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 types of covalent bonds 11.3 Molecular orbital (MO) theory and electron delocalization
The three models of chemical bonding Figure 9.2
Covalent bond formation in H2 Figure 9.11
Key Principles Structure dictates shape Shape dictates function shape = conformation Molecules can assume more than one shape (conformation) in solution!
Valence-shell Electron-Pair Repulsion (VSEPR) Theory A method to predict the shapes of molecules from their electronic structures (Lewis structures do not depict shape) Basic principle: each group of valence electrons around a central atom is located as far away as possible from the others in order to minimize repulsions Both bonding and non-bonding valence electrons around the central atom are considered. AXmEn symbolism: A = central atom, X = surrounding atoms, E = non-bonding electrons (usually a lone pair)
A periodic table of partial ground-state electron configurations Figure 8.12
The steps in determining a molecular shape molecular formula Step 1 Count all e- groups around the central atom A Lewis structure Step 2 Note lone pairs and double bonds electron-group arrangement Step 3 Count bonding and non-bonding e- groups separately. bond angles Step 4 molecular shape (AXmEn) Figure 10.12
Steps to convert a molecular formula into a Lewis structure Place the atom with the lowest EN in the center molecular formula Step 1 atom placement Step 2 Add A-group numbers Draw single bonds and subtract 2e-for each bond sum of valence e- Step 3 Give each atom 8e- (2e- for H) remaining valence e- Step 4 Figure 10.1 Lewis structure
Electron-group repulsions and the five basic molecular shapes Figure 10.5 Ideal bond angles are shown for each shape.
The three molecular shapes of the tetrahedral electron-group arrangement Examples: CH4, SiCl4, SO42-, ClO4- Examples: H2O OF2 SCl2 Examples: NH3 PF3 ClO3 H3O+ Figure 10.8
The four molecular shapes of the trigonal bipyramidal electron-group arrangement Examples: SF4 XeO2F2 IF4+ IO2F2- Examples: PF5 AsF5 SOF4 Examples: XeF2 I3- IF2- Examples: ClF3 BrF3 Figure 10.10
VSEPR (Valence Shell Electron Pair RepulsionTheory) Accounts for molecular shapes by assuming that electron groups tend to minimize their repulsions Does not show how shapes can be explained from the interactions of atomic orbitals
The Central Themes of Valence Bond (VB) Theory Basic Principle A covalent bond forms when the orbitals of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei. Three Central 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 (hybridization).
hydrogen, H2 hydrogen fluoride, HF fluorine, F2 Orbital overlap and spin pairing in three diatomic molecules Figure 11.1
Linus Pauling Proposed that valence atomic orbitals in the molecule are different from those in the isolated atoms Mixing of certain combinations of atomic orbitals generates new atomic orbitals Process of orbital mixing =hybridization; generates hybrid orbitals
Key Points Types of Hybrid Orbitals sp sp2 sp3 sp3d sp3d2 Hybrid Orbitals 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.
The sp hybrid orbitals in gaseous BeCl2 atomic orbitals hybrid orbitals VSEPR predicts a linear shape Figure 11.2 orbital box diagrams
The sp hybrid orbitals in gaseous BeCl2 (continued) orbital box diagrams with orbital contours Figure 11.2
The sp2 hybrid orbitals in BF3 VSEPR predicts a trigonal planar shape Figure 11.3
The sp3 hybrid orbitals in CH4 VSEPR predicts a tetrahedral shape Figure 11.4
The sp3 hybrid orbitals in NH3 VSEPR predicts a trigonal pyramidal shape Figure 11.5
The sp3 hybrid orbitals in H2O VSEPR predicts a bent (V) shape Figure 11.5
The sp3d hybrid orbitals in PCl5 VSEPR predicts a trigonal bipyramidal shape Figure 11.6
The sp3d2hybrid orbitals in SF6 VSEPR predicts an octahedral shape Figure 11.7
Step 1 Step 2 Step 3 Figure 10.1 Figure 10.12 Table 11.1 Conceptual steps from molecular formula to the hybrid orbitals used in bonding molecular shape and e- group arrangement molecular formula Lewis structure hybrid orbitals Figure 11.8
PROBLEM: Use partial orbital diagrams to describe how the mixing of atomic orbitals on the central atoms leads to hybrid orbitals in each of the following molecules. PLAN: Use Lewis structures to establish the arrangement of groups and the shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms. SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule (a) methanol, CH3OH (b) sulfur tetrafluoride, SF4 SOLUTION: (a) CH3OH The groups around C are arranged as a tetrahedron. O has a tetrahedral arrangement with two non-bonding e- pairs.
