Lecture Notes by Ken Marr Chapter 11 (Silberberg 3ed) Covalent Bonding: Valence Bond Theory and Molecular Orbital Theory 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

Valence Bond Theory Covalent Bonds Result from the overlap of valence shell atomic orbitals to share an electron pair s, p, or hybrid orbitals may be used to form covalent bonds e.g. Predict the Orbitals used for bonding in: H2, HF, H2S, F2

Examples of s and p Orbitals involved in Bonding Overlap of s orbitals H2 Overlap of s and p orbitals HF H2S Overlap of p orbitals F2

hybrid orbitals are used in these cases The use of only s and p orbitals does not explain bonding in most molecules!!! e.g. BeCl2, CH4 , H2O hybrid orbitals are used in these cases Hybrid Orbitals are used to hold bonding and nonbonding electrons! s, p, and d orbitals may hybridize to form to form hybrid orbitals

How to Determine an Atom’s Hybridization Write Lewis structure for the molecule or ion, then... Determine number of electron pairs around the atom in question One orbital is needed for each electron pair sp hybridization provides 2 orbitals sp2 hybridization provides 3 orbitals sp3 hybridization provides.....?...........orbitals sp3d hybridization provides......?..........orbitals sp3d2 hybridization provides....?.............orbitals

Examples of Hybrid Orbitals Example of sp hybrid orbitals: BeCl2

Examples of Hybrid Orbitals Example of sp2 hybrid orbitals BF3

Hybrid Orbitals Examples of sp3 hybrid orbitals CH4, C2H6, H2O, NH3 Example of sp3d hybrid orbitals PCl5 Example of sp3d2 hybrid orbitals SF6

Bond Angle ~92 o

Mode of Orbital Overlap Sigma vs. Pi Bonds Sigma Bonds (s-bond) Head to head overlap of s, p, or hybrid orbitals Responsible for the framework of a molecule Single bond = one s bond

Mode of Orbital Overlap Sigma vs. Pi Bonds Pi bonds (p-Bonds) Side to side overlap of p orbitals Restrict rotation Double bond = one s bond + one p bond Triple Bond = one s bond + two p bonds

Examples: Sigma vs. Pi Bonds Ethane Ethylene (ethene) Effect of p-bonding on rotation about the s-bond? Acetylene (ethyne) Nitrogen Formaldehyde

Predict the hybrid orbitals used in the following Nitrogen gas, N2 Formaldehyde: H2CO Carbon dioxide, CO2 Carbon monoxide, CO Sulfur dioxide, SO2

One option for SO2 S = [Ne] 3s2 3px2 3py1 3pz1 o o This structure is... Favored by formal charge Requires ?? hybridization Big Problems with this Structure.. How many unhybridized p-orbitals are available for p bonding? How many p-orbitals are needed?

Another Option for SO2 S = [Ne] 3s2 3px2 3py1 3pz1 ??? Hybridization Bond order? Resonance? o o

Resonance: Delocalization of electrons Shifting of p-bond electrons without breaking the s- bond Although not favored by formal charge, B.O. = 1.5 o o o o Resonance

Molecular Orbital Theory p-electron pair found in molecular orbital formed from the overlap of p-orbitals B.O. = 1.5 same as measured B.O. S – O bond length is intermediate between S – O and S = O bond lengths o o

Strengths and Weaknesses of Valence Bond Theory VB Theory  Molecules are groups of atoms connected by localized overlap of valence shell orbitals VB, VSEPR and hybrid orbital theories work well together to explain the shapes of molecules But……VB theory inadequately explains… Magnetic property of molecules Spectral properties of molecules Electron delocalization Conductivity of metals

Molecular Orbital Theory The electrons in a molecule are found in Molecular Orbitals of different energies and shapes Just as an atom’s electrons are located in atomic orbitals of different energies and shapes MOs spread over the entire molecule Major drawbacks of MO Theory Based on Quantum theory Calculations are based on solving very complex wave equations major approximations are needed! Difficult to visualize

Advantages of MO Theory VB Theory incorrectly predicts that.... O2 is diamagnetic with B.O. = 2 or.... O2 is paramagnetic with B.O. = 1 MO Theory correctly predicts that.... O2 is paramagnetic with B.O. = 2 VB Theory requires resonance structures to explain bonding in certain molecules and ions MO Theory does not have this limitation

Formation of Molecular Orbitals MO’s form when atomic orbitals overlap Bonding MOs Result from constructive interference of overlapping electron waves Stabilize a molecule by concentrating electron density between nuclei MO’s  more stable than AO’s  delocalize electron charge over a larger volume

Overlap of standing electron Waves Constructive interference Destructive interference

