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Fig. 2.1 Two three-dimensional non-superimposable molecular structures of the amino acid a-alanine. The structures are unsymmetrical and chiral; each of them is called an enantiomer constitution of all chemical bonds connecting the functional groups of a-alanine. The central carbon atom, called a-carbon, holds the amino group and the carboxylic function as well as a methyl group. Consider that the structure is given in three dimensions: The methyl group at the bottom of the left structure points towards the viewer as it is illustrated by the thick line, whereas the methyl group in the right structure points away from the viewer as indicated by the dashed line. As a result of a-alanine's three-dimensionality, these structures are non-superimposable and, therefore, not identical. In fact, these molecular structures are unsymmetrical and mirror images of each other.

Structures of organic molecules (here: a-alanine) that are not identical, but mirror images of each other are called enantiomers (from Greek e%9po?, "enemy". The old term is optical antipode). Enantiomers belong to the group of isomers called stereoisomers, so do E and Z configurations at double bonds. In contrast to constitutional isomers, stereoisomers are identical in the connectivity of the atoms, but differ in the overall shape of the molecules. The prefix stereo- (Greek oxepeo, "solid") refers to the fact that stereoisomerism involves structures that must be regarded as three-dimensional.

Structures are chiral (Greek %eip, cheir, "hand") if they cannot be superimposed onto their mirror image or - as Vladimir Prelog put it in his 1975 Nobel Prize lecture ". . . if it cannot be brought into congruence with its mirror image by translation or rotation" (Cronin and Reisse 2005). The two distinct forms of chiral molecules that can exist are said to have opposite absolute configuration. Achiral structures -on the other hand - are superimposable on their mirror images. The amino acids glycine and P-alanine are superimposable on their mirror images and give examples of achiral amino acids (Fig. 2.2).

By definition, the a-carbon atom of an amino acid is located next to the car-boxylic group. In an a-amino acid the amino group is connected at the a-carbon atom. In a P-amino acid such as P-alanine, the amino group is linked to the P-carbon atom.

Fig. 2.2 Molecular structures of the a-amino acid glycine (left) and the P-amino acid P-alanine (right). Both molecules are superimposable with their mirror images and therefore achiral. Keep in mind: Amino acids are not necessarily chiral

The essential difference between chiral and achiral molecules is that chiral molecules do not possess a plane of symmetry;1 achiral molecules, on the other hand, do have a plane of symmetry. In Fig. 2.2, the paper plane is this plane of symmetry. Any structure that has no plane of symmetry can exist as enantiomers. Any structure - on the other hand - with a plane of symmetry cannot exist as two enantiomers.

Using the definition of symmetry, the terminus "chiral" is by no means limited to molecular structures only. The same rules apply to everyday objects such as hands, gloves, scissors, pencil sharpeners, cars (with the non-symmetric position of the steering wheel2), dice (allowing to distinguish between original and imitation), snails, and shells, which have no plane of symmetry and are therefore chiral. Shoes provide another example. Your ears are chiral as well. Screws are chiral. They are manufactured so that they move forward by turning them clockwise with a screwdriver. Sometimes left-handed screws are prepared for special purposes. For example, pedals are fixed with right-handed screws on the one side and with left-handed screws on the other side of the bicycle in order to prevent them from loosening. The Moebius strip, the folding of arms, the way a person applauds, and the crossing of legs are asymmetric and chiral.

Rotating cyclones and tornados are chiral. They have a strong tendency to spin counterclockwise in the northern half of the globe, going clockwise in the southern half. The Coriolis effect based on earth's rotation causes this "symmetry-violating" spinning. As for the direction of bathtub vortices, the situation is not that clearly understood. Here, the question arose whether the Coriolis effect is strong enough to influence the right- versus left-handedness of the vortex. If the Coriolis effect had a dominating influence, this spiralling tendency of water down drains would be strongest at the poles, decreasing gradually as the tub moved toward the equator, where the tendency would vanish (Gardner 2005). Probably, however, many other factors are responsible for the vortex's right or left rotation such as the circulation the water acquires when the tub is filled and slight irregularities in the surface of the tub (see Chap. 4). Anyway, rotating vortices are chiral.

