CHEM 511 Chapter 6 page 1 of 13 Chapter 6 Molecular...
Transcript of CHEM 511 Chapter 6 page 1 of 13 Chapter 6 Molecular...
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CHEM 511 Chapter 6 page 1 of 13
Chapter 6
Molecular Symmetry
This chapter will deal with the symmetry characteristics of individual molecules, i.e., how
molecules can be rotated or imaged along certain axes and be indistinguishable form a non-
rotated/imaged molecule.
Symmetry Operation: an operation performed on an object which leaves it in a configuration
that is indistinguishable from, and superimposable on, the original configuration.
EX. BF3
Rotations (Cn)
If the object can be rotated about an axis, we say there is rotational symmetry
EX. BF3—this can be rotated by ⅓ of a circle, so it has C3 symmetry
EX. PtCl42-
EX. CCl4
The axis with the highest n is called the principal axis.
EX. BF3 EX. SF6
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Mirror Planes (σ)
A plane of symmetry (mirror plane) exists if reflection of all parts of a molecule through this
plane results in an indistinguishable configuration
EX. BF3
A σv occurs if a σ contains the primary axis (“v” for vertical).
A σh occurs if a σ is perpendicular to the primary axis (“h” for horizontal).
A σd occurs if a σ contains both the primary axis and bisects two adjacent 2 fold axes (“d” for dihedral).
Center of Inversion (i)
If reflection of all parts of an object through the center of the object produces an
indistinguishable configuration, the object has a center of symmetry aka center of inversion
EX. Which of the following have an i?
BF3
C6H6
CO2
H2O
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Improper axis of rotation (Sn) If you rotate an object about an axis (a Cn operation), then follow it by a reflection through a
plane perpendicular to the axis—and the molecule comes back indistinguishable, you have an Sn
operation.
EX. BF3
Does [PtCl6]2- have an Sn operation?
Note: S1 is the same as a mirror plane (σh), but we just use σh, not the S1 operation
What is the S2 operation equivalent to?
Identity Operator (E)
This is, in essence, a 360º rotation—leaving the molecule unchanged. At the very least, ALL
molecules have this type of symmetry element.
EX. Can you think of a molecule that has NO Cn, Sn, i, or σ(h, v, d)?
Linking operations together If an object has a Cn, then if you perform Cn n-times, you rotate the object back to the original
position.
EX. BF3
Similarly, combining a C3 with a σh is an S3 operation: S3 = C3 × σh
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Assigning point groups
Sometimes (particularly in spectroscopy and MO theory) we need to know all of the symmetry
operations that pertain to a certain chemical. Rather than try to figure these out for every species,
a flow chart (your book calls this a “decision tree”) allows us to assign a “point group” which
will characterize all of the symmetry elements. Note: it isn’t necessary to find ALL symmetry
elements when assigning a point group. Additional flow charts are at the end of this chapter
notes. The point group is indicated with a Schoenflies symbol.
Assign point groups to the following:
BF3
CHBrClF
H2O
HCN
acetylene
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Special point groups (Td, Oh, Ih)
Certain molecular shapes have a high degree of symmetry and have special designations:
Td = tetrahedral (>1 primary axis)
Oh = octahedral (>1 primary axis)
Ih = icosahedral (12 five-fold axes)
Character tables The appendix has a list of common character tables—these will show all of the symmetry
elements for a particular point group
EX.
D4h E 2C4 C2 2C2’ 2C2” i 2S4 σh 2σv 2σd
The left column has the symmetry labels:
A and B refer to singly degenerate modes or orbitals
E refers to doubly degenerate modes or orbitals
T refers to triply degenerate modes or orbitals
“h” refers to the order—the number of symmetry operations
The right columns refer to functions:
x, y, z, Rx, Ry, Rz give information relevant to IR spectroscopy
More complicated functions (x2, xz, xy, etc.) are relevant to Raman spectroscopy
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Applications of symmetry
Polarity Molecules are polar if there is a net dipole moment. Chemicals with an i can’t be polar. Why?
Additionally, molecules can’t have dipole moments perpendicular to a mirror plane or perpendicular to
any axis of rotation.
EX. From point group designations, which of the following are polar?
CH2Cl2 PCl5 cis-[PdCl2(NH3)2]
What do we find? Molecules with a D-, T-, O-, or I-related point group cannot be polar.
