General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8th Edition Chapter 12 (11 in 9 th Ed.) : Chemical Bonding II: Additional Aspects Contents 12-1 What a Bonding Theory Should Do 12-2 Introduction to the Valence-Bond Method 12-3 Hybridization of Atomic Orbitals 12-4 Multiple Covalent Bonds 12-5 Molecular Orbital Theory 12-6 Delocalized Electrons: Bonding in the Benzene Molecule 12-7 Bonding in Metals Focus on Photoelectron Spectroscopy What a Bonding Theory Should Do Bring atoms together from a distance. e - are attracted to both nuclei. e - are repelled by each other. Nuclei are repelled by each other. Plot the total potential energy verses nuclear distance. -ve energies correspond to net attractive forces. +ve energies correspond to net repulsive forces. Covalent bond forms when Attractive forces > repulsive forces. Note: Only valence-shell electrons are involved in bonding. 1
Potential Energy Diagram Bond length- The internuclear distance between two bonded atoms. Strong repulsions at close distance between the nuclei increase the P.E 12-2 Valence-Bond Method Valence -bond method: A description of covalent bond formation in terms of atomic orbital overlap is called valence bond method. Atomic orbital overlap describes covalent bonding. Covalent bond-a region of high electron density between bonding atoms resulting from the in-phase overlap of two atomic orbitals. A localized model of bonding. Bond pair is localized in the region of the orbital overlap. Lone pair and core electrons are localized on each atom as before. Valence- Bond Method: Bond types Sigma bond (σ) - Results from end- to -end overlap of a pair of orbitals. High electron density along the inter-nuclear axis. Pi bond (π)- Results only from sideways overlap of a pair of parallel p orbitals. High electron density above and below the inter-nuclear axis. A nodal plane ( ψ 2 = 0) along the inter-nuclear axis. π bonds are found in multiple bonds. 2
Sigma and Pi bond Two ways of combining P-orbitals, end-to -end and side-to-side axis Side to side overlap π p-orbitals + + axis - - Bonding in H 2 S Overlap of at.orbital in the formation of S-H bond in H 2 S. Bonding atomic orbitals with unpaired e- are shown in grey. Observed H-S-H bond angle is 92. Example Using the Valence-Bond Method to describe a molecular structure. Describe the phosphine molecule PH 3, structure by the valence-bond method.. VSEPR AX 3 E class and e - -group geometry is tetrahedral. 1. Draw valence shell orbital diagrams for separate atoms Identify valence electrons that each atom uses for bonding: 3
Bonding in PH 3 Sketch the orbitals: Overlap the bonding orbitals: Describe the shape: Trigonal pyramidal, Experimental bond angle is 93 12-3 Hybridization of Atomic Orbitals Hybridiztion Mixing of atomic orbitals to give equivalent energy orbitals (mathematical process). e.g. bonding in CH 4 (AX 4 type) Can not explain 4 bonds: Explains four bonds and nothing else. Facts about Hybrid orbitals # of hybrid orbitals formed = # of atomic orbital mixed Hybrid orbitals are subshells with same energy, size and shape but different spatial orientations. Energy of the hybrid orbitals is a weighted average of the original orbitals. Meaning of the symbol of hybrid orbital: 4sp 3 4 = Total # of hybrid orbitals formed Letters describe the types of orbitals that are mixed i.e. sp 3 = one s + three p orbitals. Different types of hybridizations: 2sp, 3sp 2, 4sp 3, 5sp 3 d and 6sp 3 d 2 4
Mixing of one s and three p orbitals to form four sp 3 hybrid orbitals. Shape of hybrid orbitals: One large lobe and one small lobe on the opposite sides of the nucleus. sp 3 Hybridization sp 3 Hybridization Bonding in methane CH 4 sp 3 Hybridization in Nitrogen (NH 3 ) Bonding in ammonia, NH 3 : VSEPR describes a tetrahedral geometry for four e- groups. 5
