Symmetry elements
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Why are we interested in symmetry?
• Governs properties such as polarity, chirality and colour - Assigning molecular vibrations
When is a molecule symmetric?
If there is a transformation that moves the molecule, but it is indistinguishable from the original molecule
What is a symmetry operation?
Movement
What is a symmetry element?
Point, line or plane or a combination
What are the 5 symmetrical elements that we consider?
Identify Rotation about a proper axis Reflection in a plane Inversion through a centre Combined rotation-reflection , an improper rotation
What is identity element?
E Present in all molecules as it leaves the molecule unchanged
What is rotation about an n-fold axis of symmetry (Cn) ?
A molecule thats rotated about an axis and generates an identical appearance n times in a complete rotation 360 degrees
What happens when a molecule contains more than one type of Cn axis with the same value of n?
They are distinguished by primes, C2’, C2’’
What is the principle axis?
When a molecule has more than one Cn axis with different n, the axis of highest order
How many operations does Cn provide?
n - including E
What operation is C₄² equal to?
C₂
What is σ?
Reflection in a mirror plane
What are the three types of mirror plane?
Horizontal mirror plane Vertical mirror plane Dihedral mirror plane
What is σh?
Horizontal mirror plane
What is σv?
Vertical mirror plane
What is σd?
Dihedral mirror plane
What is horizontal mirror plane ?
Perpenditular to the principle axis of rotation
What is vertical mirror plane?
Contains the principle axis of rotation
What is the dihedral mirror plane?
Bisects two C2 axis of symmetry and contains the principle axis
What is i?
Inversion through a centre of symmetry
When does a molecule have an inversion centre?
Has pairs of atoms that a diametrically opposite to each other
What are some examples of molecules with inversion centres?
CO₂ SF₆ Staggered ethane
Can tetrahedral molecules have a centre of inversion?
No
Does water have a centre of inversion?
No