INTERCONVERSIONS OF PROJECTION FORMULA

It is important to have a clear idea of the inter-relationship between various projections of a given organic molecule to understand the stereochemical implications of the reactions. For this, we should be well conversant with the methods of translating one projection into another. The methods used for converting one projection into another without changing the configuration are given in the following description.

Conversion of Fischer Projection into Sawhorse Projection and vice-versa:

(i) Fischer Projection to Sawhorse Projection:

Fischer projection of a compound can be converted into Sawhorse projection; first in the eclipsed form (in Fischer projection the groups on neighbouring carbons are considered to be eclipsing each other), by holding the model in horizontal plane in such a way that the groups on the vertical line point above, and the last numbered chiral carbon faces the viewer. Then, one of the two carbons is rotated by an angle of 180⁰  to get the staggered form (more stable or relaxed form).

For example, Fischer projection of an optically active tartaric acid is converted into staggered Sawhorse projection as shown.

(ii) Sawhorse Projection to Fischer Projection:

First, the staggered Sawhorse projection is converted to an eclipsed projection. It is then held in the vertical plane in such a manner that the two groups pointing upwards are away from the viewer, i.e. both these groups are shown on the vertical line. Such a conversion for 2,3-dibromobutane is shown.

Conversion of Sawhorse Projection to Fischer Projection via Newman Projection and vice-versa:

(i) Sawhorse Projection to Newman Projection And then Fischer Projection:

Conversion of Sawhorse projection to Newman projection is quite easy. The molecule is viewed from front carbon (the central C-C bond being invisible) to get the staggered Newman projection. The rear carbon is rotated by 180^o to get eclipsed Newman projection. Then, the molecule is held in the vertical plane, i.e. central bond is visible in the vertical plane in such a manner that front carbon is the lowest carbon.

(ii) Fischer Projection to Newman Projection and then Sawhorse Projection:

The molecule is viewed through the lowest chiral carbon, which becomes the front carbon, and thus eclipsed Newman projection is drawn. It is then converted into staggered conformation. Finally, the molecule is viewed through the bond connecting the front carbon with rear carbon. Such a conversion of D-erythrose is illustrated in the following scheme.

Conversion of Fischer Projection into Flying Wedge Projection and vice-versa:

(i) Fischer Projection to Flying Wedge Projection:

The vertical bonds in the Fischer projection are drawn in the plane of the paper using simple lines(—). Consequently, horizontal bonds will project above and below the plane (‘a’ and ‘b’ in the fig.). Conversion of Fischer projection of one of the enantiomers of α-bromopropanoic acid into five flying wedge formulae (without changing the configuration) is illustrated in the fig.

(ii) Flying Wedge Projection to Fischer Projection:

The molecule is rotated (in the vertical plane) in such a way that the bonds shown in the plane of the paper go away from the viewer, and are vertical.    

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Hybridization

Hybridization may be defined as the mixing of two or more than two atomic orbitals of an atom, having comparable energy, to give an equal number of identical orbitals hπaving same energy and shape. All hybrid orbitals are oriented symmetrically to have a maximum distance from each other. Thus, the molecule of methane can be represented by the overlap of a hydrogen 1s orbital with each of the four sp³  orbitals of carbon. Hybrid orbitals of other molecules may similarly be represented. Linear combination of a 2s and two of the 2p orbitals, for example in ethylene, gives rise to three trigonal sp² orbitals directed towards the corners of an equilateral triangle. The plane defined by the two original 2p orbitals leaves the remaining 2p orbitals, perpendicular to the plane of the triangle.

The planar structure of methyl radical can be represented by the overlap of each of the three sp² orbitals of carbon with an s orbital of hydrogen, forming three C-H bonds, leaving the odd electron on the third unhybridized 2p orbital free.

Likewise, hybridization of an s and p orbital gives two diagonal (sp) orbitals, directed towards the opposite ends of the line defined by the p orbital. Methane, ethylene and acetylene are the classic examples of sp³, sp² and sp hybridized carbon atom, respectively. The pictorial representation of hybridized orbitals of methane is given. Ethylene is represented by two carbon atoms combining through two sp² orbitals, and overlapping of the remaining two sp²  orbitals on each carbon atom with 1s orbitals of two hydrogen atoms. The unhybridized parallel 2p orbitals, one on each of the trigonal carbon atoms overlap each other sideways to form a π bond. The electrons involved in such a bonding are called π-electrons. The π-electron cloud (pi bond) is distributed above and below the plane of the molecule, which is the nodal plane of the pi cloud. The bond energy of the carbon-carbon pi bond is about 60 kcal or 250.8 kJ, and, is, therefore, weaker than a C-C sigma bond which is 83 kcal or 346.9 kJ of energy. As the carbon atoms are held more tightly, the carbon-carbon bond distance in ethylene is shorter (1.34 Angstrom) than the C-C sigma bond length in ethane (1.54 Angstrom). The angle between the bonds is 120^o, and the molecule is planar.

Likewise, in acetylene, as represented in the fig., each carbon atom is bonded diagonally to two other atoms, a carbon and hydrogen, through the overlap of two sp-hybridised orbitals of the carbon atoms, and of the remaining two sp orbitals of carbon atoms with two 1s orbitals of hydrogen. This leaves two p orbitals on each carbon atom, perpendicular to each other, as also to the sp hybrid orbital. The sideways overlap of the two parallel pairs of p orbitals leads to the formation of two π bonds, which merge into something like a cylindrical π electron cloud.

Hybridization and Bond Properties:

Bond properties, such as bond length and bond energy, are greatly influenced by the state of hybridization in which the atom exists. An s orbital is at a lower level than a p atomic orbital (AO), which is at a lower level than a d AO. Therefore, the greater the s contribution in the hybrid AOs of the valence state, the greater is the electronegativity of the atom relative to a second atom is determined by the electronegativity of the hybridized AO with which they enter into bonding. The dissociation energy of a bond increases with the difference in electronegativities of the bonded atoms. Therefore, it depends on the state of hybridization of the bonded atoms. The electronegativity of carbon is greatest in sp hybridized state and least in sp³ state. As a result, the C-H bond formed with a carbon orbital of high p-character. The change in hybridization of AOs in carbon, thus, produces a change in the size of covalent atomic radius, decreasing from the tetrahedral (sp³) to the diagonal type (sp). In fact, the state of hybridization in which the bonded atoms exist is the most important factor in determining bond length.

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