Chemistry ABSOLUTE CONFIGURATION OF GEOMETRICAL AND OPTICAL ISOMERS

Absolute and Relative Configuration :

While discussing optical isomerism, we must distinguish between relative and absolute configuration (arrangement of atoms or groups) about the asymmetric carbon atom. let us consider a pair of enantiomers, say (+)' and(- )' lactic acid. We know that they differ from one another in the direction in which they rotate the plane of polarised light. In other words, we know their relative configuration in the sense that one is of opposite configuration to the other. But we have no knowledge of the absolute configuration of the either isomer. That is, we cannot tell as to which of the two possible configuration corresponds to {+) - acid and which to the (- ) - acid.

D and L system : The sign of rotation of plane-polarized light by an enantiomer cannot be easily related to either its absolute or relative configuration. Compounds with similar configuration at the asymmetric carbon atom may have opposite sign of rotations and compounds with different configuration may have same sign of rotation. Thus d -lactic acid with a specific rotation + `3.82^(o)` gives I -methyl lactate with a specific rotation `-8.25^(o)`, although the configuration (or arrangement) about the asymmetric carbon atom remains the same during the change. Obviously there appears to be no relation between configuration and sign of rotation. Thus D/L system has been used to specify the configuration at the asymmetric carbon atom. In this system, the configuration of an enantiomer is related to a standard, glyceraldehyde. The two forms of glyceraldehyde were arbitrarily assigned the absolute configurations as shown below.
If the configuration at the asymmetric carbon atom of a compound can be related to `D` (+)-glyceraldehyde, it belongs to `D`- series; and if it can be related to `L`(- )-glyceraldehyde, the compound belongs to `L`-series. Thus many of the naturally occurring a -amino acids have been correlated with glyceraldehyde by chemical transformations. For example, natural alanine {2-aminopropanoic acid) has been elated to `L`(+)-lactic acid which is related to `L`(-)-glyceraldehyde. Alanine, therefore, belongs to the `L`-series In general, the absolute configuration of a substituent (`X`) at the asymmetric centre is specified by writing the projection formula with the carbon chain vertical and the lowest number carbon at the top. The `D` configuration is then the one that has the substituent 'X' on the bond extending to the 'right' of the asymmetric carbon, whereas the `L` configuration has the substituent 'X' on the 'left'. Thus,When there are several asymmetric carbon atoms in a molecule, the configuration at one centre is usually related directly or indirectly to glyceraldehyde, and the configurations at the natural (+)-glucose there are four asymmetric centres (marked by asterisk). By convention for sugars, the
configuration of the highest numbered asymmetric carbon is referred to glyceraldehyde to determine the overall configuration of the molecule. For glucose, this atom is `C- 5` and, therefore, `OH` on it is to the right. Hence the naturally occurring glucose belongs to the `D`-series and is named as `D`- glucose.

R and S System :This is a newer and more systematic method of specifying absolute configuration to optically active compounds. Since it has been proposed by `R,S` Cahn, `C,K` Ingold and `V, P` relog, this system is also known as Cahn-lngold-Prelog system. This system of designating configuration has been used increasingly since the early 1960's and may eventually replace the `DL`-system. Cahn-1 ngold-Prelog system is based on the actual threedimensional or tetrahedral structure of the compound. In order to specify configuration about an asymmetric carbon `C` abde , the groups `a, b, d` and `e` are first assigned an order of priority determined by the 'sequence rules'. These rules will be given later. For the present, let us assign priorities `1, 2, 3, 4` to the groups a, b, d, e. Thus the order of priorities may be stated as

`a > b > d > e`

`(I) (2) (3) (4)`

Now the tetrahedral model of the molecule is viewed from the direction opposite to the group `'e'` of lowest priority `(4)`. The 'conversion rule' says that :
i) If the eye while moving from `a b d` travels in a clockwise or right-hand direction, the configuration is designated `R` (Latin, Rectus = right).