In many sports we can observe the counterclockwise travel around the field: In car racing, horse racing, bicycle racing (Bremer 6-Tage Rennen), dog racing, skating rinks, Olympic games, and so on. Baseball players dash counterclockwise around the bases. Carousels and carnival rides as well. Even customers in supermarkets are guided into a couterclockwise shopping tour. As Scot Morris, a correspondent, put it (in Gardner 2005) "it seems that everything goes counterclockwise except clocks".

1 In specific cases a molecule is achiral if it shows a center of symmetry. (3S,6R)-3,6-dimethylpiperazine-2,5-dione serves as example for a cyclic molecule with a center of symmetry, but without a plane of symmetry, that is achiral. In an alternative classification based on the group theory, chiral molecules belong to the non-axial point group C1 or the purely rotational groups Cn and Dn.

2 In continental Europe cars have steering wheels on the left for right-of-the-road driving. This convention is almost universal throughout the world. Main exceptions are the British Isles, Malta, India, Australia, New Zealand but also Japan. Sweden, where the tourist accident rate was especially high, was the last nation on the continent to switch from left to right driving. The changeover that took place in 1967 was accompanied with a high costly preparation (see also Gardner 2005).

But even they are counterclockwise if you consider their motion from the clock's point of view.

A chair - on the other side - shows a plane of symmetry and is therefore achi-ral. An empty room shows three planes of symmetry and is achiral. Throw your glove into it, and the room will become chiral, too. Wonderful examples and impressive, colourful illustrations of chiral macroscopic structures were given by Brunner (1999). The lettering on book spines is chiral and differs between Europe and the Anglo-Saxon room. University libraries are faced with this irregularity particularly when half of the books are from Continental Europe and the other half from England and the United States. Clothing tends to follow the bilateral symmetry as well: Cravats (ties) in the United States show diagonal stripes in an inverse direction to European ones.

Occasionally, chemical reactions develop beautiful macroscopic chiral structures. They can be visualized - to give an intriguing example - by the Belousov-Zhabotinskii reaction (Fig. 2.3). Here, spiral structures form and move due to spatial

Fig. 2.3 Formation and growth of helical structures (spiral-waves) formed during the Belousov-Zhabotinskii reaction. In the vicinity of a right-handed helix, a left-handed helix is formed, moving synchronously. The photo was taken 40 min after mixing aqueous solutions of 0.33 mol L-1 ma-lonic acid, 0.33 mol L-1 NaBrO3, 0.2mol L-1 H2SO4, and putting them onto a petri dish covered with a 1.4mm gel produced by 5mL filtered 14% (w/w) Na2OxSiO2 and 2mL 25mmol L-1 ferroin solution. Gel formation was induced by adding 1.2mLof 1.4molL-1 H2SO4. The diameter of the petri dish is 85 mm. Photo: Christoph Gottschling, Dept. Phys. Chemistry, University of Bremen

Fig. 2.3 Formation and growth of helical structures (spiral-waves) formed during the Belousov-Zhabotinskii reaction. In the vicinity of a right-handed helix, a left-handed helix is formed, moving synchronously. The photo was taken 40 min after mixing aqueous solutions of 0.33 mol L-1 ma-lonic acid, 0.33 mol L-1 NaBrO3, 0.2mol L-1 H2SO4, and putting them onto a petri dish covered with a 1.4mm gel produced by 5mL filtered 14% (w/w) Na2OxSiO2 and 2mL 25mmol L-1 ferroin solution. Gel formation was induced by adding 1.2mLof 1.4molL-1 H2SO4. The diameter of the petri dish is 85 mm. Photo: Christoph Gottschling, Dept. Phys. Chemistry, University of Bremen oscillations in a chemical system far away from chemical equilibrium but consistent with the laws of thermodynamics. It is clearly visible that 50% of the chiral waves evolve as right-hand spirals and 50% evolve as left-hand spirals. Often, in the near vicinity of a right-hand spiral a left-hand spiral evolves simultaneously and vice versa.3

Liesegang rings serve as a further beautiful example of the formation of macroscopic chiral helical structures developing during chemical reactions (Fig. 2.4). Here also, "ordered" structures evolve from a highly disordered mixture of molecules in solution: Visible helices develop spontaneously in this system far from chemical equilibrium involving reactions of higher order kinetics. 50% of the evolving spirals are right-helices and 50% are left-helices. It is worth mentioning that similar thermodynamic and kinetic conditions involved in the BZ-reaction and Liesegang ring structures, creating "order" out of "disorder" are discussed to be required for distinct steps of chemical and biological evolution as well. Other molecular systems to be studied in the laboratory that lead to observable chiral macroscopic phenomena include the left and right rotation of Benard-cells, chiral crystals, chiral liquid crystals, and chiral membranes.

