COVALENT BONDINGCOVALENT BONDING

ORBITALSORBITALS

The localized electron model The localized electron model views views

a molecule as a collection of a molecule as a collection of atoms atoms

bound together by sharing bound together by sharing electrons electrons

between their atomic orbitals. between their atomic orbitals.

The arrangement of valence The arrangement of valence

electrons is represented by the electrons is represented by the

Lewis structure and the Lewis structure and the molecular molecular

geometry can be predicted from geometry can be predicted from the the

VSEPR model. VSEPR model.

There are 2 problems with this.There are 2 problems with this.

Using the 2p and the 2s orbitals from Using the 2p and the 2s orbitals from

carbon in methane would result in 2 carbon in methane would result in 2

different types of bonds when they different types of bonds when they

overlap with the 1s from hydrogen. overlap with the 1s from hydrogen.

[three 2p/1s bonds and one 2s/2p [three 2p/1s bonds and one 2s/2p

bond]bond]

However,However,

Experiments show that Experiments show that methane methane

has has FOUR IDENTICALFOUR IDENTICAL bonds. bonds.

Uh oh…Uh oh…

Since the 3 p orbitals occupy Since the 3 p orbitals occupy the x, the x,

y, and z-axes, you would y, and z-axes, you would expect expect

those overlaps of those overlaps of atomicatomic orbitals to orbitals to

be at bond angles of 90be at bond angles of 90. .

Darn those experiments! Darn those experiments!

All 4 angles are 109.5All 4 angles are 109.5..

It’s not that the localized It’s not that the localized electron electron

model is wrong, it’s just that model is wrong, it’s just that carbon carbon

adopts a set of orbitals rather adopts a set of orbitals rather than than

its “native” 2s & 2p.its “native” 2s & 2p.

THIS IS WHY THESE ARE THIS IS WHY THESE ARE

MODELS/THEORIESMODELS/THEORIES

rather than LAWS!!rather than LAWS!!

Valence Bond TheoryValence Bond Theory

an extension of the LE modelan extension of the LE model

It’s all about hybridization!It’s all about hybridization!

Two atoms form a bond when Two atoms form a bond when bothboth

of the following conditions occur:of the following conditions occur:

1. There is orbital overlap between 1. There is orbital overlap between

two atoms. two atoms.

2. A maximum of two electrons, of 2. A maximum of two electrons, of

opposite spin, can be present in opposite spin, can be present in the the

overlapping orbitals.overlapping orbitals.

Because of orbital overlap, the Because of orbital overlap, the pairpair of electrons is found within a region of electrons is found within a region influenced by both nuclei. influenced by both nuclei.

Both electrons are attracted to both Both electrons are attracted to both atomic nuclei and this leads to atomic nuclei and this leads to bonding.bonding.

As the extent of overlap increases, As the extent of overlap increases, the strength of the bond increases. the strength of the bond increases.

The electronic energy drops as the The electronic energy drops as the atoms approach each other but atoms approach each other but increases when they become too increases when they become too close. close.

This means there is an This means there is an optimum optimum

distance, the observed bond distance, the observed bond

distance, at which the total distance, at which the total energy energy

is at a minimum.is at a minimum.

Sigma (σ) BondSigma (σ) Bond

overlap of two overlap of two ss orbitals or an orbitals or an ss and and

a a pp orbital or head-to-head orbital or head-to-head pp

orbitals. orbitals.

Electron density of a sigma bond is Electron density of a sigma bond is

greatest greatest along the axis along the axis of the bond. of the bond.

Maximum OverlapMaximum Overlap

forms the strongest possible bond forms the strongest possible bond

Two atoms are arranged to give the Two atoms are arranged to give the

greatest possible orbital overlap. greatest possible orbital overlap.

Tricky with Tricky with pp orbitals since they are orbitals since they are

directional.directional.

Hybrid OrbitalsHybrid Orbitals

a blending of atomic orbitals to a blending of atomic orbitals to

create orbitals of intermediate create orbitals of intermediate

energyenergy

Methane: All of the C-H bonds are Methane: All of the C-H bonds are

109109°° apart while apart while pp orbitals are only orbitals are only

9090°° apart apart

Pauling explained:Pauling explained:

The orbitals on the left are for a The orbitals on the left are for a

carbon atom [no bonding].carbon atom [no bonding].

Once the carbon atom begins to Once the carbon atom begins to

bond with say, H to keep it simple, bond with say, H to keep it simple,

the atomic orbitals HYBRIDIZE which the atomic orbitals HYBRIDIZE which

changes their shape considerably! changes their shape considerably!

There’s an energy payoff, else they There’s an energy payoff, else they

wouldn’t behave this way!wouldn’t behave this way!

Leads to Leads to

Ammonia also Ammonia also

has sphas sp33

hybridization hybridization

even though it even though it

has a lone pair.has a lone pair.

