Theories of Covalent Bonding Chapter 11 Theories of Covalent Bonding

Theories of Covalent Bonding 11.1 Valence Bond (VB) Theory and Orbital Hybridization 11.2 The Mode of Orbital Overlap and the Types of Covalent Bonds 11.3 Molecular Orbital (MO)Theory and Electron Delocalization

The Central Themes of VB Theory Basic Principle A covalent bond forms when the orbtials of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei. Themes A set of overlapping orbitals has a maximum of two electrons that must have opposite spins. The greater the orbital overlap, the stronger (more stable) the bond. The valence atomic orbitals in a molecule are different from those in isolated atoms.

Orbital overlap and spin pairing in diatomic molecules Atomic Orbital Overlap Orbital overlap and spin pairing in diatomic molecules Hydrogen, H2 Hydrogen fluoride, HF Fluorine, F2

Hybrid Orbitals Key Points The number of hybrid orbitals obtained equals the number of atomic orbitals mixed. The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed. Types of Hybrid Orbitals sp sp2 sp3 sp3d sp3d2

The sp hybrid orbitals in gaseous BeCl2 atomic orbitals hybrid orbitals orbital box diagrams

The sp hybrid orbitals in gaseous BeCl2 (continued) orbital box diagrams with orbital contours

The sp2 hybrid orbitals in BF3

The sp3 hybrid orbitals in CH4

The sp3 hybrid orbitals in NH3

The sp3 hybrid orbitals in H2O

The sp3d hybrid orbitals in PCl5

The sp3d2 hybrid orbitals in SF6

Molecular shape and e- group arrangement The conceptual steps from molecular formula to the hybrid orbitals used in bonding. Figure 10.1 Step 1 Figure 10.12 Step 2 Step 3 Table 11.1 Molecular shape and e- group arrangement Molecular formula Lewis structure Hybrid orbitals

SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule PROBLEM: Use partial orbital diagrams to describe mixing of atomic orbitals on the central atoms leads to hybrid orbitals in each of the following: (a) Methanol, CH3OH (b) Sulfur tetrafluoride, SF4 PLAN: Use the Lewis structures to ascertain the arrangement of groups and shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms. SOLUTION: (a) CH3OH The groups around C are arranged as a tetrahedron. O also has a tetrahedral arrangement with 2 nonbonding e- pairs.

SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule continued single C atom single O atom hybridized C atom hybridized O atom (b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs. S atom hybridized S atom

Types of Covalent Bonds Sigma () Bonds - Bonding that results from the end-to-end overlap is called a sigma bond. It has the highest electron density along the axis between the two nuclei. Single bonds are sigma bonds. Pi () Bonds - Bonds that result from the side-to-side overlap of unhybridized p orbitals. The electron density is above and below the axis between the two nuclei. (This is why multiple bonds counted as one group of electrons in VSEPR theory) The multiple part of multiple bonds are  bonds. In a double bond, there is one  and one  bond. In a triple bond, there is one  and two  bonds.

relatively even distribution of electron density over all s bonds The s bonds in ethane. both C are sp3 hybridized s-sp3 overlaps to s bonds sp3-sp3 overlap to form a s bond relatively even distribution of electron density over all s bonds

The s and p bonds in ethylene (C2H4) overlap in one position - s p overlap -  electron density

The s and p bonds in acetylene (C2H2) overlap in one position - s p overlap - 

SAMPLE PROBLEM 11.2 Describing the Bonding in Molecules with Multiple Bonds PROBLEM: Describe the types of bonds and orbitals in acetone, (CH3)2CO. PLAN: Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps. SOLUTION: sp3 hybridized sp2 hybridized bond bonds

Restricted rotation of p-bonded molecules Rotation about the C-C bond can’t take place without breaking the  electron overlap. CIS TRANS

The Central Themes of MO Theory A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals. Atomic wave functions are summed to obtain molecular wave functions. If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei). If wave functions cancel each other, an antibonding MO (*) is formed (a node of zero electron density occurs between the nuclei).

An analogy between light waves and atomic wave functions. Amplitudes of wave functions added Amplitudes of wave functions subtracted.

Contours and energies of the bonding and antibonding molecular orbitals (MOs) in H2.

The MO diagram for H2

MO diagram for He2+ and He2 He2+ bond order = 1/2 (exists) Energy s*1s s1s s*1s AO of He 1s AO of He+ 1s AO of He 1s AO of He 1s Energy s1s MO of He+ MO of He2 He2 bond order = 0 He2+ bond order = 1/2 (exists)

SAMPLE PROBLEM 11.3 Predicting Species Stability Using MO Diagrams PROBLEM: Use MO diagrams to predict whether H2+ and H2- exist. Determine their bond orders and electron configurations. PLAN: Use H2 as a model and accommodate the number of electrons in bonding and antibonding orbitals. Find the bond order. SOLUTION: bond order = 1/2(1-0) = 1/2 bond order = 1/2(2-1) = 1/2 s s s s H2+ does exist H2- does exist 1s AO of H AO of H- 1s AO of H 1s AO of H configuration is (s1s)2(s2s)1 MO of H2- MO of H2+ configuration is (s1s)1

Be2 Li2 Bonding in s-block homonuclear diatomic molecules. Energy s*2s Li2 bond order = 1 (is observed) Be2 bond order = 0 (not observed)

Contours and energies of s and p MOs through combinations of 2p atomic orbitals

Relative MO energy levels for Period 2 homonuclear diatomic molecules. without 2s-2p mixing with 2s-2p mixing MO energy levels for O2, F2, and Ne2 MO energy levels for B2, C2, and N2

MO occupancy and molecular properties for B2 through Ne2

SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties PROBLEM: As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecules, whereas the ion formed from O2 has a stronger, shorter bond: Bond energy (kJ/mol) Bond length (pm) N2 N2+ O2 O2+ 945 110 498 841 623 112 121 Explain these facts with diagrams that show the sequence and occupancy of MOs. PLAN: Find the number of valence electrons for each species, draw the MO diagrams, calculate bond orders, and then compare the results. SOLUTION: N2 has 10 valence electrons, so N2+ has 9. O2 has 12 valence electrons, so O2+ has 11.

SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties continued N2 N2+ O2 O2+ 2p s2s s2s 2p 2p 2p 2p antibonding e- lost bonding e- lost 2p 2p 2p s2s s2s bond orders 1/2(8-2)=3 1/2(7-2)=2.5 1/2(8-4)=2 1/2(8-3)=2.5

The lowest energy p-bonding MOs in benzene and ozone.

The MO diagram for HF AO of H Energy AO of F MO of HF s 1s s 2p 2px 2py MO of HF

possible Lewis structures sp *p s*s The MO diagram for NO 2s AO of N 2p 2s AO of O 2p Energy possible Lewis structures s*s ss MO of NO

End of Chapter 11

The steps in converting a molecular formula into a Lewis structure. Figure 10.1 The steps in converting a molecular formula into a Lewis structure. Place atom with lowest EN in center Molecular formula Step 1 Atom placement Add A-group numbers Step 2 Sum of valence e- Draw single bonds. Subtract 2e- for each bond. Step 3 Give each atom 8e- (2e- for H) Remaining valence e- Step 4 Lewis structure

The steps in determining a molecular shape. Figure 10.12 The steps in determining a molecular shape. See Figure 10.1 Molecular formula Step 1 Lewis structure Count all e- groups around central atom (A) Step 2 Electron-group arrangement Note lone pairs and double bonds Step 3 Count bonding and nonbonding e- groups separately. Bond angles Step 4 Molecular shape (AXmEn)