Sachse Mohr’s Theory (Theory of Strainless Rings)

Baeyer’s strain theory successfully explained the relative stability of cyclic compounds having 6-membered rings (or more appropriately having 5-membered rings), but it failed to explain the stability of higher compounds. Since the valency deviation (d) of seven, eight. etc., membered rings is significantly high, these compounds should also be unstable; but the stability of these compounds is found to be similar to cyclohexane or cyclopentane.

Thus, valency deviation which is the criteria for determining the stability of cyclic compounds, failed to explain the stability of large rings (6 onwards). This was noticed by Sachse who proposed that 6- or more membered rings are not planar but puckered. The carbon atoms lie in different planes, thus the normal valency angle is retained and the rings become strainless rings.

The two strainless, multiplanar, or puckered conformations of cyclohexane are the more stable chair and the less stable boat. The stability of twist-boat conformer is lesser than that of chair by 5.5kcal/mole, but greater than that of boat. Twist-boat conformer is formed by moving one ‘flagpole’ hydrogen of the boat conformer to the left ant the other to the right.

Sachse Mohr's Theory

The chair and boat conformational isomers of cyclohexane rapidly inter-convert at ordinary temperature and are still not isolated individually, because only 5kcal/mole energy is utilised for the inter-conversion of these forms. However, the stability of chair form is more than that of boat form and the conformation is normally assumed by cyclohexane and its derivatives. At room temperature under equilibrium, the ratio of chair to boat conformation is about 100:1.

Relative Stability of Chair and Boat Forms

The relative stability of boat form to the chair form is due to the following reasons:

Hydrogen atoms are staggered in the chair conformation of cyclohexane (i.e., hydrogen atoms are present far away from each other), thus no steric repulsion occurs. As a result, the conformation has lower energy. On the other hand, in the boat conformation the hydrogen atoms on all the four carbon atoms (C2−C3 and C5-C6) are eclipsed (i.e., present considerably close to each other), thus a definite interference and repulsion (steric) develops between the hydrogen atoms. As a result, a considerable torsional strain develops. Therefore, the stability of boat form is less than that of chair form.

Note: Newmann projection formulas explain the eclipsing of hydrogen atoms in the best way.

The two forms of cyclohexane sketched according to Newmann projection formulas are as shown:

Newmann projection formulas

The boat conformation experiences an additional strain from the crowding of flagpole hydrogen atoms on C1 and C4. The two hydrogen atoms on C1 and C4, pointing towards each other are very close (183pm), while the sum of their Van der Waals radii is around 250pm; thus giving rise to van der Waals or steric repulsion and reducing the stability of boat conformer by 6.9kcal/mole.

Relative stability of chair and boat forms

The ratio of boat to chair conformation is very small (1:1000), therefore the chair form is considered more important than boat. The bonds in chair conformation of cyclohexane and its derivatives are divided into two types. Six of these bonds (full lines) are parallel to the axis of the ring, i.e., they point either up or down from the molecule, and are called axial bonds (a); while the other six bonds (dotted lines) lie along the equator of the molecule, i.e., they point sideways from the molecule, and are called equatorial bonds (e).

Axial bonds

The atoms or substituents attached to axial and equatorial bonds are known as axial or equatorial atoms or substituents. Since the chair form is mobile, each equatorial bond becomes axial and vice versa on inter-conversion of both the chair forms.

Presence of two types of bonds in cyclohexane gives rise to another problem related to its substituted derivatives. The problem is that whether a particular substituent (e.g., a methyl group in methylcyclohexane) will be axial or equatorial: The axial and equatorial substituents in monosubstituted cyclohexanes are in a dynamic equilibrium, and the equatorial form predominate the axial form in the equilibrium mixture.

Conformations of Rings Larger than Six

Like cyclohexane, cycloheptane also shows chair and boat forms as well as the chair conformation predominates at equilibrium. Partial eclipsing of hydrogen atoms in medium-sized rings (8 to 11 membered) results in crowding in even the most favourable conformation. This results in steric repulsion and increases the internal energy, thus these compounds are synthesised with much difficulty. On the other hand, they are strainless from the point of view of distortion of the tetrahedral bond angles; and are quite stable once formed, e.g., cyclodecane can assume the staggered conformation as shown:

Strainless Rings

In large ring compounds (12 and more membered), staggered hydrogen atoms which lie far from each other are present. As a result the distance between them is increased and no repulsion occurs. Thus, the internal energy of these compounds becomes less, their stability increases, and they can be synthesised easily.

Theory of Strainless Rings

It has been proved that cyclopentane and cyclobutane assume puckered conformation which allows staggering of adjacent hydrogen atoms. But cyclopropane exists as a true planar molecule as it has no conformational alternative.

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Santhakumar Raja

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