Fig. 2.4 Formation and growth of helical Liesegang rings in a viscous medium. In order to perform this "swinging" chemical reaction with oscillating properties in the lab, 4 g gelatin were added to 20 g of an aqueous potassium dichromate solution (0.2% (w/w)) by heating slightly. 10 mL of the warm yellow solution were given into a test tube. After cooling, 10 mL of 10% (w/w) silver nitrate solution were added cautiously onto the gel. Because of the light-sensitivity of silver salts, the test tube was mantled with aluminum foil. After 24 h, macroscopic chiral helical structures develop due to silver ion diffusion into the gel and precipitation of brownish silver chromate. By introducing the silver nitrate solution into the gel with the help of a Pasteur pipette, a capillary, or a dissolving medicinal drug capsule, onion layer-like three-dimensional structures form

Fig. 2.4 Formation and growth of helical Liesegang rings in a viscous medium. In order to perform this "swinging" chemical reaction with oscillating properties in the lab, 4 g gelatin were added to 20 g of an aqueous potassium dichromate solution (0.2% (w/w)) by heating slightly. 10 mL of the warm yellow solution were given into a test tube. After cooling, 10 mL of 10% (w/w) silver nitrate solution were added cautiously onto the gel. Because of the light-sensitivity of silver salts, the test tube was mantled with aluminum foil. After 24 h, macroscopic chiral helical structures develop due to silver ion diffusion into the gel and precipitation of brownish silver chromate. By introducing the silver nitrate solution into the gel with the help of a Pasteur pipette, a capillary, or a dissolving medicinal drug capsule, onion layer-like three-dimensional structures form

3 Chemical kinetics of the Belousov-Zhabotinskii (BZ) reaction are described by the Field-Koros-Noyes (FKN) model and can be followed using Mathematica® software (Kondepudi and Prigogine 1998). The BZ-reaction can easily be reproduced in the chemical laboratory at secondary school or high school level.

Coming back to chiral structures on the microscopic molecular level we note that bromochlorofluoromethane is chiral because it does not have a plane of symmetry. In fact, it cannot have a plane of symmetry, because it contains a tetrahedral coordinated carbon atom carrying four different groups (substituents): Br, Cl, F, and H. Such a carbon atom is known as a stereogenic center.4

For quite a while and beside amino acids, bromochlorofluoromethane was the "uncontested star" of chiral molecules. Among other experiments, one was able to determine its absolute configuration by a specific technique called Raman optical activity (Costante et al. 1997). Nowadays, particular interest is given to a chirally deuterated version of neopentane that represents the archetype of all molecules that are chiral as a result of a dissymmetric mass distribution (Barron 2007). The absolute configuration of enantioenriched ^-[2Hi, 2H2, 2H3]-neopentane (Fig. 2.5) was determined by Raman optical activity as well (Haesler et al. 2007).5 Also here, the central carbon atom is called a stereogenic center.

If the two enantiomers of bromochlorofluoromethane (or [2Hi,2H2,2H3]-neopentane) are formed in equal quantities, the pair of enantiomers is called a racemic mixture (compare Latin racema, "grape") or more loosely a racemate. The abbreviation is rac-bromochlorofluoromethane. This principle is very important. Never forget that if the starting materials of a reaction are achiral and the products are chiral, they will be formed as a racemic mixture of enantiomers. Amino acids produced by the Strecker synthesis must be racemic, because the starting compounds (aldehyde, ammonia, and KCN) are achiral. However, if we isolate alanine from a natural protein-rich source by hydrolysis, we find solely one enantiomer (Fig. 2.1 structure on the right). Samples of chiral compounds that contain only one enantiomer are called enantiomerically pure. We know from X-ray crystal structure

