Chapter 3 Introduction to Molecular Symmetry

Transcription

1 CHEM 511 Chapter 3 page 1 of 12 Chapter 3 Introduction to 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 nonrotated/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. PtCl4 2- EX. CCl4 The axis with the highest n is called the principal axis. EX. BF3

2 CHEM 511 Chapter 3 page 2 of 12 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 σd occurs if a σ both contains the primary axis and bisects two adjacent 2 fold axes. 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

3 CHEM 511 Chapter 3 page 3 of 12 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? 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

4 CHEM 511 Chapter 3 page 4 of 12 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 allows us to assign a point group which will characterize all of the symmetry elements (Figure 3.10). Note: it isn t necessary to find ALL symmetry elements when assigning a point group. Additional flow charts are at the back of this chapter notes. Assign point groups to the following: BF3 CHBrClF H2O

5 CHEM 511 Chapter 3 page 5 of 12 HCN acetylene Special point groups (Td, Oh, Ih) Certain molecular shapes have a high degree of symmetry and have special designations: Td = tetrahedral Oh = octahedral Ih = icosahedral 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

6 CHEM 511 Chapter 3 page 6 of 12 The left column has the symmetry labels: A and B refer to singly degenerate modes E refers to doubly degenerate modes T refers to triply degenerate modes 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?

7 CHEM 511 Chapter 3 page 7 of 12 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 (z 2, x 2, xy, etc) in the character table, the mode is Raman active

8 CHEM 511 Chapter 3 page 8 of 12 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?

9 CHEM 511 Chapter 3 page 9 of 12 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? Your text goes over several other point groups and their respective IR-active bands: Point Group Example molecule shape Degrees of freedom Do some modes represent an unchanged dipole? C2v ClF3

10 CHEM 511 Chapter 3 page 10 of 12 Point Group Example molecule shape Degrees of freedom Do some modes represent an unchanged dipole? D4h PtCl4 2- Td CCl4 Oh SF6

11 CHEM 511 Chapter 3 page 11 of 12 Chirality To determine if a molecule is chiral, what two characteristics (operations) do we seek? 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 Δ-trioxalatoferrate(III) Note this molecule of tetrafluorospiropentane: Does it have an i? a σ? is it chiral?

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