Right-handed molecules

Evidence on the mechanism of reactions can also come from examining the exact molecular geometry of the overall process, its stereochemistry. For example, if a reactant with defined handedness (chirality) is converted to a product that is an equal mixture of the left- and right-handed forms, the loss of handedness indicates that a particular geometry must have been involved along the path. If a right-handed molecule is converted only to a left-handed product, we say that an inversion of configuration has occurred, and this also tells us a lot about how the reaction occurred. 

In the case of MAP, the concept of chirality was used so as to prevent centrosymmetry a chiral molecule cannot be superimposed on its image by a mirror or center of symmetry so that a crystal made only of left or right-handed molecules can accomodate neither of these symmetry elements. This use of the chirality concept ensures exclusion of a centrosymmetric structure. However as we shall see in the following, the departure of the actual structure from centrosymmetry may be only weak, resulting in limited nonlinear efficiencies. A prerequisite to the introduction of a chiral substituent in a molecule is that its location should avoid interfering with the charge-transfer process. 

Fig. 1. (a) The dipole-dipole attraction, illustrated by two molecules of chloromethane favourably orientated, end-to-end in van der Waals contact (b) the dipole-induced-dipole attraction, due to polarization of the right-hand molecule when it comes close to the left-hand molecule. (S signifies a fractional net charge, normally less than the full electronic unit.)... 

In the late nineteenth century, Vant Hoff and Le Bel announced the tetrahedral bonding of carbon atoms. This provided an explanation of the existence of enantiomers. But whereas processes in living nature often produced either left- or right-handed molecules, chemists in the laboratory were at first able to... 

To understand the symmetry considerations that emerge from the results, we defined a chirality pseudoscalar, c, to have the value +1 for right-handed molecules and —1 for left-handed molecules. For preferred photoemission, the sign of the... 

Figure 4.2 Anisotropy of SCF and correlated components of interaction energy in (HF) . P refers to the angle between right-hand molecule and F F axis. Centers of mass of two molecules are held fixed at 2.8 A.

This is a very puzzling fact. Nobody knows why it is that we are built of L-amino acid molecules, rather than of D-amino acid molecules. All the proteins that have been investigated, obtained from animals and from plants, from higher organisms and from very simple organisms—bacteria, molds, even viruses—are found to have been made of L-amino acids. Now right-handed molecules and left-handed molecules have exactly the same properties, so far as their interaction with ordinary substances is concerned—they differ in their properties only when they interact with other tight-handed or left-handed molecules. The... 

The third type of symmetry operation considered here involves inversion, the act of turning an object inside out. If a glove is taken as an example, the reader can verify that inversion will also convert a left hand to a right hand. The point about which inversion of an object occurs is called a center of symmetry (or a center of inversion. Figure 4.5). If an object lies at a distance r from a center of symmetry, its symmetry-related object lies at an equal distance (-r) in the opposite direction. This means that if a center of symmetry lies at the origin of a unit cell, it converts an object at x,y,z to one at -x,-y,-z. This type of symmetry operation will convert a left-handed molecule into a right-handed molecule, and vice versa. 

FIGURE 4,12. A glide plane causes a reflection across a mirror plane plus a translation of half the unit cell edge (translation = a/2) A left-handed molecule is converted to a right-handed molecule by this symmetry operation. Two such operations give the original molecule translated to the next unit cell (translation = a). 

Chiral molecules of one handedness can only crystallize in space groups lacking any symmetry operations that would convert a left-handed molecule into a right-handed molecule. 

We can also see on Fig. 2-18 that it is the interaction of the HOMO of the left hand molecule and the LUMO of the right hand molecule that leads to the largest drop in energy (2EA > 2EB). The interaction of other occupied orbitals with other unoccupied orbitals—as in Fig. 2-19—is less effective, because the closer the interacting orbitals are in energy, the greater is the splitting of the levels (see p. 15). Now we can see why it is the HOMO/LUMO interaction... 

LEFT-HANDED AND RIGHT-HANDED MOLECULES OF ALANINE... 

The nematic phase has point group symmetry Dooh- If we add some amount of chiral, e.g., right-handed molecules, the symmetry is reduced from Dooh to Dqo (symmetry of a twisted cylinder). Such a phase is called chiral nematic phase. Chiral molecules used as a dopant (solute) in nematic solvent considerably modify the nematic surrounding and the overall structure becomes twisted with a helical pitch Pc, incommensurate with a molecular size a, na (n is an integer) and usually Po a. Typically, a < 10 nm, Pq = 0.1-10 pm. 

What has been said above shows that the macroscopic helicity as such has no direct relation to the polarity of the SmC phase. One can select chiral molecules without dipoles and construct a helical SmC that will have a polar axis without polarisation. But, is it possible to have finite polarisation without helical structure in the bulk Can we make a uniform polar phase with infinite helical pitch The answer is Yes . To this effect we should prepare a mixture of left-handed and right-handed molecules of dijferent chemical structure. An example is shown in Fig. 13.5 [7]. In this case, R-DOBAMBC is mixed with L-HOBACPC (p-hexyloxybenzylidene -p -amino-chloropropyl-cinnamate). The sample is rather thick, d = 200 pm. With a... 

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