sp 2 Hybridization (B) Valence- shell orbital diagram for mixing of one s and two p orbitals to form three sp 2 hybrid orbitals in Boron that has 3 valence electron. Orbitals in Boron (BF 3 ) sp Hybridization (Be) Valence-shell orbital diagram for beryllium in sp hybridization. Mixing of one s and one p orbital to form two sp hybrid orbitals 6
Orbitals in Beryllium sp 3 d and sp 3 d 2 Hybridization Predicting Hybridization of central atom from Lewis structure and VSEPR The number of hybrid orbitals required = number of electron groups present around the central atom. The hybrid orbital geometry is same as electron group geometry. Method Write a plausible Lewis structure. Use VSEPR to predict electron geometry. Describe the molecular geometry. Select the appropriate hybridization 7
Hybrid Orbitals and their Geometry No of e- groups No. of Hybrid Designation Geometry orbital 2 2 sp linear 3 3 sp 2 Triangular planar 4 4 sp 3 Tetrahedral 5 5 sp 3 d Triangular bipyramidal 6 6 sp 3 d 2 octahedral Hybrid Orbitals and VSEPR Examples: Predict the shape of the following molecules and a hybridization scheme consistent with this prediction; BeH 2, AlI 3, NH 3, BrF 3, SF 6. Write a plausible Lewis structure. Use VSEPR to predict electron geometry. Describe Molecular geometry Select the appropriate hybridization Hybridization of the central atom Example: Determine the hybridization for the central atom in IF 5, BrF 3 and AsF 5. Solution: Determine the electron -dot structure for each of these molecules, predict the e- group geometry based on VSEPR theory and then assign hybridization to central atom. IF 5 -has 6 e- groups around the central I atom» Hybridization is 6 sp 3 d 2 Octahedral (square pyramidal due to one lone pair). BrF 3 and AsF 5 -both have five e- groups around the central atom, therefore the hybridization is sp 3 d. BrF 3 = two lone pair on the central atom and 3 bond pairs, T shape AsF 5 = five bond pairs trigonal bipyramidal 8
Multiple Covalent Bonds Ethylene has a double bond in its Lewis structure. VSEPR says trigonal planar at each carbon. Two types of bond Sigma (σ) and pi (π) Sigma bond involve more extensive overlap than does the pi bond. So the order of strength of bonds is Triple>double> single ( BE= 837, 611 and 347 kj mol -1 ) Ethylene Acetylene Acetylene, C 2 H 2, has a triple bond. VSEPR says linear at carbon 9
Proposing hybridization scheme involving sigma (σ) and pi (π) bond Example: Formaldehyde gas H 2 CO is used in the manufacture of plastics; in aqueous solution, it is familiar biological preservative called formalin. Describe molecular geometry and a bonding scheme for the H 2 CO molecule. Solution 1 Write plausible Lewis structure. 2. Determine the e- group geometry of the central C atom. 3. Identify the hybridization scheme that conforms to the electrongroup geometry. 4. Identify the orbitals of the central atom that are involved in the orbital overlap. 5. Sketch the bonding orbitals of the central and terminal atoms and estimate the bond angles. Bonding in formaldehyde Molecular Orbital Theory Principle: Electrons in a molecule occupy molecular orbitals (MO) formed by the overlap of atomic orbitals (AO) of the bonding atoms Atomic orbitals are isolated on atoms. Molecular orbitals span two or more atoms. Bonding molecular orbital ( σ, π)- An orbital with high electron density between the nuclei. This provides the increased shielding of the nuclei from each other decreasing nuclear repulsion. This decreases the MO energy than the bonding atomic orbitals. LCAO : Linear combination of atomic orbitals. Ψ 1 = φ 1 + φ 2 Ψ 2 = φ 1 -φ 2 10