Fig. 2.5 Molecular structures of [2Hi , 2H2, 2H3]-neopentane enantiomers. The molecules are mirror images, non-superimposable, and therefore chiral. The K-enantiomer is depicted on the left, the ¿-enantiomer on the right. The specific rotation of these molecules is not yet known

4 If, on the other hand, a molecule possesses a stereogenic center, it is not necessarily chiral. The mirror plane of symmetry may pass through a (pseudo-) stereogenic center which has four different substituents among them one substituent in ^-configuration and the same substituent in ¿-configuration. 2,3,4-Trihydroxyglutaric acid serves as example for an achiral molecule although it has a stereogenic center. Here, the stereogenic center is called pseudochiral center. The substituents are called enantiotopic groups (see for example Denmark 2006).

5 For the ROA measurements Haesler et al. (2007) synthesized enantiopure K-[2Hi, 2H2, 2H3]-neopentane. In order to eliminate deterministic offset problems the authors did require neither the physical optical antipode ¿-[2Hi , 2H2, 2H3]-neopentane nor the racemic neopentane mixture. Instead, ¿-[2Hi , 2H2, 2H3]-neopentane was "created optically" by the use of optical half-wave re-tarders (Hug 2003). This "virtual enantiomer" has the optical properties of the "strict" enantiomer, i.e., the geometrical enantiomer composed of antimatter (see Chap. 5).

analysis that biologically produced alanine contains only this enantiomer. Life uses homochiral monomers for the construction of proteins (enzymes) and DNA. In fact, nature does rarely use the deviant "wrong" enantiomer, which we will learn in more detail in Chap. 3.

Before continuing, one issue that often gives rise to confusion should be addressed. All molecules that do not have a plane of symmetry are chiral. If the molecules are of the same enantiomer, such as naturally isolated a-alanine, they are enantiomerically pure or homochiral. But all a-alanine is chiral. Even racemic a-alanine that is produced by the Strecker-mechanism is chiral.

Students have to be aware of the fact that - on the other hand - processes as such are never chiral. Terms as chiral synthesis, chiral catalysis, chiral recognition, chiral chromatography, or the recent book titles "Chiral Separations" (Humana Press), and "Chiral Photochemistry" (Marcel Dekker) should be avoided. Chromatography on a chiral stationary phase should better be called "enantioselective". An asymmetric synthesis or a chemical catalysis might be "enantiospecific".

If a mixture of chiral molecules is neither racemic nor homochiral the quantity of one enantiomer over the other is given according to Eq. 2.1 by the enantiomeric excess (e.e.), in which c designates the concentration of the indicated enantiomer. The enantiomeric excess is identical to the optical or enantiomeric purity or (sometimes) optical yield (Rau 2004).

Enantiomers show identical physico-chemical properties. Scalar (i.e. nonvecto-rial) values of enantiomers are identical. In sharp contrast to diastereoisomers, they have identical vapour pressures, boiling points, melting points, solubilities, diffusion constants, ionic mobilities, refractive indices, and reaction rates including excited state lifetimes. Enantiomers show identical activation energies, heat of formation, entropies, and thus Gibbs energies, identical bond lengths, bond strengths, and angles between the bonds. They provide identical absorption spectra in the UV or in the IR,6 they show identical NMR spectra, and their mass spectra show identical fragmentation patterns. The important exception is the distinguishable interaction of enantiomers with linearly-polarized electromagnetic radiation. Chiral molecules can be (but must not)7 optically active. The experimental way to determine this basic chiroptical property will be outlined in the upcoming paragraph.

6 Photochromic compounds change their absorption spectra by photoirradiation. Photochromism phenomena of chiral molecules are more and more studied e.g. in the context of the photochemical control of liquid crystalline properties. For a recent review on chirality in photochromism see Yokoyama and Saito (2004).

7 Some chiral molecules possess an optical activity too small to be measured. They are not optically active. Examples are 1-lauryl-2,3-dipalmitylglycerid and trialkylmethanes such as enan-tiomerically pure 4-methylnonane.

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