In post 20.27, we saw that optical isomerism occurs when a molecule is not identical to its mirror image. The two forms of the molecule are called optical isomers. They exist as the D or the L form that are mirror images of each other.
Books sometimes give the impression that the chemical reactions (post 16.33) that produce optical isomers produce an equal number of D and L forms; this mixture of optical isomers is called a racemic mixture. This is usually true but not always!
We have seen (post 20.27) that vitamin C consists solely of L ascorbic acid molecules (shown in the picture above). So plants that are sources of vitamin C (oranges, peppers etc.) must be able to synthesis L ascorbic acid and not a racemic mixture.
How can pure D or L forms be synthesised? Suppose that smaller molecules react together to make a chiral molecule (one that is not identical to its mirror image, post 20.27). If they bind to a chiral site on a larger molecule, they will produce a chiral product. This is because the molecules are held together in a chiral arrangement during the reaction. Then the larger molecule is acting as a catalyst (post 16.33) for the reaction. These catalysts can be either synthetic or natural polymers.
Enzymes, which are biological catalysts (post 16.33) normally have chiral sites which bind smaller molecules. If we think of the enzyme as a lock and a binding molecule as a key, only one of the optical isomers of a chiral molecule will then fit the lock. (In the picture above, the key won’t fit if you turn it upside-down. Turning it upside-down is the same as reflecting it in a mirror perpendicular to the plane of the picture. This reflection creates the optical isomer of the original key.) This explains, for example, why only L ascorbic acid, and not D ascorbic acid, has biological activity.
If we shine polarised light through a solution of the pure D form or the pure L form, the plane of polarisation is rotated – see post 20.28 to understand what this means. The direction of rotation is the opposite for the two forms. So one form will rotate the plane to the right (dextrorotatory) and the other to the left (laevorotatory or levorotatory). But be careful – the D form may be laevorotatory and the L form dextrorotatory! The labels D and L tells us nothing about the direction of rotation.
The ability of a chiral molecule to rotate the plane of polarisation is called optical activity and molecules that have this effect are optically active.
If you would like an explanation of why this effect occurs, see the appendix.
Dextrorotation is conventionally defined to be a positive rotation and laevorotation is negative. The angle of rotation, α, depends of the length, λ, of solution that the light passes through and the concentration of the solution; because increasing either of these variables increase the number of molecules that interact with the light beam. Since increasing the concentration of dissolved molecules will also increase the density, ρ, of the solution (post 16.44), we could also say that the magnitude of rotation depends on λ and ρ. Then the specific optical rotation is defined to be
[α] = α/λρ.
You might expect that the units of [α] would be degrees (or radians, post 17.11) divided by m.kg.m-3 = kg.m-2 (post 16.12). But you would be wrong! Why? Because, by convention, λ is measured in decimetres (dm, 1 dm = 1 m/10) and ρ is measured in g.cm-3 (1 g = 1 kg/1000, 1 cm = 1 m/1000). This weird convention arises because 1 dm is a convenient length of solution for measuring optical rotation and densities were measured in g.cm-3 before SI units were adopted (post 17.14). So, the units of [α] are o(dm.g.cm-3)-1; many authors mistakenly believe that [α] is measured in degrees! I will deal with this mess by giving values for specific optical rotation in “units” where a unit means o(dm.g.cm-3)-1.
Optical rotation also depends on the temperature of the solution and the wavelength of the light. So temperature and wavelength have to be specified when we give a value for [α]. The temperature is often given as a superscript of [α], for example, [α]25 degrees, for a measurement at 25oC. The wavelength is often given as a subscript so that for a measurement at 25oC with a wavelength of 589 nm we would write
589 nm is the wavelength of the most intense light from a sodium vapour lamp. This is called the D line in the optical emission spectrum of sodium, so you will often see D in place of 589 nm when specifying specific optical rotation values. This wavelength is very commonly used for measuring optical rotation. The reason is that, in the nineteenth century (when optical rotation was intensely investigated), this light could be produced by hanging a large lump of salt in a flame produced by burning gas.
There is a convention for showing whether an optical isomer is dextro- or laevo-rotatory. For example, L alanine (post 20.27) is dextrorotatory with a specific optical rotation of 2.4 units at 25oC at a wavelength of 589 nm. We can show this when naming L alanine by writing L(+) alanine where L defines which optical isomer (post 20.27) we are considering and (+) shows that it is dextrorotatory.
