Shapes of Molecules 2b. Point Groups PDF
Document Details
Tags
Summary
This document describes methods for summarizing molecular symmetry through assigning point groups. It includes examples for various molecules like H2O, NH3, ClF3, SF4, and BF3 to demonstrate the application of these techniques. These methods involve identifying crucial symmetry elements and applying a series of established rules.
Full Transcript
2b. Point groups We can summarise the full symmetry of a molecule by giving it a point group. However, we do not need to know all of the symmetry of the molecule to determine its point group. We can find some key symmetry elements. Hence it is important that we are able to quickly iden...
2b. Point groups We can summarise the full symmetry of a molecule by giving it a point group. However, we do not need to know all of the symmetry of the molecule to determine its point group. We can find some key symmetry elements. Hence it is important that we are able to quickly identify the point group of a molecule. We do this by following some simple rules However, before we do this we can simply identify some very regular shapes such as a tetrahedron (Td) and an octahedron (Oh) – don’t need to use the rules 21/09/2024 1 Assigning point groups - 1 For all others we can follow a series of questions as shown below; 1. Find the highest axis of rotational symmetry (Cn) and call this the z-axis 2. If n = 1; has the molecule a centre of symmetry? Ci has the molecule a plane of symmetry? Cs has the molecule got no symmetry? C1 3. If n ≥ 2 are there n C2 axes perpendicular to Cn? If yes molecule is dihedral (D) 4. If dihedral has the molecule a horizontal plane? Dnh Has the molecule n vertical planes? Dnd 5. Not dihedral does it have and S2n axis coincident with Cn? S2n 6. Not dihedral has molecule a horizontal plane? Cnh has molecule n vertical planes? Cnv does it have neither of these? Cn 21/09/2024 2 Assigning point groups – example 1 H2O NB1: by convention we say that the molecule lies in the xz plane NB2: the axes (vectors) x,y and z are all inequivalent 21/09/2024 3 Assigning point groups – example 2 NH3 NB1: now we see that x and y are the same (equivalent) NB2: we use the term “degenerate” to describe this NB3: x and y are doubly degenerate 21/09/2024 4 Assigning point groups – example 3 ClF3 NB1: we can draw the molecule in a number of different ways NB2: there are two chemically inequivalent types of fluorine 21/09/2024 5 Assigning point groups – example 4 SF4 NB1: the C2v point group is common but the molecules look different NB2: the different types of fluorine can interconvert – dynamic not static 21/09/2024 6 Assigning point groups – example 5 BF3 21/09/2024 7 Summary of Intended Learning Outcomes Identify key symmetry elements and assign a point group We can summarise the symmetry of a molecule by assigning a point group – to do this we need to identify some key symmetry elements – the axis of highest rotation is always defined as the z-axis – a planar molecule lies in the xz plane. Sometimes x,y and z are different but other times they can be the same – triply (x = y = z) degenerate or double (x = y) degenerate The point group defines the symmetry of the ground (lowest energy) state 21/09/2024 8