I find it helpful to think of electron I find it helpful to think of electron pair “sites” of electron density that pair “sites” of electron density that can be occupied by can be occupied by eithereither a lone a lone

pair pair or a shared pair. If there are 4 or a shared pair. If there are 4 ““sites”, then the 4 orbitals need to sites”, then the 4 orbitals need to hybridize so use one s and 3 p’s to hybridize so use one s and 3 p’s to make 4 spmake 4 sp33 [for lack of a better [for lack of a better name] orbitals.name] orbitals.

Multiple BondingMultiple Bonding

lowers the number of lowers the number of

hybridizing orbitalshybridizing orbitals

Pi (Pi () bonds) bonds

Come from the sideways overlap of Come from the sideways overlap of

pp atomic orbitals; the region above atomic orbitals; the region above

and below the internuclear axis. and below the internuclear axis.

NEVERNEVER occur occur without without a sigma a sigma

bond first!bond first!

Pi (Pi () bonds) bonds

May form May form onlyonly if unhybridized if unhybridized pp

orbitals remain on the bonded orbitals remain on the bonded

atoms.atoms.

Occur when Occur when spsp or or spsp22 hybridization hybridization

is present on central atom, NOT is present on central atom, NOT spsp33

hybridization.hybridization.

Carbon often does this with N, O, P, Carbon often does this with N, O, P,

and S since they have and S since they have pp orbitals. orbitals.

This is the formation of an spThis is the formation of an sp22 set set of of

orbitals [3 orbitals formed, 3 sites, orbitals [3 orbitals formed, 3 sites, 3 3

letters!]. letters!].

This molecule would contain a This molecule would contain a

double bond like ethene. double bond like ethene.

The molecule reserves a set of The molecule reserves a set of p’s p’s

to form the to form the bond. bond.

leads to

The set of p’s that The set of p’s that

are unhybridized are are unhybridized are

not pictured here at not pictured here at

left, they are left, they are

hovering above and hovering above and

below this page.below this page.

A different view, A different view,

without the without the

hydrogens, hydrogens,

centering on the centering on the

C atoms, shows the unhybridized C atoms, shows the unhybridized p p

orbitals that are making the orbitals that are making the

sideways overlap necessary to sideways overlap necessary to

create the double (create the double ()) bond. bond.

Here’s the whole mess, Here’s the whole mess, altogether:altogether:

Carbon #1 Carbon #2 OVERLAPPIN

G

This is the formation of an sp set of This is the formation of an sp set of

orbitals [2 orbitals formed, 2 sites, 2 orbitals [2 orbitals formed, 2 sites, 2

letters!]. letters!].

This molecule would contain a triple This molecule would contain a triple

bond like ethyne or the double-bond like ethyne or the double-

double arrangement in carbon double arrangement in carbon

dioxide. dioxide.

leads to:

The molecule reserves TWO The molecule reserves TWO

sets of p’s to form the 2 sets of p’s to form the 2

-bonds.-bonds.

At right, is a At right, is a

picture of the picture of the

2 unhybridized 2 unhybridized

p’s on the C p’s on the C

atom that is about atom that is about

to make a triple bond. to make a triple bond.

Look at the COLook at the CO22 Lewis diagram. Lewis diagram. The The

carbon has 2 sites and is therefore carbon has 2 sites and is therefore

sp hybridized while the oxygens sp hybridized while the oxygens

have 3 sites [2 lone pairs and a have 3 sites [2 lone pairs and a

double bond]. The oxygen’s have double bond]. The oxygen’s have

spsp22 hybridization. hybridization.

This should help:This should help:

Check out Benzene…Check out Benzene…

The Sigma Bond

Formations

The Pi Bond Formations

Draw the Lewis Structure for Draw the Lewis Structure for

Benzene:Benzene:

Exercise 1Exercise 1The Localized Electron The Localized Electron Model IModel I

Describe the bonding in the Describe the bonding in the

ammonia molecule using the ammonia molecule using the

localized electron model.localized electron model.

SolutionSolution

tetrahedraltetrahedral

spsp33 hybrid hybrid

Exercise 2Exercise 2 The The Localized Electron Model IILocalized Electron Model II

Describe the bonding in the NDescribe the bonding in the N22

molecule.molecule.

SolutionSolution

linear linear

sp hybridsp hybrid

Exercise 3Exercise 3 The Localized Electron The Localized Electron Model IIIModel IIIDescribe the bonding in the Describe the bonding in the

triiodide triiodide

ion (Iion (I33--).).

SolutionSolution

trigonal bipyramidal arrangement trigonal bipyramidal arrangement

ee-- pair geometry, linear molecular pair geometry, linear molecular

geometrygeometry

central iodine is dspcentral iodine is dsp33 hybridized hybridized

Exercise 9Exercise 9 The The Localized Electron Model Localized Electron Model IVIVHow is the xenon atom in XeFHow is the xenon atom in XeF44

hybridized?hybridized?

