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

1. Covalent Bonds» Result from the overlap of valence shell

atomic orbitals to share an electron pair

2. 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

1. Overlap of s orbitals» H2

2. Overlap of s and p orbitals» HF

» H2S

3. Overlap of p orbitals» F2

Hybrid Orbitals

1. 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 cases2. 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...

1. Determine number of electron pairs around the atom in question

2. One 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 Orbitals

Example of sp hybrid orbitals:

» BeCl2

Examples of Hybrid Orbitals

Example of sp2 hybrid orbitals

BF3

Hybrid Orbitals

1. Examples of sp3 hybrid orbitalsCH4, C2H6, H2O, NH3

2. Example of sp3d hybrid orbitalsPCl5

3. Example of sp3d2 hybrid orbitalsSF6

Bond Angle ~92 o

Mode of Orbital OverlapSigma vs. Pi Bonds

1. Sigma Bonds (bond)

» Head to head overlap of s, p, or hybrid orbitals

» Responsible for the framework of a molecule

Single bond = one bond

Mode of Orbital Overlap Sigma vs. Pi Bonds

2. Pi bonds (Bonds)» Side to side overlap of p orbitals» Restrict rotation

Double bond = one bond+ one bond Triple Bond = one bond+ two bonds

Examples: Sigma vs. Pi Bonds

Ethane Ethylene (ethene)

» Effect of bonding on rotation about the 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 3py

1 3pz1

This structure is...» Favored by formal charge» Requires ?? hybridization

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

S OOo o

Another Option for SO2

S = [Ne] 3s2 3px2

3py1 3pz

1

• ??? Hybridization• Bond order?• Resonance?

S

O O

o o

Resonance: Delocalization of electrons

Shifting of -bond electrons without breaking the - bond

Although not favored by formal charge, B.O. = 1.5

S

OO

S

O O

Resonanceo o o o

Molecular Orbital Theory

-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

S

OO

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

Fig. 11.13

(High e- density)

(Low e- density)

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 1s

* cancel the PE lowering of 1s

Sigma vs Pi Molecular Orbitals

Molecular Orbitals form when.....» s - atomic orbitals overlap» p - atomic orbitals overlap head to head

Molecular Orbitals form when.....» p - atomic orbitals overlap side to side

Why are -bonds more stable than 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 of2s and

2s MO– Energy of2p < Energy 2p

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 of2s and

2s MO– Energy of2p > Energy 2p

Bonding in Diatomic Molecules of Period 2

Rules for filling of Molecular OrbitalsApply the Rules for the filling of Atomic Orbitals

(Aufbau principle)

1.Electrons 1st fill MOs of lowest energy2.Only 2 electrons with opposite spin per MO3.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

1. Why are oxygen’s AO’s at lower a energy than nitrogen’s?

2. Bond order?3. 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