Chapter 4

1 CM1502 AY11/12

Theories of Covalent Bonding

2

A Closer Look at Lewis “Structures” and VSEPR

• Lewis “dot” structures are based on completing the octet, neglects all differences in the energies of subshells.

• We have also seen that we can not say just where

electrons are, due to the uncertainty principle. – Yet Lewis dot structures clearly indicate where

electron are.

• Is there a better treatment of bonding that is consistent with quantum mechanics?

• Is there a way to explain the rules given in VSEPR?

3

Valence Bond Theory • Linus Pauling took up the idea of Lewis (electron sharing)

and Heitler-London (exchanging the electrons) to produce a theory for all covalent chemical bonding.

• As an example, consider the molecule H-F

4

Introducing Hybridization • Consider CH4. It is tetrahedral in shape.

• The 2p AO all are at 900 to each other. • How can C have a set of AO that are pointing to the apices of a

tetrahedron? • The answer lies in Pauling’s idea of hybridization.

5

Hybridization • By taking certain linear

combinations of AO’s it is possible produce a new set of orbitals.

• In 1931 Pauling proposed that if we combine the s AO and all three p AO together in the right linear combination we can obtain a perfect tetrahedral set of AO.

Figure from. http://cwx.prenhall.com/petrucci/medialib/media_portfolio/12.html

Note that small negative lobes are present

Atomic orbitals hybrid orbitals overlap with other orbitals to form bonds

6

Bonding in CH4

Figure from. http://cwx.prenhall.com/petrucci/medialib/media_portfolio/12.html

Note that the overlap of the AOs must reinforce the electron probability amplitude.

“+” lobes should overlap with “+” lobes and/or “-” lobes with “-” lobes, but not “+” lobes with “-” lobes.

sp3 hybridization provides 4 equivalent orbitals pointing to the apices of a tetrahedron. 4 AO mix to produce 4 sp3 hybrid orbitals.

Types of Hybridization

Atomic Orbitals Hybrid Orbitals s, p sp (2 of them) s, p, p sp2 (3 of them) s, p, p, p sp3 (4 of them) s, p, p, p, d sp3d (5 of them) s, p, p, p, d, d sp3d (6 of them)

The number of hybrid orbitals formed equals the number of atomic orbitals mixed

8

Bonding in BeCl2

Figure from. http://cwx.prenhall.com/petrucci/medialib/media_portfolio/12.html

sp Hybridization

9

Bonding around the Al in AlF3

Figure from. http://cwx.prenhall.com/petrucci/medialib/media_portfolio/12.html

Review of sp, sp2 and sp3 hybridization and bonding in NH3 (movie- IVLE workbin -videos)

sp2 Hybridization

Bonding in Ammonia

Trigonal Pyramidal.

sp3d Hybridization

sp3d hybridization gives us a trigonal bipyramidal shape 5 AO combine to give us 5 hybrid orbitals.

sp3d2 Hybridization

sp3d2 hybridization gives us an octahedral shape 6 AO combine to give us 6 hybrid orbitals

These are the 6 “+” lobes of 6 orbitals, unlike px, py and pz.

Molecular formula

Lewis Structure

Electron Group Arrangement

Hybridization Step 1 Step 2 Step 3

BeCl2 2 electron pairs sp hybridized

H2O

4 electron pairs NH3

4 electron pairs sp3 hybridized

sp3 hybridized

14

Sigma (σ) Bonds

• The strength of the covalent bond is solely due to exchange of electrons between the atoms bonding and arises because of significant orbital overlap.

• σ-bonds are chemical bonds of the covalent type, where a single lobe of one involved electron orbital overlaps a single lobe of the other involved electron orbital.

• The bonding orbital has no node/nodal plane which go through both atoms.

• σ-bonds are the strongest type of covalent bonds.

15

Some examples of σ-bonds.

-

2p - 2p

+

s + s

16

Ethane comprises all σ-bonds.

• From the Lewis structure, VSEPR tells us that both C’s should be tetrahedral. • sp3 hybridize both carbons and overlap the 1s AO of H onto each. • Note the two sp3 orbitals also overlap to form a C-C σ-bond.