This is complicated. But measurements of optical rotation, made as described in post 20.28, are useful for identifying optical isomers and detecting whether, for example, a dextrorotatory form is contaminated with a laevorotatory form.
1 Circularly polarised light
To explain why optical rotation occurs, I am first going to explain the concept of circularly polarised light.
In circularly polarised light, electric vector (post 20.28) rotates with an angular speed of ω (see post 18.11 for the relationship between wave motion and motion in a circle). In a given interval of time, the wave will travel a distance along the z-axis and rotate. So the motion of the electric vector describes a helix – a shape like a corkscrew. If you find it difficult to imagine what this looks like, see the pictures at https://en.wikipedia.org/wiki/Circular_polarization.
Circularly polarised light is chiral (post 20.27) because the electric vector can rotate either clockwise or anticlockwise – these rotations are non-identical mirror images.
To find out more about circularly polarised light see part 4 of this appendix.
2 Plane polarised light
I am now going to explain that the plane polarised light, that we met in post 20.28, can be considered as the resultant of two beams of circularly polarised light – one with a clockwise rotation and the other with an anticlockwise rotation. If the first has an angular speed of ω, the other has an angular speed of –ω. When the beams of circularly polarised light add together, the electric vector makes an angle α = (ω – ω)t = 0 with the direction of propagation of the light. This result comes from the definition of angular speed (post 18.11) but further justification appears in part 4 of this appendix. The result means that the electric vector is not rotating and so the light is plane polarised.
3 Optical activity
We have seen that plane polarised light can be considered to have two chiral components. Optical activity occurs when these components interact with chiral molecules. In a solution, molecules will have random rotations but this doesn’t affect optical rotation because rotation of molecules doesn’t affect their chirality (post 20.27).
In post 20.28 we saw that light is propagated through a material because it causes electrons to oscillate; these oscillating electrons then act as a source of light. When plane polarised light meets a chiral molecule, the two circularly polarised components will not be propagated identically because they too are chiral. We can think that the symmetry of one component matches the symmetry of the electron distribution in the molecule butt the symmetry of the other component doesn’t. The difference means that, when we combine the two circularly polarised components, the plane of polarisation of the resulting plane polarised light does not remain the same but is rotated.
4 More about circularly polarised light
In this section, I will show how circularly polarised light can be generated by two beams of plane polarised light.
Let’s think about a beam of polarised light (post 20.28) whose direction of propagation defines the z-axis direction, in the picture above; the x and y directions are defined to make a right-handed orthogonal Cartesian coordinate system (post 16.50 appendix 2). The vectors i and j are unit vectors (post 17.2) in the x and y-axis directions, respectively. Suppose the electric vector (post 20.28) is confined to oscillate in the x-direction. Then it can be represented by
Ex = iEosin(ωt – kz)
where Eo is the amplitude of the light wave, ω is its angular frequency, t represents time, k is the angular spatial frequency of the light (post 19.20) and z is a distance along the direction of propagation (post 19.12).
Now let’s think about another beam of polarised light that is identical except that it is polarised in the y-axis direction and is 90o out of phase (post 18.10) with the first. Then its electric vector can be represented by
Ey = jEocos(ωt – kz)
because a cosine wave is 90o out of phase with a sine wave (post 16.50).
If we add the two waves together, the resultant electric vector is given by
E = Ex + Ey = iEosin(ωt – kz) + jEocos(ωt – kz).
What angle does E make with the z-axis direction? We answer this question at a fixed point in space that we can define to be z = 0, so that
E = iEosinωt + jEocosωt.
The tangent of the angle, α, that E makes with the direction of propagation (see picture above and appendix 5 of post 16.50 for information on tangents of angles) is given by
tanα = (Eosinωt)/(Eocosωt) = tan(ωt).
This means that
α = ωt.
So, the electric vector rotates with an angular speed of ω (see post 18.11 for the relationship between wave motion and motion in a circle). In a given interval of time, the wave will travel a distance along the z-axis and rotate. So the motion of the electric vector describes a helix.
The light whose electric vector rotates in this way is circularly polarised.