SolutionSolution

dd22spsp33 hybridized hybridized

Exercise 5Exercise 5 The Localized Electron The Localized Electron Model VModel VFor each of the following molecules For each of the following molecules

or ions, predict the hybridization of or ions, predict the hybridization of

each atom, and describe the each atom, and describe the

molecular structure.molecular structure.

a. COa. CO b. BFb. BF44-- c. XeFc. XeF22

SolutionSolution

A: linear, sp hybridizedA: linear, sp hybridized

B: tetrahedral, spB: tetrahedral, sp33 hybridizied hybridizied

C: trigonal bipyramidal eC: trigonal bipyramidal e-- pair, pair,

Xe dspXe dsp33, linear, linear

The Molecular Orbital The Molecular Orbital ModelModel

Though the molecular orbital model Though the molecular orbital model

will not be covered on the AP exam, will not be covered on the AP exam,

I feel that students should be I feel that students should be

exposed to a little of this theory for exposed to a little of this theory for

several reasons.several reasons.

1.1. Electrons are not always Electrons are not always

localized as in the VSEPR localized as in the VSEPR theory, therefore resonance theory, therefore resonance must be added and explained must be added and explained as best possible.as best possible.

2.2. Molecules containing Molecules containing unpaired unpaired

electrons are not easily dealt electrons are not easily dealt with using the localized with using the localized model.model.

3.3. Magnetism is easily described Magnetism is easily described for molecules using the MO for molecules using the MO

theory. theory.

( Oxygen is paramagnetic ( Oxygen is paramagnetic which is unexplained by the which is unexplained by the localized electron model. )localized electron model. )

4.4. Bond energies are not easily Bond energies are not easily

related using the localized related using the localized model.model.

TERMS TO KNOW:TERMS TO KNOW:

Bonding Molecular Bonding Molecular Orbital Orbital

An orbital lower in energy than An orbital lower in energy than the the

atomic orbitals of which it is atomic orbitals of which it is

composed.composed.

(favors formation of molecule) (favors formation of molecule)

Antibonding Molecular Antibonding Molecular OrbitalOrbital

An orbital An orbital higherhigher in energy than the in energy than the

atomic orbitals of which it is atomic orbitals of which it is

composed. (favors separated composed. (favors separated

atoms). atoms).

Represented by a * [The diagrams Represented by a * [The diagrams

use A for antibonding and B for use A for antibonding and B for

bonding.]bonding.]

Bond OrderBond Order

The difference between the The difference between the number number

of bonding electrons and the of bonding electrons and the

number of antibonding electrons number of antibonding electrons

divided by two. divided by two.

Indicates bond strength. Indicates bond strength.

Homonuclear Diatomic Homonuclear Diatomic MoleculesMolecules

Those composed of two Those composed of two identical identical

atoms. atoms.

Heteronuclear Diatomic Heteronuclear Diatomic MoleculesMolecules

Those composed of two Those composed of two different different

atoms. atoms.

ParamagnetismParamagnetism

Causes the substance to be Causes the substance to be drawn drawn

into a magnetic field; into a magnetic field;

Associated with unpaired Associated with unpaired electrons.electrons.

DiamagneticDiamagnetic

Causes the substance to be Causes the substance to be repelled by repelled by

the magnetic field; the magnetic field;

Associated with paired electrons. Associated with paired electrons.

General Energy Level General Energy Level Diagram for Diagram for

Filling Using the MO TheoryFilling Using the MO Theory

1s1s22 1s1s22* * 2s2s22 2s2s22* (* (2p2pxx222p2pyy

22))

2p2p22((2p2pxx22* * 2p2pyy

22*) *) 2p2p22**

If we assume that the molecular If we assume that the molecular

orbitals can be constructed from orbitals can be constructed from the the

atomic orbitals, the quantum atomic orbitals, the quantum

mechanical equations result in mechanical equations result in two two

molecular orbitals.molecular orbitals.

MOMO11 = 1s = 1sAA + 1s + 1sBB

andand

MOMO22 = 1s = 1sAA - 1s - 1sBB

Let’s start simple. Let’s start simple. 2 Hydrogen atoms.2 Hydrogen atoms.

Where 1sWhere 1sAA and and

1s1sBB represent the represent the

1s orbitals from 1s orbitals from

the two the two

separated separated

hydrogen atoms.hydrogen atoms.

This is actually a This is actually a

simple model to simple model to

follow.follow.

Look at the Look at the

diagram on the diagram on the

right, each H right, each H

entered with its entered with its

lone 1s electron. lone 1s electron.

As they approach each other, their As they approach each other, their

atomic orbitals [two of them] blend atomic orbitals [two of them] blend

to form molecular orbitals [two of to form molecular orbitals [two of

them—no magic here]. them—no magic here].

