Lecture Notes by Ken MarrChapter 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 TheoryCovalent BondsResult from the overlap of valence shell atomic orbitals to share an electron pairs, p, or hybrid orbitals may be used to form covalent bondse.g. Predict the Orbitals used for bonding in:H2, HF, H2S, F2

Examples of s and p Orbitals involved in BondingOverlap of s orbitalsH2Overlap of s and p orbitalsHFH2SOverlap of p orbitalsF2

Hybrid OrbitalsThe use of only s and p orbitals does not explain bonding in most molecules!!!e.g. BeCl2, CH4 , H2Ohybrid orbitals are used in these casesHybrid 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 Atoms Hybridization Write Lewis structure for the molecule or ion, then...Determine number of electron pairs around the atom in questionOne orbital is needed for each electron pairsp hybridization provides 2 orbitalssp2 hybridization provides 3 orbitalssp3 hybridization provides.....?...........orbitalssp3d hybridization provides......?..........orbitalssp3d2 hybridization provides....?.............orbitals

Examples of Hybrid OrbitalsExample of sp hybrid orbitals:BeCl2

Examples of Hybrid OrbitalsExample of sp2 hybrid orbitalsBF3

Hybrid OrbitalsExamples of sp3 hybrid orbitalsCH4, C2H6, H2O, NH3 Example of sp3d hybrid orbitalsPCl5 Example of sp3d2 hybrid orbitalsSF6

Bond Angle ~92 o

Mode of Orbital OverlapSigma vs. Pi BondsSigma Bonds (s-bond)Head to head overlap of s, p, or hybrid orbitalsResponsible for the framework of a moleculeSingle bond = one s bond

Mode of Orbital Overlap Sigma vs. Pi BondsPi bonds (p-Bonds)Side to side overlap of p orbitalsRestrict rotationDouble bond = one s bond + one p bondTriple Bond = one s bond + two p bonds

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

Predict the hybrid orbitals used in the followingNitrogen gas, N2Formaldehyde: H2COCarbon dioxide, CO2Carbon monoxide, COSulfur dioxide, SO2

One option for SO2S = [Ne] 3s2 3px2 3py1 3pz1This structure is...Favored by formal chargeRequires ?? hybridization

Big Problems with this Structure..How many unhybridized p-orbitals are available for p bonding?How many p-orbitals are needed?o o

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

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

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

Strengths and Weaknesses of Valence Bond TheoryVB Theory Molecules are groups of atoms connected by localized overlap of valence shell orbitalsVB, VSEPR and hybrid orbital theories work well together to explain the shapes of moleculesButVB theory inadequately explainsMagnetic property of molecules Spectral properties of moleculesElectron delocalization Conductivity of metals

Molecular Orbital TheoryThe electrons in a molecule are found in Molecular Orbitals of different energies and shapes Just as an atoms electrons are located in atomic orbitals of different energies and shapesMOs spread over the entire moleculeMajor drawbacks of MO Theory Based on Quantum theoryCalculations are based on solving very complex wave equations major approximations are needed!Difficult to visualize

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

Formation of Molecular OrbitalsMOs form when atomic orbitals overlapBonding MOs Result from constructive interference of overlapping electron wavesStabilize a molecule by concentrating electron density between nucleiMOs more stable than AOs delocalize electron charge over a larger volume

Overlap of standing electron WavesConstructive interferenceDestructive interference

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

H2 is more stable than the separate atoms

Antibonding MOsAntibonding MOs Result from destructive interference of overlapping electron wavesReduce electron density between nucleiDestabilize a moleculeHigher in energy than bonding MOs of the same type

Using MO Theory to Calculate Bond OrderVB definition of Bond Order.... Number of electron pairs shared between 2 nucleiMO TheoryB.O. = (No. Bonding e- - No. Antibonding e-) Meaning of B.O.B.O. > 0, then molecule more stable than separate atomsB.O. = 0, then zero probability of bond formationThe 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 PEMolecules 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 formHydride 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 Orbitalss Molecular Orbitals form when.....s - atomic orbitals overlapp - atomic orbitals overlap head to headp Molecular Orbitals form when.....p - atomic orbitals overlap side to sideWhy are s-bonds more stable than p- bonds?

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

Explaining MO Energy Levels for Period 2 ElementsO2, F2 and Ne2Paired electrons in 2p sublevel Repulsions 2s and 2p different in Energy No mixing occurs between 2s and 2p orbitalsRaises energy of s2s and s*2s MOEnergy of s2p < Energy p2p

B2, C2 and N2Only unpaired electrons in 2p sublevel 2s and 2p are very close in energy Mixing occurs between 2s and 2p orbitalsLowers energy of s2s and s*2s MOEnergy of s2p > Energy p2p

Bonding in Diatomic Molecules of Period 2Rules for filling of Molecular OrbitalsApply the Rules for the filling of Atomic Orbitals (Aufbau principle)Electrons 1st fill MOs of lowest energyOnly 2 electrons with opposite spin per MOMOs of same energy (sublevel) half fill before electrons pairPredict 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 AOs

Why are oxygens AOs at lower a energy than nitrogens?Bond order?Para- or diamagnetic?

Delocalized Molecular OrbitalsMO 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 atomsDelocalized 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 SolidsWhy do metals conduct electricity and nonmetals do not?Band Theory to the rescue!!

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

Energy Bands (MO Orbitals) for Na

Fig. 12.37

Electrical ConductorsHave 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 bondsHave a large band gap between the filled valence band and the empty conduction band Some examplesGlass, diamonds, rubber, most plastics

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

Doping of Semiconductorsp-type semiconductorsDoped with a Group IIIA elementHave one less electron than SiCauses positive holes in semi conductor Electricity flows through these positive holesn-type semiconductorsDoped with a Group VA elementHave one more electron than SiCauses negative holes in semiconductor Electricity flows through these negative holes