Symmetry and Group Theory Flashcards
What does the symbol Cn mean?
A rotational axis of order n, where a rotation of 360/n leaves the object unchanged
What is C1?
E - the indentity - everything has this
What directions are rotations?
Clockwise
What is the principal axis?
The axis of the highest rotational symmetry
What is the coincident of a C4 axis?
A C2 axis (if it has a C4 it has a C2)
What is an improper operation?
An operation that you cannot physically perform
Represented by Sn
It is a rotation of Cn, followed by a reflection in the plane PERPENDICULAR to that Cn axis.
What is S1?
A rotation of 360 followed by a reflection - so just a reflection
Represented by σ
What is σv?
the vertical reflection
contains principal axis
What is σd?
The dihedral reflection, bisects 2 C2 axes (C2, C2’)
Contains Principal axis
What is σh?
The horizontal reflection (PERPENDICULAR to principal axis)
What is coincident of a C6 axis?
A C2 and a C3
What is S2?
A rotation of 180, and a reflection in the perpendicular plane
Also known as an inversion (i)
How do you check if the centre of an object is an inversion centre?
Take each point of the object through the inversion centre to the equivalent point on the other side, and if the object remains unchanged, there is an inversion centre.
What is the relation of gerade and ungerade have to do with inversion centres?
When an object has an inversion centre, orbitals can be labelled g or u,
If no inversion centre, no orbitals are g or u
What is ungerade?
Charge inverts
What is gerade?
Charge retained
What is an S4 operation?
Rotation of 90 followed by reflection in the perpendicular axis
How do you find the point group?
Find all the symmetry elements of the object, determine the number of proper vs improper operations.
They should be the same, if the object has both proper + improper operations
What is a point group?
A group of symmetry operations which form a closed set
What is a closed set?
A set of symmetry operations such that successive applications of the operations is equivalent to another operation which is also a property of the object
What does a proper operation followed by a proper operation give?
A proper operation
What does an improper operation followed by an improper operation give?
A proper operation
What does an improper operation followed by a proper operation (and vice versa)?
An improper operation
Where can you find the point groups?
In the data book
Where can you find the flow chart for point groups?
in the data book
Are chiral objects symmetrical?
No they are dissymetric, the chiral carbon is asymmeric
Can chiral objects have improper operations?
NO, only proper operations
How can you determine what the mirror plane means (e.g. xz, yz)?
Draw a 3D axis with x y and z
In a character table for a point group what do the 2 far right column show?
1st - The p oribitals and the rotations
2nd - d orbitals
What does an irreducible representation describe?
The symmetry of a particular property of the point group of intererest
What is an E irreducible?
A doubly degenerate irreducible
Represents a pair of properties that are symmetry indistinguishable
What does the label A mean ?
Singly degenerate and totally symmetric (1) about the principle axis
What does the label B mean?
Singly degenerate and antisymmetric (-1) about the principle axis
What does the label T mean?
Triply degenerate
What is C2’ mean?
Perpendicular to the principal axis
What does subscipt 1 mean
The property is symmetric under C2’
What does subscript 2 mean<
Antisymmetric under C2’
What does superscript ‘ mean?
Symmetric under σh
No inversion centre
What does superscript ‘’ mean?
unsymmetric under σh
No inversion centre
What does subscript g mean?
symmetric under i (inversion)
What does subscript u mean?
unsymmetric under i (inversion)
What is a degenerate property?
When two group properties (can be orbitals) are interconverted by a symmetry element in the point group, they are regarded as degenerate and must be treated together
What is the trace?
the diagonal of a matrix, can give the eigen value (add it up)
where can u find the formula for the reducible representations? and what will your answer be?
data book - answer will always be an integer
What is LCAO?
Linear Combination of Atomic Orbitals
What do you need to do for an LCAO (linear combination of atomic orbitals) ?
Determine symmetry of orbitals on central atom and on the ligated groups
Can atomic orbitals of DIFFERENT symmetries overlap?
NO
What does + mean in an LCAO symmetric representatin?
IN phase with
What does - mean in LCAO symmetric representation?
Out of phase with
what can mix on a molecular orbital diagram?
Orbitals of the same symmetry
How do you know which MO atom shoukd be lower on the diagram?
The highest electronegative atom is lower
What is the equation for bond order ?
no. of bonding e- - no. of antibonding e- /2.
should be the same as the no of bonds