One MO is of high energy and one One MO is of high energy and one

MO is of low energy.MO is of low energy.

Which will the electrons choose? Which will the electrons choose?

The LOW, of course! The LOW, of course!

The electrons occupy the lower The electrons occupy the lower

energy level and thus a bond is energy level and thus a bond is

formed.formed.

This diagram at left uses the symbols we want to use.

Try this again Try this again with He: with He:

Since 4 electrons are involved, the first 2 get to be lazy and go to the low E state, the other 2 must occupy the higher energy state and cancel out the bond, therefore He2 DOES NOT EXIST!!

Now Now bond orderbond order can be redefined can be redefined

in this theory:in this theory:

Bond order = Bond order =

(number of bonding electrons – (number of bonding electrons – number of antibonding number of antibonding electrons)/ 2electrons)/ 2

If the bond order is zeroIf the bond order is zero no bond! no bond!

Shall we predict if LiShall we predict if Li22 is possible? is possible?

Li has its valence electrons in the Li has its valence electrons in the 2s sublevel.2s sublevel.

Yes! It may also exist. Yes! It may also exist.

What is it’s bond order?What is it’s bond order?

Can BeCan Be22 exist? exist?

Things get slightly more Things get slightly more

complicated when we leave Be complicated when we leave Be and and

move to 2p…move to 2p…

General Energy Level Diagram General Energy Level Diagram

for Filling Using the MO Theoryfor Filling Using the MO Theory

1s1s22 1s1s22* * 2s2s22 2s2s22* ( * ( 2p2pxx22 2p2pyy

22) )

2p2p22((2p2pxx22* * 2p2pyy

22*) *) 2p2p22**

The filling order for p’s is pi, pi, The filling order for p’s is pi, pi,

sigma all bonding followed by sigma all bonding followed by pi, pi, pi, pi,

sigma all antibonding.sigma all antibonding.

Hund’s Rule and Pauli Hund’s Rule and Pauli Exclusion Principles Exclusion Principles Apply!!Apply!!

Try to predict the configuration of BTry to predict the configuration of B22..

One of the most useful parts of One of the most useful parts of this this

model is its ability to accurately model is its ability to accurately

predict para- and predict para- and diamagnetism as diamagnetism as

well as bond order. well as bond order.

This device is used to This device is used to

test the paramagnetism test the paramagnetism

of homonuclear samples. of homonuclear samples.

When the electromagnet When the electromagnet

is on, a paramagnetic is on, a paramagnetic

substance is drawn substance is drawn

down into it and appears down into it and appears

heavier on the balance.heavier on the balance.

BB22 is paramagnetic! is paramagnetic!

That means that the That means that the

pi orbitals are of pi orbitals are of

LOWER energy than LOWER energy than

the sigma’s and the sigma’s and

Hund’s rule demands Hund’s rule demands

that the 2 electrons that the 2 electrons

fill the 2 bonding pi fill the 2 bonding pi

orbitals singly first before paring.orbitals singly first before paring.

Will CWill C22 exist? exist?

Will it be para- or diamagnetic?Will it be para- or diamagnetic?

Exercise:Exercise:

Write the appropriate energy Write the appropriate energy

diagram using the MO theory for the diagram using the MO theory for the

nitrogen molecule. nitrogen molecule.

Find the bond order for the molecule Find the bond order for the molecule

and indicate whether this substance and indicate whether this substance

is paramagnetic or diamagnetic. is paramagnetic or diamagnetic.

If you use the usual models to If you use the usual models to

examine the paramagnetism of examine the paramagnetism of

oxygen, you’d say it was oxygen, you’d say it was

diamagnetic. diamagnetic.

The truth is that it is The truth is that it is paramagnetic. paramagnetic.

If you pour liquid oxygen into the If you pour liquid oxygen into the

space between the poles of a space between the poles of a strong strong

horseshoe magnet, it says there horseshoe magnet, it says there

until it boils away in the warm until it boils away in the warm

room!room!

Exercise 6Exercise 6

For the species OFor the species O22, O, O22++, O, O22

--, give , give

the electron configuration and the electron configuration and the the

bond order for each. bond order for each.

Which has the strongest bond?Which has the strongest bond?

Exercise 7Exercise 7

Use the molecular orbital model to Use the molecular orbital model to

predict the bond order and predict the bond order and

magnetism of each of the following magnetism of each of the following

molecules.molecules.

a) Nea) Ne22

b) Pb) P22

This model This model

also works also works

in in heteronucleaheteronuclear r

molecules.molecules.

Exercise 8Exercise 8

Use the MO Model to predict Use the MO Model to predict the the

magnetism and bond order of magnetism and bond order of the the

NONO++ and CN and CN-- ions. ions.