The document discusses improper rotation, which is a combination of a rotation about an axis and a reflection in the plane perpendicular to that axis. It can be described as a rotation followed by a reflection. An improper rotation axis (Sn axis) exists in a molecule when rotating it 360/n degrees followed by reflection produces an indistinguishable configuration from the original. Examples of molecules exhibiting improper rotation include boron trifluoride (S3), methane (S4), staggered ferrocene (S10), staggered ethane (S6), and a staggered molecule (S12).

2. BY
MUHAMMAD HASNAIN
IMPROPER
ROTATION

3. In geometry, an improper rotation, also
called rotoreflection or rotary reflection is, depending
on context, a linear transformation or affine
transformation which is the combination of
a rotation about an axis and a reflection in a plane
perpendicular to the axis.
In 3D, equivalently it is the combination of a rotation and
an inversion in a point on the axis. Therefore it is also
called a rotoinversion or rotary inversion.
What is Improper Rotation?

4. An improper rotation is performed by rotating the
molecule 360°/n followed by reflection through the
plane perpendicular to the rotation axis. If the
resulting configuration is indistinguishable from the
original, we say there exists an n-fold improper
rotation axis (or Sn axis) in the molecule
Formula of Improper Rotation (Sn): Cn + σh
What is Improper Rotation?

5. What is Improper Rotation?

6. EXAMPLES OF IMPROPER
ROTATION

7. EXAMPLES OF IMPROPER
ROTATION
BF3 Boron Trifluoride
Sn= S3

8. EXAMPLES OF IMPROPER
ROTATION
CH4 Methane
Sn= S4

9. EXAMPLES OF IMPROPER
ROTATION
Staggered Ferrocene
Sn= S10
Fe
Staggered Ferrocene
Top View
C10 Fe Fe
σh

10. EXAMPLES OF IMPROPER
ROTATION
Staggered Ethane
Sn= S6
σh
H
H
H
H H
H
OR
C6
H
H
H
H H
H
H
H
H
H H
H

11. EXAMPLES OF IMPROPER
ROTATION
Staggered Molecule
Sn= S12
σh
Cr
Staggered Molecule
Top View
C12

12. EXAMPLES OF IMPROPER
ROTATION
Sn= S7
σh
H
H
HH
H
H
H
C7
H
HH
H
H
H
H H
H
HH
H
H
H

13. THANK YOU