Chirality What two simple symmetry operations prevent a molecule from being chiral? E, Cn, i, or σ(h, v, d)
Note that an improper axis of rotation is compatible with these and a better way to determine if a
molecule is nonsuperimposable on its mirror image is to look for an Sn operation. Chiral
molecules lack an Sn.
EX. Determine the point group of trioxalatoferrate(III). Will it be chiral?
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Note this molecule of tetrafluorospiropentane: Does it have an i? a σ? is it chiral?
Relating symmetry to vibrational spectroscopy For molecules to give rise to strong absorptions in the IR spectrum, they must change the
molecule’s dipole moment
An additional technique called Raman spectroscopy will give rise to strong signals if there is a
change in the polarizability of the molecule
Rule of mutual exclusion: for centrosymmetric molecules, IR active modes will NOT be
Raman active and vice versa
For linear molecules, the number of fundamental vibrational modes is: 3n-5 (n = # of atoms)
For nonlinear molecules, the number of fundamental vibrational modes is: 3n-6 (n = # of atoms)
EX. How many vibrational modes are in CO2? H2O?
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So how do character tables help us with this?
For H2O (C2v) the character table is
Consider the symmetry operations on H2O—how many bonds remain unchanged after each operation?
Looking at the C2v character table, which rows add up to give the reducible representation?
For the A1 we note all values are “1”—this means the molecule is left unchanged with this
operation. In B2, some values are -1, which means the molecule is reversed. Use this approach
for the stretching or bending modes.
How are the vibrational modes of the symmetric stretch affected by the symmetry operations in C2v?
Asymmetric stretch affected by symmetry operations?
Recall that H2O will have 3 modes—we’ve described two stretching, so the last one must be the
scissoring (bending).
If the symmetry label (A1, B2, etc) has an x, y, or z in the character table, the mode is IR active
If the symmetry label has a product term (z2, x2, xy, etc) in the character table, the mode is Raman active
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XY3 molecules with D3h symmetry Consider SO3: how many vibrational modes will it have?
What values do we find for the reducible representation:
D3h E C3 C2 σh S3 σv
Which rows sum up to be this reducible representation?
Are these IR-active, Raman-active, both, or neither?
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XY3 molecules with C3v symmetry Consider NH3: How many vibrational modes would it have?
What values do we find for the reducible representation:
C3v E C3 σv
Which rows sum up to be this reducible representation?
Are these IR-active, Raman-active, both, or neither?
Relating symmetry to molecular orbitals For non-linear molecules, it is helpful to consider outer atoms as a group—and look at their
symmetry as a unit. Your text calls this a SALC (symmetry-adapted linear combination), other
texts use the term LGO (ligand group orbitals). Your text provides pictures of various SALCs in
Resource Section 5.
SALCs that match the symmetry of atomic orbitals will overlap and form MOs.
For the H’s in NH3, perform symmetry operations like finding the reducible representation (but
only for the hydrogen atoms as a group), then determine the irreducible representations. This will
give A1 and E.
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Which ATOMIC ORBITALS on the nitrogen will match these symmetries?
Build the MO from corresponding overlaps.
Projection operators (deriving what the SALCs will “look” like)
Consider the chlorine sigma bonding SALC in [PtCl4]2-. What is the reducible representation?
E 2C4 (z) C2 2C'2 2C''2 i 2S4 σh 2σv 2σd
E 2C4 (z) C2 2C'2 2C''2 i 2S4 σh 2σv 2σd
A1g 1 1 1 1 1 1 1 1 1 1 x2+y2, z2
A2g 1 1 1 -1 -1 1 1 1 -1 -1 Rz
B1g 1 -1 1 1 -1 1 -1 1 1 -1 x2-y2
B2g 1 -1 1 -1 1 1 -1 1 -1 1 xy
Eg 2 0 -2 0 0 2 0 -2 0 0 (Rx, Ry) (xz, yz)
A1u 1 1 1 1 1 -1 -1 -1 -1 -1
A2u 1 1 1 -1 -1 -1 -1 -1 1 1 z
B1u 1 -1 1 1 -1 -1 1 -1 -1 1
B2u 1 -1 1 -1 1 -1 1 -1 1 -1
Eu 2 0 -2 0 0 -2 0 2 0 0 (x, y)
What are the irreducible representations?
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Now perform a projection of how one wavefunction transforms to the other locations:
E C4 (z) C43 (z) C2 (C42) C'2 C'2 C''2 C''2 i S4 S43 σh σv σv σd σd
1
...and multiply by the characters in the irreducible representations.
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