Lecture 34: Symmetry Elements

Lecture 34: Symmetry Elements The material in this lecture covers the following in Atkins. 15 Molecular Symmetry The symmetry elements of objects 15.1 Operations and symmetry elements 15.2 Symmetry classification of molecules (a) The groups C 1,C i, and C s (b) The groups C n,c nv, and C nh (c) The groups D n,d nh, and D nd Lecture on-line Symmetry Elements (PowerPoint) Symmetry Elements (PDF) Handout for this lecture

Symmetry elements The systematic discussion of symmetry is called Some objects are more symmetrical than others Any rotation of sphere around axis through center brings sphere over into itself Some of the symmetry elements of a cube. The twofold, threefold, and fourfold axes are labelled with the conventional symbols. Only some rotations of sphere brings cube into itself

Symmetry elements (a) An NH 3 molecule has a threefold (C 3 ) axis (b) an H 2 O molecule has a twofold ( ) axis. Both have other symmetry elements too. NH3 has more rotation symmetry than H 2 O

Symmetry elements An action that leaves an object the same after it has been carried out is called a : Symmetry operations are : For each symmetry operation there is a : symmetry element Which is with respect to which the operation is performed

Operators and Symmetry elements The classification of objects according to symmetry elements corrsponding to operations that leave at least one common point unchanged gives rise to the : There are five kinds of symmetry operations and corresponding symmetry elements 1. The identity E Consists of doing nothing Cl I F Br Only element for CFClBrI

Operators and Symmetry elements C 3 and C 3-1 C 6 (b) an H2O molecule has a twofold (C2) axis. The principle rotation axis is the axis of the higest fold C 5 C ; C ; C 6 3 2 6-1 3-1 and C ; C

Operators and Symmetry elements The H 2O molecule has two mirror planes. They are both vertical (that is contain the vertical axis) and as so are denoted σ and σ ' v v

C 6 Operators and Symmetry elements Benzene has one mirror plane perpendicular to the principle C6 - axis ( σ h) Dihedral mirror planes ( σ d) bisect the axis perpendicular to the principle axis

Operators and Symmetry elements A regular octahedron has a centre of inversion (i).

Operators and Symmetry elements (a). A CH 4 molecule has a fourfold improper rotation axis (S 4 ): the molecule is indistinguishable after a 90 rotation followed by a reflection across the horizontal plane, but neither operation alone is a symmetry operation. C 4 σ

Operators and Symmetry elements (b) The staggered form of ethane has an S 6 axis composed of a 60 rotation followed by a reflection.

The Schoenflies system Hermann Mauguin

C, C, C 1 i s The groups C, C, C 1 i s F A molecule belongs to C if it has only the identitity E 1 Cl I Br COOH HO H A molecule belongs to C i if it has only the identitity E and i H HOOC OH Meso-tartaric acid A molecule belongs to Cs if it has only the identity and a mirror plane N Quinoline

C n The groups C n, C nv, and C nh A molecule belongs to C n if it has a C axis and the identitity E only n C 3 C 4 C 5 C 6 H O O H H 2 O 2

The groups C n, C nv, and C nh A molecule belongs to C nv if it has a C n axis and n vertical mirror planes C nv cone C C C 4v C 5v C6v C v 2v 3v NH 3 C 3v H 2 O C2v CO Heteronuclear diatomics are C v

The groups C n, C nv, and C nh A molecule belongs to C nh if it has a C n axis and a horizontal mirror plane C nh h C 3h C 4h C C 5h 6h Cl C H O H C H Cl Trans CHCl=CHCl H O B O H B(OH) 3

The groups C n, C nv, and C nh C nh σ i The presence of a twofold axis and a horizontal mirror plane jointly imply the presence of a centre of inversion in the molecule.

D n The groups D n, D nv, and D nh A molecule belongs to D n if it has a C n axis and n two fold axes (C ) perpendicular to C. 2 n N Pt N N N N D 3 N A molecule with n twofold rotation axes perpendicular to an n-fold rotation axis belongs to the group Dn.

The groups D n, D nv, and D nh D n D 2 D3 D 4 D5 D 6

The groups D, D, and D A molecule belongs to D nh if it has a C n axis and n two fold axes () perpendicular to C n as well as a horizontal mirror plane. n nv nh D nh A molecule with a Mirror plane perpendicular to a C n axis, and with n twofold axes in the plane, belongs to the group D nh.

The groups D, D, and D n nv nh A molecule belongs to D nh if it has a C n axis and n two fold axes () perpendicular to C n as well as a horizontal mirror plane. H H C C 4 C H H D nh σ h D 2h C 4 D 2h D 3h Cl Cl σ h Au Cl Cl C' 2 D 4h D 4h D 5h D6h

The groups D, D, and D A molecule belongs to D nh if it has a C n axis and n two fold axes () perpendicular to C n as well as a horizontal mirror plane. n nv nh F B D nh F F E, C 3, 3, σh E, C 6, 3,3C' 2, σh

The groups D n, D nv, and D nh D nh F F P C 3 F F σ h F D 3h

The groups D, D, and D A molecule belongs to D nd if in addition to the elements of D n it posesses n dihedral mirror planes n nv nh D nd D 2d D 3d D 4d D 5d D 6d C C C D2d

What you must learn from this lecture 1. Given a molecule, you should be able to identify the different symmetry elements (C n,σ v,σ h,σ d,i,s n, etc. ) 2. Having identified the symmetry elements of a molecule, you should be able to establish the point group to which the molecule belong