Signs of Rotations

The Larmor relation, Eq. 2.45, is the basis for determining the nuclear precession frequency. In many instances we are concerned only with the magnitude of the 

A positive rotation about z then leads to magnetization precessing in the order x — y —x — —y.  

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Although the alkyl halide and alcohol given in this ex ample have opposite config rations when they have opposite signs of rotation it cannot be assumed that this will be true for all alkyl halide/alcohol pairs... 

Techniques for determining the absolute configuration of chiral molecules were not developed until the 1950s and so it was not possible for Eischer and his contemporaries to relate the sign of rotation of any substance to its absolute configuration A system evolved based on the arbitrary assumption later shown to be correct that the enantiomers... 

It is convenient to distinguish between enantiomers by prefixing the sign of rotation to the nfflne of the substance. For exanple, we refer to one of the enantiomers of 2-butanol as (-l-)-2-butanol and the other as (—)-2-butanol. Optically pure (-l-)-2-butanol has a specific rotation [a]o of +13.5° optically pure (—)-2-butanol has an exactly opposite specific rotation [a]o of —13.5°. 

Because hydrogenation of the double bond does not involve any of the bonds to the chirality center, the spatial ariangement of substituents in (-l-)-3-buten-2-ol must be the sane as that of the substituents in (-l-)-2-butanol. The fact that these two compounds have the sfflne sign of rotation when they have the sane relative configuration is established by the hydrogenation experiment it could not have been predicted in advance of the experiment. 

An elaborate network connecting signs of rotation and relative configurations was developed that included the most important compounds of organic and biological chemistry. When, in 1951, the absolute configuration of a salt of (3-)-taitaiic acid was... 

Would you expect the 2-octanol formed by Sn2 hydrolysis of (-)-2-bromooctane to be optically active If so, what will be its absolute configuration and sign of rotation What about the 2-octanol formed by hydrolysis of racemic 2-bromooctane ... 

It was found that the signs of rotation of the recovered a-phenylbutyric acid corresponded to the known absolute configurations of the deuteriated alcohols if and only if the size relationships CH3 > CD 3 and H>D were valid. In the case of (-t-)-(S)-2-propanol-l,l,l-d3 (4), the optical yield was between 0-4 and 0 5% (Horeau et al., 1965), corresponding to A AG value of about 23 cal mol at 25°C. For the primary alcohols, quite analogous results were obtained (Horeau and Nouaille, 1966). 

One of these must be an inversion and the other a retention of configuration, but the question is which is which The signs of rotation are of no help in answering this question since, as we have seen (p. 138), rotation need not be related to configuration. Another example discovered by Walden is... 

An independent and virtually simultaneous report by Eabom and coworkers described the preparation of germyl hydride (5), the ethyl analogue of 3, by an analogous route (equation l)3. However, only one of the diastereomeric menthyloxy derivatives (4) could be separated by crystallization the other was not readily purified. Assignment of absolute configuration was not made for 5 but, based on the sign of rotation, it is most likely R. 

Our Form II has two uncommon features. In the first place it contains two hydroxyl groups attached to the same carbon but we have that in chloral hydrate. In the second place there is an ethylene oxide oxygen linkage. This might be called an alpha lactone with the water not split off. This formation of a ring structure is believed to account for the reversal of the sign of rotation. It is well known that the formation of the lactide from lactic acid, while not a lactone formation in the same... 

Usually polarimetric measurements are carried out to find out a given optical antipode and the result is reliable, but the sign of rotation, is not always a direct expression of configuration because rotation, as already stated, depends on nature of solvent, concentration of solution and temperature etc. as the following example shows -... 

The letter D and L are always written in capital and the sign of rotation is then represented in brackets. This means that these letters have nothing to do with rotation. On similar reasoning, tartaric acid would be... 

This curious phenomenon of inversion of groups about the asymmetric carbon atom, first studied by Walden (1893, 1985) is called Walden Inversion. In a number of other reactions, the inversion was so quantitative that the yield of the opitcal isomer was 100% while in others the product was a mixture of the (+) and (-) forms in unequal amounts signifying that the inversion was partial. The above conversion has been shown to occur in two steps. The step in which the actual inversion occurs constitutes a Walden inversion. Change in the sign of rotation does not necessarily mean that an inversion of configuration has occurred as is clear from the oxidation of D(+) glyceraldehyde to D(-) glyceric acid. 

In B the straight line is inclined and so is different from A. Since according to a general rule, the configurations of compounds forming a quasi-racemate must be opposite, in the above example, the acids with the same sign of rotation have the same configuration. 

Some further peculiar observations have been made regarding optically active malic acid. Since at that time, 1896 X-ray analysis was not available, Walden suggested the change to be taking place through the following cycle, based on the sign of rotation. 

In Cotton effect curves, we use the terms peaks and troughs. The use of maxima and minima is not recommended because of the confusion that may arise. Since these terms are employed to describe ultra violet spectra, the sign of rotation is unimportant. Sometimes we also use the terminology amplitudes and widths of Cotton effects. The meanings of these terms are clear from Fig. (10.6). The plain curves are much less useful than Cotton effect curves. 

Optically active phenyl-t-butylphosphine oxide with the same sign of rotation has been prepared by the reaction of Raney nickel with the (+)-selenide (107) and the (+)-sulphide (108),82 which suggests that the latter compounds have the same sign of rotation for the same absolute configuration. The absolute configuration of (—)-phenyl-t-butylphosphine oxide was apparently established by conversion into (—)-methylphenyl-t-butylphosphine oxide, but no details have been given. 

The designations (+) and (-) indicate the sign of rotation of the predominant enantiomer at the sodium D line the absolute configuration was not determined. 

Sign of rotation at the sodium D line shown in parentheses absolute configuration unknown. 

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