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Molecular Shapes, Symmetry and Molecular Orbital Theory 1st year Inorganic Chemistry Lecture Course

6 Lectures: Hilary Term, weeks 1-3 L. J. Smith

Synopsis

1. Initial models of inorganic molecules: Lewis structures, the valence shell electron pair repulsion (VSEPR) model. An introduction to molecular symmetry.

2. Symmetry elements and operations and the identification of molecular point

groups. 3. Introduction to molecular orbital theory

The electron distribution in H2. The LCAO method. The exclusion principle and antibonding orbitals. MO diagrams. Bond orders.

4. Homonuclear diatomics.

pπ and pσ MOs. MO diagrams and bond orders for N2, O2 and F2. Bond energy trends. Symmetry classification of MOs.

5. Heteronuclear diatomics.

MO diagrams and charge distribution. Examples of HF, BH. Hybridisation and the simultaneous use of s and p orbitals. Electronegativity difference and bond strengths.

6. Polyatomic molecules.

‘Directed valence’, hybridisation and bond angles. 3-centre molecular orbitals; simple application to electron deficient and hypervalent molecules.

Bibliography Adequate accounts are given in inorganic textbooks , e.g. Shriver and Atkins’ Inorganic Chemistry OUP 5th edition Jack Barrett “Structure and Bonding” RSC Tutorial Chemistry Text, 5 David Hayward “Quantum Mechanics” RSC Tutorial Chemistry Text, 14 Mark J Winter “Chemical bonding” Oxford Chemistry Primers, 15 For Molecular Symmetry introductory chapters in Alan Vincent “Molecular Symmetry and Group Theory” J.S. Ogden “Introduction to Molecular Symmetry” Oxford Chemistry Primer 97 David Willock “Molecular Symmetry” For more thorough accounts of Molecular Orbital Theory McWeeny “Coulson’s Valence” OUP, 3rd edition DeKock and Gray “Chemical Structure and Bonding “ University Science books Murrell, Kettle and Tedder “The Chemical Bond”, Wiley

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Lecture 1 Molecular Shapes and Symmetry 1. Initial models of inorganic molecules G. N. Lewis (1875-1946) – covalent bonding described in terms of shared pairs of electrons. Octet rule – In many molecules each atoms shares electrons with neighbouring atoms to achieve 8 valence electrons (an octet). Lewis structures provide a simple representation of the bonding. To draw

a) identify the total number of valence electrons present in each contributing atom

b) if the molecule is charged subtract or add extra electron(s) to account for the positive or negative charge respectively

c) distribute electrons in the structure so that there is an electron pair forming a single bond between each pair of atoms that are bonded together. The extra electrons are then added as lone pairs or form multiple bonds until each atom has an octet.

e.g. NO2

– Resonance – when several alternative low energy Lewis structures are available the bonding can be described in terms of resonance between the structures. Heavier elements can show octet expansion or hypervalence. e.g. ClF3 Formal charge – the charge an atom would have if all covalent bonds in a molecule were broken and the electrons assigned equally to the atoms involved. Formal charge = (no. of valence electrons in neutral atom)

– (no. of lone pair electrons) – (1/2)(no. of electrons in bonds formed).

Lewis structures with low formal charges typically have the lowest energy e.g. ONC–

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VSEPR (Valence Shell Electron Pair Repulsion) model This simple model predicts the structure of molecules by assuming that the geometry of a molecule depends only upon electron-electron interactions. To make a VSEPR prediction:

a) Write down Lewis structure for a molecule and identify the central atom b) Count the number of σ bonding electron pairs and lone pairs around the

central atom. To achieve the lowest energy these electron pairs position themselves so they are as far apart as possible:

Number of electron pairs Arrangement 2 Linear 3 Trigonal planar 4 Tetrahedral 5 Trigonal bipyramid 6 Octahedral 7 Pentagonal bipyramid

From the arrangement of electron pairs, the location of the atoms and hence the shape of molecule can be identified. In a trigonal bipyramidal arrangement the lone pairs occupy equatorial sites. In an octahedral arrangement if there are two lone pairs these are positioned trans to each other. c) Refinement of the basic shape is then made by recognising i) Electron-electron repulsions decrease in the sequence: lone pair- lone pair > lone pair-bonding pair > bonding pair-bonding pair ii) When the central atom is involved in multiple bonds electron-electron repulsions decrease in the order: triple bond-single bond > double bond-single bond > single bond-single bond iii) Repulsions between bonding pairs in ABx depends on the electronegativity difference of the central (A) and terminal (B) atoms. As the terminal atoms become more electronegative the bonding electron pairs are drawn away from the central atom and the electron-electron repulsions reduce.

e.g. ClF3 e.g. XeOF4 e.g. NO2

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Exceptions VSEPR is a useful tool that works well for most main group compounds (but not transition metal compounds) although some exceptions are known e.g. XeF6 (6 bonding pairs and one lone pair) has a distorted octahedral structure in the gas phase. SbPh5 and InCl5

2- (5 bonding pairs) adopts a square pyramidal structure. SeCl6

2- and TeCl62- (6 bonding pairs and one lone pair) adopt regular octahedral

structures. 2. Symmetry operations and symmetry elements A symmetry operation is an action that leaves a molecule apparently unchanged. For example, if we take an H2O molecule and rotate it by 180° about an axis passing through the central O atom (between the two H atoms) it will look indistinguishable.

Each symmetry operation has an associated symmetry element, which is the axis, plane, line or point with respect to which the symmetry operation is carried out. Important symmetry elements and their corresponding symmetry operations Symbol Symmetry element Symmetry operation E “whole of space” Identity Cn n-fold axis of rotation Rotation by 360°/n σ mirror plane Reflection i Centre of inversion Inversion Sn n-fold axis of Rotation by 360°/n followed by

improper rotation reflection in plane perpendicular to the rotation axis

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Mathematically the operation of ‘doing nothing’ is a symmetry operation called the identity operation (E). The corresponding symmetry element is the entire molecule. Every molecule has at least this element. A molecule possesses an n-fold rotation axis if the molecule appears unchanged after rotation by 360°/n about the axis (symbol Cn) C3 e.g. BF3 C4 e.g. XeF4 C5 e.g. IF7 C6 e.g. C6H6 A molecule possesses a plane of symmetry (mirror plane, symbol σ) if reflection in the plane leaves the molecule looking the same. e.g. The H2O molecule contains two perpendicular mirror planes

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An improper rotation consists of rotating through an angle of 360°/n about an axis, followed by reflecting in a plane perpendicular to the axis. The axis is called an n-fold axis of improper rotation (symbol Sn).

The inversion operation is carried out with respect to a centre of inversion (symbol i). In this operation every atom is projected in a straight line though the centre of inversion and then an equal distance on the other side. If the centre of symmetry is defined as the origin (0, 0, 0) then inversion involves moving each point (x,y,z) to (-x,-y,-z). Molecules with a centre of inversion are termed centrosymmetric.