(High e- density) (Low e- density) Fig. 11.13

H2 is more stable than the separate atoms

Antibonding MOs Antibonding MOs Result from destructive interference of overlapping electron waves Reduce electron density between nuclei Destabilize a molecule Higher in energy than bonding MOs of the same type

Using MO Theory to Calculate Bond Order VB definition of Bond Order.... Number of electron pairs shared between 2 nuclei MO Theory B.O. = ½ (No. Bonding e- - No. Antibonding e-) Meaning of B.O. B.O. > 0, then molecule more stable than separate atoms B.O. = 0, then zero probability of bond formation The greater the B.O., the stronger the bond

Why Do Some Molecules Exist and Others Do Not? Why do H2 and He21+ exist , but He2 does not? Recall…..Bonding results only if there is a net decrease in PE Molecules with equal numbers of Bonding and antibonding electrons are unstable...Why?...... Antibonding MOs raise PE more than Bonding MOs lower PE

Use MO theory to predict if the following can form Hydride ions: H2 1- and H2 2- Li2 , Li2 1+ , Li2 2+ , Li2 1- Be2 , Be2 1+ , Be2 2+ , Be2 1-

In He2, the antibonding electrons in s1s* cancel the PE lowering of s1s

Sigma vs Pi Molecular Orbitals s Molecular Orbitals form when..... s - atomic orbitals overlap p - atomic orbitals overlap head to head p Molecular Orbitals form when..... p - atomic orbitals overlap side to side Why are s-bonds more stable than p- bonds?

No mixing of 2s and 2p orbitals Mixing of 2s and 2p orbitals AO MO AO MO Energy Levels for O2, F2 & Ne2 AO MO AO MO Energy Levels for B2, C2 & N2

Explaining MO Energy Levels for Period 2 Elements O2, F2 and Ne2 Paired electrons in 2p sublevel  Repulsions  2s and 2p different in Energy No “mixing” occurs between 2s and 2p orbitals Raises energy of s2s and s*2s MO Energy of s2p < Energy p2p B2, C2 and N2 Only unpaired electrons in 2p sublevel  2s and 2p are very close in energy “Mixing” occurs between 2s and 2p orbitals Lowers energy of s2s and s*2s MO Energy of s2p > Energy p2p

Bonding in Diatomic Molecules of Period 2 Rules for filling of Molecular Orbitals Apply the Rules for the filling of Atomic Orbitals (Aufbau principle) Electrons 1st fill MOs of lowest energy Only 2 electrons with opposite spin per MO MOs of same energy (sublevel) half fill before electrons pair Predict the bond order for each of the following molecules involving period 2 elements Li2, Be2, B2, C2, N2, O2, F2, Ne2, NO

High Z effective of F results in lower energy or its AO’s

Why are oxygen’s AO’s at lower a energy than nitrogen’s? Bond order? Para- or diamagnetic?

Delocalized Molecular Orbitals MO Theory (unlike VB Theory) does not require resonance to explain the bonding in..... Carbonate ion, Nitrate ion, Formate ion, Acetate ion, Benzene, etc. MO Theory: Electron pairs can be shared by 3 or more atoms .......Why? MOs can overlap 3 or more atoms Delocalized Bonds form when an electron pair is shared by 3 or more atoms Offers stability in the same way that resonance offers stability

Bonding in Solids Why do metals conduct electricity and nonmetals do not? Band Theory to the rescue!!

Band Theory Energy Bands form from the overlap of atomic orbitals of similar energy from all atoms in a solid Energy bands containing core (nonvalence) electrons are localized i.e. Do not extend far from each atom Energy Bands containing valence electrons are delocalized I.e. extent continuously throughout the solid Conduction band : Valence bands that are either partially filled or empty

Energy Bands (MO Orbitals) for Na

Fig. 12.37

Electrical Conductors Have a conduction band that is partially filled (e.g. Group IA & Transition Metals) ....or.... Have an empty conduction band that overlaps a filled valence band (i.e. Have a narrow band gap) e.g. Group IIA Metals

Fig. 12.38

Nonconductors (Insulators) All valence electrons are used to form covalent bonds Have a large band gap between the filled valence band and the empty conduction band Some examples Glass, diamonds, rubber, most plastics

Semiconductors Have a small band gap between the filled valence band and the empty conduction band Thermal Energy can promote electrons from filled valence band to empty conduction band e.g. Silicon

Doping of Semiconductors p-type semiconductors Doped with a Group IIIA element Have one less electron than Si Causes positive holes in semi conductor Electricity flows through these positive holes n-type semiconductors Doped with a Group VA element Have one more electron than Si Causes negative holes in semiconductor Electricity flows through these negative holes