Chemical Bonding: Valence Bond & Molecular Orbital Theories Chapter 10 Section 4 through 8 of Jespersen 6th ed) Dr. C. Yau Fall 2011 1 1

VSEPR Theory You had previously learned how to predict the molecular geometry of a species from examining its Lewis structure. It utilizes the concept of repulsion amongst the charge clouds of the central atoms. This was the Valence Shell Electron Pair Repulsion Theory (VSEPR Theory). It does not explain how a bond is formed and how bonding relates to the s, p, d orbitals. 2 2

Valence Bond Theory (VB Theory) The VB Theory explains bonding as an overlap of valence orbitals. H2 bonds are due to the overlap of their 1s valence orbitals. 1s 1s A B Fig 10.15 p.425 A. Two separate H atoms B. H2 molecule with covalent bond due to overlap of the 1s orbitals. 3 3

Valence Bond Theory Consider H2S. The valence electrons of S are 3s2 3p4     3s 3p and the orbitals would be overlapping with the 1s orbitals from the two H atoms. FIG. 9.15 The formation of the hydrogen molecule according to valence bond theory. FIG. 9.16 The formation of the hydrogen fluoride molecule according to valence bond theory. For clarity, only the half-filled 2p orbital of fluorine is shown. The other 2p orbitals of fluorine are filled and cannot participate in bonding. Chem FAQ: Explain the bonding in simple molecules in terms of overlapping of half-filled atomic orbitals. 4

Difficulties With VB Theory Most experimental bond angles do not support those predicted by mere atomic orbital overlap. For example: C 1s22s22p2 and H 1s1 One might expect C and H to form CH2 with a bond angle of 90o. Why might one expect that? Experimental bond angles in methane CH4 are in fact, 109.5° and all angles are the same p orbitals are 90° apart, and not all valence e- in C are in the p orbitals Also, how can multiple bonds form? Chem FAQ: What are hybrid orbitals? 5

Hybridization in VB Theory Atomic orbitals are mixed to allow formation of bonds that have realistic bond angles The newly mixed orbitals that result are called “hybrid orbitals” with specified shapes: Review: # charge clouds Hybridization Bond Angles 2 sp 180o 3 sp2 120o 4 sp3 109.5o 5 sp3d 120o & 90o 6 sp3d2 90o & 180o 6

How are sp3 hybrid orbitals formed? __ __ __ __ p s __ __ __ __ four sp3 hybrid orbitals 109.5o If we take s and all three p we form four sp3 hybrid. These hybrid orbitals are “degenerate.” That is, they are of the same E, higher than s but lower than p. Note that # orbitals is conserved.

How are sp2 hybrid orbitals formed? __ __ __ __ p s __ p __ __ __ three sp2 hybrid orbitals If we take s and just two p orbitals, we form three sp2 hybrid orbitals leaving one pure p untouched. These three sp2 hybrid orbitals are planar with angles of 120o. The un-hybridized p (pure p) are used in double and triple bonds.

How are sp hybrid orbitals formed? __ __ __ __ p s __ __ two p __ __ two sp hybrid orbitals p If we take s and just one p orbital, we form two sp hybrid orbitals leaving two pure p untouched. p sp sp These two sp hybrid orbitals are linear with angles of 180o.

How are hybrid orbitals formed? When we run out of p orbitals, we start using d orbitals, but this would not be possible for elements smaller than Ne (Period 2 and smaller) because they do not have d-orbitals. Thus we have sp3d hybrid orbitals and sp3d2 hybrid orbitals (but only for elements beyond Period 2). 10

Bonding in CH4 H The 4 hybrid orbitals are evenly distributed around the C The H s-orbitals overlap the sp3 hybrid orbitals to form the bonds. FIG. 9.22 Formation of the bonds in methane. Each bond results from the overlap of a hydrogen 1s orbital with an sp3 hybrid orbital on the carbon atom. 11

Bonding Types Two types of bonds result from orbital overlap: sigma () bonds from head-on overlap lie along the bond axis account for the first bond pi ()bonds pi bonds are perpendicular to bond axis account for the second and third bonds in a multiple bond Chem FAQ: Use VB theory to describe double bonds. Use VB theory to describe triple bonds. 12

Sigma() and Pi () Bonding Please refer to lecture notes on  and  bonding of C2H4 and C2H2. Here is what you should be able to do: Given the structural formula of a compound, be able to specify the hybridization of each atom, state the bond angles and determine the # of sigma and pi bonds. 13

That’s a -bond between sp3-sp3 of the 2 C’s. Let us build a model for CH3CH3 (ethane) Each C is sp3 hybridized. First build the following with angles of 109.5o. Now join the 2 C’s together. That’s a -bond between sp3-sp3 of the 2 C’s.

Next we are going to build CH2CH2 Each C is sp2 hybridized. First build the following with angles of 120O, with a pure unhybridized p orbital. Now join the 2 C’s together with a -bond. Follow the directions on how to form the -bond with the 2 parallel p-orbitals. You have formed a sp2-sp2 -bond and a p-p -bond.

Now we are going to build C2H2 (acetylene). First build the following with angles of 90O, with 2 pure, unhybridized p orbitals, perpendicular to it. Now join the 2 C’s together with a -bond. Follow directions on how to form 2 -bonds with parallel p-orbitals. You have formed a sp-sp -bond and 2 p-p -bonds.

KNOW THIS WELL! X X single bond =  bond X X double bond =  bond +  bond X X triple bond =  bond + two  bonds 17

Always start with hybridization. 1 2 3 4 Always start with hybridization. Give the hybridization of each C and each O. Give the bond angles. How many  bonds are there? How many  bonds are there? Ans. C1 = sp C2 = sp C3 =sp2 C4 = sp3 O = sp3 C1-C2-C3 = 180o C2-C3-O = 120o C2-C3=O = 120o O-C4-H = 109.5o 9  bonds 3  bonds 18

Molecular Orbital Theory (MO Theory) Oh No! Yet another theory! VSEPR and VB theories do not explain everything. MO Theory considers the molecule as an entity rather than just a collection of atoms. Instead of considering atomic orbitals or hybrid orbitals, the MO theory considers molecular orbitals and molecular energy levels. 19

MO Theory When two atomic orbitals overlap, their wave functions interact by constructive and destructive interference to form bonding and antibonding orbitals. Electrons in bonding molecular orbitals stabilize the molecule. Electrons in antibonding molecular orbitals de-stabilize the molecule. The Bond Order is # bonds, and calculated thus: Bond order = ½ (# bonding electrons - # antibonding electrons). 20

MO Energy Diagram of H2 Two 1s orbitals of H atoms combine to form two molecular orbitals: 1s (bonding) and 1s* (antibonding). H2 has 2 electrons, both in bonding MO orbitals. bond order = 2/2 = 1 (a single bond) 21

MO Theory See handout for application of MO theory on diatomic molecules such as N2, O2 etc. Know how to fill electrons into the MO energy diagram and calculate bond order. 22