sym 3 Flashcards
when is the symmetry plane given sigma h
when its perpendicular to the principal axis.
when does a symmetry point group occur
when molecules can undergo the exact set of operations
aka they all only undergo the same 5 operations
what must apply for a set of operations to form a proper group
- make sure the group is closed aka u cannot genberate a new symmetry operation by combining ones in the group,, if u combine operations, the result must also be in the group.
- u must remember to write the identity operation as all objects have one!! E
- every memeber // operation of the group must also have an inverse operation that gives u E. aka NH3: C1/3 inverse is C2/3 as them added gives C3/3 which is E.
inverse operation of sigmav
sigma v
bc doing it twice gets u back to E
inverse of C1/3
C2/3
bc doing both of them gets u back to E.
how to check the group is closed
make sure the product of 2 operations gives the same result as a single operator from the group.
lecture 3 slide 5
when do operations commute with one another
when the pair can be carried out in any order
when doing all the operations,, what should u include on the atoms to see how theyre changing
number the atoms if theyre the same but also draw an arrow perpendicular to the plane of the molecule to see how it changes with rotations and mirrors etc.
where do u draw sigma d’s
between C2s!!
do all operations commute aka can all operations be done in any order and give the same result
nope!! some operations just dont commute and wont give us the same final orientation.
point group shorthand notation: belonging in the C2v group explanation
C: only one axis present
2: principal axis has an order of 2
V: there are 2 vertical planes of symmetry
point group shorthand notation: C3v group explanation
C: principal axis is the only axis
3: the order of the principal axis = 3
V = there are 3 vertical planes of symmetry.
sigma h
has no z character
look for principal axis!!!
sigma v’
has z character
look for principal axis
point group subscript D3h explanation
D: there are multiple rotational axis present,, not just the principal axis
3: order of the principal axis
h: bc it has a horizontal plane of symmetry.
subscript d is used whennn
there are only dihedral planes,, no vertical ones
what is the idea of point group theory
every molecule will conform to one of the point groups that help describe their symmetry properties
C2v D3h etccc
example of point groups
C2v D3h D3d
these are important and we should assign a molecule to these to help us with group theory problems
closed point group meaning
that the product of any 2 operations will equal another single operation in the group,, if the group is closed.
sub group meaning
complex groups have subgroups of operations.
D3 is the rotational subgroup of D3h and D3d.
theyre just easier to work with.
product of 2 operations meaning
doing one operation after another.
sigmav C2 means do a C2 rotation and then reflect in the sigma v plane!!!
bc theyre written the wrong way around.
commute
when the product of operations depends on the order of operations!!
they are said to commute when the order doesnt matter.
if the order does matter they dont commute.
