments, let’s look at a 1H NMR spectrum.

First, notice that we have a number line which goes positive values to negative values, left to right. The units are parts per million, or ppm.

The energy gap between ⍺ and β states is translated into a measure called chemical shift. If there is a large gap between the ⍺ and β spin states, i.e. if the ¹H atom is connected to an electronegative oxygen, this gives us a large chemical shift. If the energy gap is small, and the nuclei is well-shielded from the external magnetic field, the chemical shift is small.

When we talk about chemical shift, we are always talking about the shift from the 0 ppm point. If there is a large energy gap between the ⍺ and β spin states, there will be a large chemical shift, and the signal will appear further towards the left on this number line.

We often talk about these signals relative to one another, using up- and downfield. A signal that appears at 10 ppm is downfield from a signal that is at 1 ppm. The converse is also true. A signal that is at 1 ppm is upfield from that at 10 ppm.

What is an "environment"?

Before we go any further, we are going to practice identifying hydrogen environments in different molecules. If the hydrogen atoms are in the same electronic environments, they will have the same ΔE, and the same chemical shift. They will be equivalent. By counting hydrogen environments, we can predict how many peaks will be in our NMR spectrum, and how many hydrogens each peak will represent!

Let's start with acetic acid (CH3COOH), which is produced by food as it spoils:

The ¹H NMR spectrum of acetic acid will have 2 signals. Why not 4? The methyl hydrogens (those attached to the terminal carbon) are equivalent. They have the same electronic environment - the same amount of deshielding, so the same DE between the low and high energy states, and the same chemical shift. They appear as the same 1 signal. The hydrogen attached to the oxygen is in a different environment, so will have a different chemical shift. 

Which peak would you expect to be more downfield? The -OH or the -CH3? 

That's right! The -OH peak is more downfield, because the oxygen is more electronegative. The attached hydrogen is deshielded. 

Why are the peaks different heights? The integral - the area under each peak - corresponds to the number of hydrogens found in that environment. So the peak which represents our -CH3 has an area under the peak of 3. 3 hydrogens are found in this environment. The area under the -OH peak is 1. 1 hydrogen is found in this environment.  

Index of hydrogen deficiency:

The structures of organic molecules can be varied and complex. For instance, many molecules will have double bonds, and even rings in their structures. How will this impact our ¹H NMR spectrum? Let's have a look.

Compare the number of hydrogens in the following molecules:

The molecule one the right has 1 double bond. It also has 2 fewer hydrogens. 

Both of the molecules have the same number of carbons, however the one on the right has 2 fewer carbons. 

So when we add double bonds or rings to our structures, we must remove some hydrogens. 

Wouldn't it be helpful if we could generalise these observations into something like a rule?

Thankfully we can! It is called the index of hydrogen deficiency (IHD), and it tells us how many double bonds or rings we have. 

Where X is the number of halogens - Cl, Br, F, I - in the molecule, if any.  

It is important to note that the IHD value does not tell me whether I have a double bond or a ring. Only that I have one or the other (or a combination of both, if IHD > 1).

Calculate the IHD for each of the following examples:

• Acetone C3H6O

• Acetic acid CH3COOH

• Ethanol C2H5OH

• 4-chloroaniline ClC6H4NH2

Count the number of double bonds and/or rings in the below structures. Did you get the right IHD value?

Multiplicity

So far we have discussed how electronegativities affect chemical shift, how to identify hydrogen environments, and what the integrals mean. There is one final, crucial piece of information we can get from ¹H NMR, relating to how the atoms are connected. Specifically, we need to be able to differentiate between the hydrogens attached to different carbons in a chain. We can do this by looking at the multiplicity, or splitting, of the signals.

Consider ethyl acetate:

Fact check: how many double bonds do we have? We have one double bond, and no rings. Therefore an IHD of 1 makes sense!

How many hydrogen environments do we have? What are their integrals?

Now take a look at the ¹H NMR spectrum for ethyl acetate:

We correctly predicted the number of environments, and the integrals. But hang on - why have the signals been split into multiple lines?! 

This splitting or multiplicity is due to neighbouring hydrogen environments. Have a look at the signal marked with an orange dot. It is called a triplet, because it has been split into 3 lines by the 2 neighbouring purple hydrogens. The signal marked with a purple dot has been split into 4 lines (quartet), by the 3 hydrogens attached to the neighbouring carbon. Why hasn't the green signal been split? The 3 hydrogens marked by a green dot do not have any neighbouring hydrogens. Therefore the signal appears as a single line, called a singlet.

The rule for peak multiplicity - or how many lines a peak will be split into - is (n + 1), where n is the number of neighbouring hydrogens in a different environment. 

For our purple peak, the number of neighbours n is 3, therefore the peak is split into (3 + 1) = 4 lines.

For our orange peak, the number of neighbours n is 2, therefore the peak is split into (2 + 1) = 3 lines.

For our green peak, the number of neighbours n is 0, therefore the peak is split into (0 + 1) = 1 line; i.e. there is no splitting! 

Carbon-13 NMR

Just as with ¹H NMR, the number of signals in a 13C NMR spectrum is given by the number of non-equivalent carbons in the molecule. The theory behind the technique is the same. However, 13C NMR does not show splitting/multiplicity. The areas under the peaks are also not typically used to tell us the number of carbons in an environment. 

How many 13C NMR signals would you expect for the following molecules (i.e. how many non-equivalent carbons are there)?