Symmetry operation
0Symmetry operation, by Wikipedia https://en.wikipedia.org/wiki?curid=10087606 / CC BY SA 3.0
#Physical_chemistry
#Symmetry
An action that leaves an object looking the same after it has been carried out is called a symmetry operation .
For example rotations, reflections and inversions etc.
There is a corresponding symmetry element for each symmetry operation.
For instance a point, a line or a plane can be a symmetry element.
The symmetry operation is performed with respect to a symmetry element （ a point, line or plane）.
In the context of molecular symmetry, a symmetry operation is a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state.
Two basic facts follow from this definition, which emphasizes its usefulness.
Physical properties must be invariant with respect to symmetry operations.
Symmetry operations can be collected together in groups which are isomorphic to permutation groups.
Wavefunctions need not be invariant, because the operation can multiply them by a phase or mix states within a degenerate representation, without affecting any physical property.
It corresponds to an operation of doing nothing to the object.
Because every molecule is indistinguishable from itself if nothing is done to it, every object possesses at least the identity element.
The Identity operation is denoted by E or I. In Identity operation, no change can be observed for the molecule.
Even the most asymmetric molecule can undergo identity operation.
The need for such an identity operation arises from the mathematical requirements of group theory.
Reflection operation The reflection operation is carried out with respect to a symmetry element known as mirror plane.
It is denoted as σ （sigma）.
This mirror plane must pass through the molecule and can’t be completely outside of it.
When this plane of symmetry is parallel to the principal axis of the molecule （molecular z-axis）, it is considered as a vertical plane （σv）....
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