Combining Atomic Orbitals Anti-bonding molecular orbital (superscript asterisk e.g. σ, π )- An orbital with low electron density between the two nuclei, Provides very little shielding of the nuclei from each other increasing nuclear repulsion ( weak bond). This increases the antibonding MO energy compared to combining AO. Molecular Orbitals of Hydrogen (H 2 ) Basic Ideas Concerning MO s Basic ideas concerning MO s and assigning of electrons to these orbitals. 1. Number of MOs = Number of AOs. Number of molecular orbitals formed is equal to the number of atomic orbitals mixed. 2. Two types of MO are formed formed from mixing of two AOs bonding and antibonding MOs. Bonding MO is at lower energy than the original AOs from which it is formed. Antibonding MO is at higher energy than the original AOs from which it is formed. 3. e - fill the lowest energy MO first. 4. A MO can accommodate only two e - s with opposite spin (Pauli exclusion). 4. In ground state electron configuration, electrons enter MO of identical energies singly before they pair up (Hund s rule). 11
Bond Order Stable species have more electrons in bonding orbitals than antibonding. Bond Order = (No. e- in bonding MOs - No. e - in antibonding MOs) 2 Diatomic Molecules of the First-Period BO = (e - bond - e - antibond )/2 BO H 2 + = (1-0)/2 = ½ BO = (2-0)/2 = 1 H 2 BO He 2 + = (2-1)/2 = ½ BO = (2-2)/2 = 0 He 2 Energy level diagrams Energy level diagrams for 1st period diatomic species H 2, He 2 and He 2 + 12
Molecular Orbitals of the Second Period Elements First period use only 1s orbitals. Second period have 2s and 2p orbitals available. p orbital overlap: End-on overlap is best sigma bond (σ). Side-on overlap is good pi bond (π). Molecular Orbitals of the Second Period Bonding MO (in phase) Antibonding MO out of phase Combining p orbitals Two σ-type MO Orbitals (end-on overlap) Four π-type orbital (parallel overlap) 13
Expected MO Energy-Level Diagram of C 2 Why do π 2p and σ 2p orbital change places? MO Diagrams of 2 nd Period Diatomics You don t need to memorize this, but know how to fill in electrons in orbitals. MO Diagrams of Heteronuclear Diatomics 14
MO of Heteronuclear Diatomic molecules The energy of bonding MO is closer to the more electronegative element. Energy of antibonding MO is closer to less electronegative element. The number of molecular orbitals formed from mixing of s and p orbitals is same. If one of the element in the molecule is O or F use the unmodified order for MO energy-level diagram. Delocalized Electrons Delocalized Pi (π) MO s are produced from continuous overlap of 2p z orbitals in 3 or more consecutive atoms. Present in resonance structures e.g. C 6 H 6, O 3, NO 3-, SO 3 Benzene F. Kekule (1865) First good proposal for benzene structure. Flat hexagonal ring of six carbon atoms joined by alternating single and double covalent bonds. All C-C bonds are alike. Single bond and double bond continually oscillate from one position to the other. Dame Kathleen Londsdale; first to determine the X-ray crystal structure of benzene ( flat molecule). 15
Benzene Benzene All six carbon atoms are identical, Class AX 3. Each carbon is triangular planar, each carbon has three electron groups around it. C 6 H 6 is a flat molecule. Six pi MO by the overlap of six 2p orbitals. Ideas leading to structures other than benzene with delocalized MO For O 3 molecule 1 With VSEPR predict the e - group geometry. Select a hybridization scheme for the central and terminal O atom in O 3 molecule (sp 2 hybridization).each O atom uses sp 2 +p Orbital for bonding. 2. V.e = 18. Assign 14 to sp 2 hybrid orbitals of σ- bond frame work. 4 of these are bonding electron and 10 are lone pairs. 3. Three un-hybridized 2p orbitals combine to form three MO s of π-type Bonding,antibonding and nonbonding MO. A nonbonding MO has same energy as the combining AO. It neither adds or detracts from bond formation. 4. The remaining 4 electrons are assigned to the π MOs. Two in bonding and 2 in nonbonding MO. 5. Bond order associated with π MO s is (2-0)/2 =1. The π bond is distributed among two O-O bonds. 16
Ozone Electron sea model Nuclei in a sea of e -. Metallic lustre. Malleability. Conductivity. Bonding in Metals Force applied A metal crystal is a network of cations in a sea of electrons. 17