hybridized S atom S atom SAMPLE PROBLEM 11.1 (continued) hybridized C atom hybridized O atom single C atom single O atom (b) SF4 has a seesaw shape with four bonding and one non-bonding e- pairs. distorted trigonal bipyramidal
both carbons 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 Covalent Bonds Between Carbon Atoms - Single Bonds s bonds in ethane, CH3-CH3 ~109.5o Figure 11.9 free rotation
overlap in one position - s p overlap - electron density Covalent Bonds Between Carbon Atoms - Double Bonds s and bonds in ethylene, C2H4 hindered rotation ~120o Figure 11.10
overlap in one position - s p overlap - Covalent Bonds Between Carbon Atoms - Triple Bonds s and p bonds in acetylene, C2H2 hindered rotation 180o Figure 11.11
PROBLEM: Describe the types of bonds and orbitals in acetone, (CH3)2CO. PLAN: Use the Lewis structure to determine the arrangement of groups and the shape at each central atom. Postulate the hybrid orbitals, taking note of multiple bonds and their orbital overlaps. sp3 hybridized sp3 hybridized sp2 hybridized Describing bonding in molecules with multiple bonds SAMPLE PROBLEM 11.2 SOLUTION: bond bonds
Restricted rotation in p-bonded molecules cis trans No spontaneous interconversion between cis and trans forms (isomers) in solution at room temperature! Figure 11.12
Limitations of VB Theory Inadequately explains magnetic/spectral properties Inadequately treats electron delocalization VB theory assumes a localized bonding model
Molecular Orbital (MO) Theory A delocalized bonding model A quantum-mechanical treatment of molecules similar to that used for isolated atoms Invokes the concept of molecular orbitals (MOs) (extension of atomic orbitals) Exploits the wave-like properties of matter (electrons)
Central themes of molecular orbital (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).
Amplitudes of wave functions are added Amplitudes of wave functions are subtracted An analogy between light waves and atomic wave functions Figure 11.13
Contours and energies of the bonding and antibonding molecular orbitals in H2 Figure 11.14
number of AOs combined = number of MOs produced Bonding MO: lower in energy than isolated atoms Antibonding MO: higher in energy than isolated atoms To form MOs, AOs must have similar energy and orientation Sigma (s) and pi (p) bonds are denoted as before; a star (asterick) is used to denote antibonding MOs.
Molecular orbital diagram for the H2molecule MOs are filled in the same sequence as for AOs (aufbau and exclusion principles, Hund’s rule) Figure 11.15
The MO bond order [1/2 (no. of e- in bonding MOs) - (no. of e- in antibonding MOs)] higher bond order = stronger bond Has predictive power!
s*1s Energy 1s 1s 1s 1s s1s AO of He AO of He+ AO of He AO of He MO diagrams for He2+ and He2 s*1s Energy s1s MO of He+ MO of He2 He2+ bond order = 1/2 He2 bond order = 0 can exist! cannot exist! Figure 11.16
PROBLEM: Use MO diagrams to predict whether H2+ and H2- can 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. Calculate the bond order. s s 1s 1s 1s 1s AO of H- AO of H AO of H s s SAMPLE PROBLEM 11.3 Predicting species stability using MO diagrams bond order = 1/2(1-0) = 1/2 bond order = 1/2(2-1) = 1/2 SOLUTION: H2+ does exist! H2- does exist! AO of H+ MO of H2- MO of H2+ configuration is (s1s)2(s1s)1 configuration is (s1s)1
s*2s s*2s 2s 2s 2s 2s s2s s2s s*1s s*1s 1s 1s 1s 1s s1s s1s Figure 11.17 Bonding in s-block homonuclear diatomic molecules Be2 Li2 Energy Li2 bond order = 1 Be2 bond order = 0
Bonding and antibonding MOs for core electrons cancel = no net contribution to bonding Only MO diagrams showing MOs created by combining valence-electron AOs are important.
Contours and energies of s and MOs through combinations of 2p atomic orbitals end-to-end overlap side-to-side overlap Figure 11.18
Relative energies s2p < p2p < p*2p < s*2p More effective end-to-end interaction relative to side-to-side in bonding MOs