Centre of symmetry and alternating axis of symmetry

What is elements of symmetry ?

Organic molecules are covalent compounds having definite bond length and bond angles among the constituents atoms.

Organic molecules can be confidently taken as idealised statics entities that can be represented by rigid mechanical models.

Mechanical models having definite geometric shapes, like symmetric and non symmetric depending on certain basic elements of symmetry.

In stereo chemistry,the elements of symmetry can be considered as a specific operations that generate the repetition of the geometric shapes of the molecule which observed before carrying out symmetry operation.

What is centre of symmetry ?

A centre of symmetry is an imaginary point in the molecules such that if a line is drawn from any group of the molecule to this point and then extended to an equal distance beyond the point,it meets the mirror images of the original group.

Centre of symmetry is also called centre of inversion, denoted by Ci .For example, 2,4-dimethyl cyclobutane-1,3-di-carboxylic acid exhibit centre of symmetry and so it is optically inactive.

2,4-dimethyl cyclobutane-1,3-di-carboxylic acid 

Why  cis form of 2,5-dimethyldihydropyrimidine-4,5-dione is optically active,but trans form optically inactive ?

The cis form of 2,5-dimethyldihydropyrimidine-4,5-dione has no centre or plane of symmetry, so it is optically active whereas trans form of 2,5-dimethyldihydropyrimidine-4,5-dione has a centre of symmetry, hence it is optically inactive.

What is alternating axis of symmetry ? 

A molecules possess an alternating axis symmetry ( Sn) of n fold if rotation of the molecule about the axis by 2π / n followed by reflection through a plane perpendicular to this axis produces an indistinguishable with the original.

It is also called rotation or reflection of symmetry. For example,1,3,7,8-tetramethyl-5-azaspiro-[4,4] nonan-5-ium have alternating axis of symmetry.

This compound possess alternating axis of symmetry and also has a plane of symmetry, so it is optically inactive.




Summary

• Elements of symmetry
• Centre of symmetry.
• Alternating axis of symmetry.

Click here: Racemic modification and resolution