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Chiral molecules are molecules that do not have a plane of symmetry, an inversion center, or so-called improper rotation symmetry axes. For example, the water molecule has a plane of symmetry but sugar molecules don't. As a consequence, chiral molecules such as sugars, amino acids, and most other bio-molecules come in two forms (enantiomers) that are mirror images of each other and that are not the same. The concept of chirality is not restricted to molecules; one can also speak of chiral objects in general terms. The term "chiral" means "handedness" and refers to the fact that our hands are mirror images of each other [when you press a hand flat against a mirror it looks the same as if you press your hands flat together] but a hand and its mirror image are not identical since one cannot superimpose images of them. Chiral objects always come in pairs, conceptually. Back to molecules: two enantiomers have the same chemical reactivity, the same mass, volume, and so on. One can distinguish them most easily in two ways: First, enantiomers react differently with other chiral molecules. Second, chiral molecules are said to be optically active.

Optical rotation

Two phenomena play an important role in the context of optical activity. One of them is optical rotation. Optical rotation means the rotation of the plane of polarization of a linearly polarized light beam as it passes through an optically active medium, for instance a solution of chiral molecules. The rotation angle is proportional to the path length through the medium, and in case of a solution also to the concentration of the chiral substance. The graphics below shows an animation of a linear polarized light wave as it passes through an optically active medium (indicated by the rectangular box). The plane of polarization of the light wave rotates proportional to the path length. The box dimension, the amount of rotation, and the amplitudes are not to scale. The wavelength used for this experiment is typically 589.3 nm (yellow light from a sodium lamp) and the length of the cuvette is usually 10 cm (1/3 foot).

Circular Dichroism

Another important phenomenon that is only observed for chiral substances is called "circular dichroism" (CD). In a nutshell, if we record the electronic absorption spectrum (typically in the UV-Vis range) with circularly polarized light instead of linearly polarized light, the spectra for one of the enantiomers recorded with left- or right-hand circular polarized light differ slightly. Compare the red and green curves in the graphics below. (See the next paragraph for some animations of circularly and elliptically polarized waves and further explanations). If we plot the difference between the two absorption spectra we have what is called the CD spectrum shown in the graphics below in blue (here: "red minus green"). The CD spectrum (the delta-epsilon curve) for the other enantiomer would have the opposite sign, i.e. we would obtain the blue curve mirrored at the horizontal axis. Nonchiral substances to not exhibit CD.

Circularly Polarized Light

The fact that the absorption spectra of a chiral substance measured with left- and right-hand circularly polarized light differ somewhat can be rationalized by the fact that circularly polarized light is "chiral" in itself. Why is that? Helical objects are chiral. Look at the pictures of the bike-stand below:

Any helical object like this one has a mirror image that is also helical but with the opposite sense of rotation. The mirror image and the original are not identical. In a sense, every chiral molecule also has such a helicity built into it

.The two forms of circular polarization of light (left or right) are mirror images of each other. First, let's see what a circularly polarized light wave looks like. We consider only the electric field component of the electromagnetic wave. Suppose you superimpose (add) two linearly polarized electromagnetic waves with the same amplitude and frequency (wavelength) but where the electric field vector in the one case oscillates, say, in the xz plane and in the other case it oscillates in the yz plane. Suppose the waves propagate in the z direction. If the two waves have a phase shift of exactly one quarter of the wavelength, voila! We obtain a light wave where the resulting electric field vector at any point along the z direction turns around on a circle either clock-wise or anti-clock-wise. This is why we call this light wave circularly polarized. See the animation below on the left. In case the two amplitudes are not exactly equal, the electric field vector rotates clock-wise or anti-clock-wise on an ellipse instead and we obtain elliptically polarized light. See the animation below on the right. You can also download interactive versions of these animations and change the key parameters yourself. (Right-) click on the animations and choose "Save link as" to save the file to your computer. You need the Mathematica Player (free download from http://www.wolfram.com/products/player/download.cgi).

These two forms of circularly polarized light interact slightly differently with a chiral molecule which causes the circular dichroism. A difference in interaction of the two forms of circularly polarized light with an enantiomer of a chiral molecule also causes the optical rotation which is explained further below.

As an example, consider the molecule "Hexa-helicene". Its chemical formula is shown below on the left (Hexa because of the 6 six-rings). The molecule adopts a helical shape as shown in the middle, otherwise the atoms at the ends of the molecule would get too close. There are two possible forms: a left-handed helical form as shown below ("M" for "Minus"), or the mirror image which has a right-handed helical shape (not shown. This molecule is named (P)-Hexahelicene, with "P" for "Plus"). Because of its helical shape, the molecule is chiral. It has a very intense CD spectrum shown below on the right. In green is the experiment. In red is the results of a computation that we did in 2002 (Ref. [9]) which agrees quite well with the experiment except at the shortest wavelengths where we cut off the computation. (P)-Hexahelicene would have a CD spectrum of the opposite sign.

What causes the optical rotation?

Interestingly, a monochromatic linearly polarized light beam can be considered as a superposition of two circularly polarized electromagnetic waves that are propagating in the same direction with the same frequency but the opposite sense of rotation. Consider the animation of circularly polarized light above. If we superimpose this wave with a circularly polarized wave of the opposite "handedness" where the blue component is 1/4 wavelength behind (instead of ahead), the two blue components will completely cancel because they are 180 degrees (half a wavelength) out of phase. Thus, we would be left with just a linearly polarized wave.

The plane of polarization of the resulting linearly polarized wave thus prepared can be changed (rotated) by applying a phase shift between its two circularly polarized components. With the help of this concept we can explain the phenomenon of optical rotation: We have seen that chiral molecules interact slightly differently with the two circularly polarized components of a linearly polarized light beam. This is true both for absorption and refraction. Left- and right hand circularly polarized light beams also have slightly different refractive indices in a chiral medium. This means that even if they are not absorbed they travel at different speeds through the medium. Therefore, this causes a phase shift between the two circularly polarized components which increases proportional to the path length that the light travels through the chiral medium. This phase shift manifests itself as a rotation of the plane of polarization of the resultant linearly polarized light beam - optical rotation. In fact this is exactly how the animation of optical rotation at the top of the page was created with the Mathematica program.

Ellipticity

Suppose we investigate optical rotation at a wavelength where the medium absorbs some of the light's intensity. Since a chiral medium absorbs left- and right-hand circularly polarized light differently (the CD effect), the amplitudes of the outgoing two circularly polarized components of the light beam are not equal anymore after they have passed through the absorbing chiral medium. They have a phase shift and a different amplitude. We end up with a situation similar to the one depicted in the animation above on the right (different amplitudes). I.e. the outgoing light beam is not linearly polarized anymore but elliptically polarized. See the animation below which was created with Mathematica in the same way as the one on the top of the page but where one of the circular components is also reduced in amplitude as it passes through the optically active medium. The ellipticity of the outgoing light is clearly visible in the electric field vector (orange) at some fixed position.

You need the Mathematica Player to open the downloaded file (free download from http://www.wolfram.com/products/player/download.cgi)