Opttcal lsomensm in Compounds With More Than On Asymmetnc Carbon Atom :

carbon atom can produce molecular asymmetry. Thus the molecules containing an asymmetric carbon exist in two optically active forms, `(+)-` isomer and `(-)-` isomer, and an equimolar mixture of the two. `( pm )-` mixture, which is optically inactive. When there are two or more asymmetric carbon atoms in a molecule, the problem is complicated considerably. An organic compound which contains two issimilar asymmetric carbons, can give four possible stereoisomeric forms. Thus `2`-bromo-`3`-chlorobutane may be written as The two asymmetric carbons in its molecular are dissimilar in the sense that the groups attached to each of these are different.
`C_2` has `CH_3, H, Br, CHClCH_3`

`C_3` has `CH_3, H, Cl, CHBrCH_3`

Such a substance can be represented in four configurational forms.
The forms I and II are optical enantiomers (related as object and mirror image) and so are forms III and IV. These two pairs of enantiomers will give rise to two possible racemic modifications. It may be noted that forms I (`2 S, 3R`) and III (`2 S, 3 R`) are not mirror images or enantiomers, and yet they are optically active isomers. Similarly, the other two forms i.e., II (`2 R, 3S`) and IV (`2 R, 3 S`) are also not enantiomers but optically active isomers.

lsomensm of Tartaric Acid :

let us now proceed to discuss the optical isomerism of tartaric acid which contains two similar asymmetric carbon atoms, in
detail. The two asymmetric carbon atoms in tartaric acid,

`ast CH(OH)COOH`

`ast CH(OH)COOH`

Its molecule can be represented by space models of two tetrahedra joined corner to corner but for the sake of convenience we will use the planed formulas. The end groups being identical. in all four arrangements are possible according as one or both `H ` groups and `OH` groups are on the left or on the right.
Out of these, formula IV when rotated through `180^(o)` in the plane of the paper becomes identical with formula III. Therefore, for tartaric acid we can have only three different arrangements, viz. I, II and III. Now, if the force which rotates the plane of polarised light be directed from `H ` to `OH`,

i) structure I will rotate the plane of polarised light to the right and will represent (`+`)-tartaric acid;

ii) structure II will rotate the plane of polarised light to the left and will represent (`-`)-tartaric acid; and

iii) structure Ill will represent optically inactive tartaric acid, since the rotatory power of the upper half of the molecules is balanced by that of the lower half. It may also be noted that formulas I and II are mirror images of each other and hence represent (`+`) and (`-` ) isomers. Formula III, however, has a plane of symmetry (dotted line) and hence represents and inactive isomer of tartaric acid. In actual practice, four tartaric acids are known :

i) ( `+`)-Tartaric acid ;
ii) (`-`)-Tartaric acid;
iii) Inactive or i- t artaric acid; this is also known as meso - tartaric acid or m- t artaric acid ;
iv) ( `pm` ) Tartaric acid ; this form of tartaric acid being a mixture of equal amounts of (`+`) and (`-` )-isomers .

Number of optical isomers :

As it has been discussed above, a compound containing two dissimilar carbon atoms can exist in four optically active forms. Reasoning in the same fashion, we will find that a compound containing three such asymmetric carbon atoms can exist in eight different configurations which represent optical isomers. Thus in general, the number of stereoisomers for a compound with `n` distinct (different) asymmetric carbon atoms in `2^n`.
When an organic compound contains two similar asymmetric carbon atoms in its molecule, `abdC - Cabd`, the number of optically active isomers would be less than `2^n`. Thus, tartaric acid `[HO_2C CH(OH)CH(OH)CO_2H]` has two similar asymmetric carbon atoms and exists in only three forms. of which two are optically active and one is optically inactive (meso form). Thus, the general guidelines for predicting the number of optical isomers is given as under.

1. When the molecule is unsymmetrical:

Number of d and I isomers `(a) = 2^n`

Number of meso forms `(m) = 0`.

Total number of optical isomers `(a+ m) = 2^n`.

where `n` is the number of chiral carbon atom (`s`).

Common example is `CH_3CH(Br)CH(Br)CO OH`.

2. When the molecule is symmetrical and has even number of chiral carbon atoms:

Number of d and I isomers `(a) = 2^n * 1` .

Number of meso forms `(m) = 2^(n/2-1)`.

Total number of optical isomers `= (a+ m)`.

Common example is tartaric acid, `HO OC CH(OH)CH(OH)CO OH`.

3. When the molecules is symmetrical and has an odd number of chiral catbon atoms:

Number of d and I forms `(a)= 2^(n-1)`

Number of meso forms `(m) = 2^(n/2-1/2)`

Total number of optical isomers `= (a+ m) = 2^(n-1)`

Common example is `CH_3CH(OH)CH(OH)CH(OH)CH_3` .