17

Pi (π) Bonds

+

+

• Pi bonds (π bonds) are chemical bonds of the covalent type, where two lobes of one involved electron orbital overlap the two lobes of the other involved electron orbital.

• Of the orbital's nodal planes, only one goes through both atoms and contains the line joining the atoms.

18

Bonding in Ethene (ethylene)

• The Lewis structure gives us a double bond between the C’s.

• VSEPR tells us the each C has a trigonal planar structure.

• sp2 hybridize each C. • Form σ-bonds for the skeleton

of the molecule. • Form the π-bond to make the

double bond.

a b

Note, there is only 2 electrons in the π-bond, NOT 4

electron density

19

σ and π Bonds • Lewis double bonds consist of two,

nonequivalent types of bonds, one σ and one π. – There are no nodes in the σ-bond. – There is a nodal plane in the π-bond.

• Unlike the σ-bond, the π-bond exposes electron density above and below the nodal plane, making it more susceptible to attack by other atoms or molecules which are hungry for electrons.

20

Bonding in Ethyne (acetylene)

• From the Lewis structure of ethyne, VSEPR predicts a linear structure.

• sp hybridize each C. • Form σ-bonds for the skeleton

of the molecule. • Form a π-bond to make a

double bond. • Form a second π-bond to make

the triple bond.

21

Bonding in H2CO

• Form the Lewis structure.

• Use VSEPR to determine the structure.

• Hybridize and form σ-bonds.

• Form π-bonds. • Draw structure with

angles and hybridization of atoms.

O

HHC

C OH

H

π bond

lp

lp

C OH

H

lp

lp

C OH

H sp2sp2

1200

C O

Top View

H

H

lp

lp

22

Lewis Structure, VSEPR, VB Theory. • Can answer the type of question: Given a certain formula, what is its structure? • Can not answer the question: Is a certain formula allowed.

– E.g., SeF4 is predicted not to exist because Se has violated the octet rule.

– E.g. BX3 X = H or any halogen is predicted not to exist because B can never form an octet.

• What does hybridization actually tell us? – It shows how covalent bonds can form between metals and

nonmetals. – It provides an explanation of the VSEPR rules. – It shows why covalent bonds are so strong due to overlap of

orbitals and therefore exchange of electrons between bonded atoms.

23

σ-Bond → σ Energy Level π-Bond → π Energy Level

• Atoms have AO and energy levels associated with them, εAO.

• Molecules have σ and π orbitals and energy levels associated with them, εσ and επ.

• Thus for a molecule like CH4, we have 4 equivalent σCH bonds and VB theory predicts we should have 4 identical εσ for the energy levels.

E

0

} 4 degenerate σ orbitals

VB Theory predicts

24

Photoelectron Spectrum • A photoelectron spectrum is a plot of number of photoelectrons

detected on the vertical axis versus KE of the photoelectrons on the horizontal axis.

• Recall that for CH4, VB theory predicts 4 equivalent σ-bonds, and 4 degenerate εσ. – VB theory therefore predicts that for CH4 there should only

be one low-energy IE in the photoelectron spectrum giving the εσ.

– Experiment shows not 1, but 2 low-energy IE peaks. – This occurs for many molecules, so VB theory does not

properly describe bonding in molecules. – Despite this, VB theory is still widely used by many scientists

today.

• See the URL: http://www.pes.arizona.edu/facility/aboutPES.htm

25

Alert! Lewis Structures v1.3/VSEPR/VB SYSTEM FAILURE

• Do not ask questions using Lewis structures, VSEPR and VB theory regarding orbital energies and expect the answer to be correct. – Lewis structures v1.3 + VSEPR + VB theory crashes

irreparably when questions of orbital energy arise.

• To account for orbital energies we need an entirely new model/treatment.

• The strength of the covalent bond is solely due to this exchange of electrons. • VB theory is based on this idea, and utilizes hybridization of AO to direct orbitals

more appropriately. • Once a molecular shape has been determined from VSEPR, VB theory is then

used to hybridize the AOs. • The number of AOs mixed together equals the number of new hybrid orbitals. • The AOs that were mixed together are replaced by the new hybrid orbitals. • Hybrid orbitals have “+” and “-” lobes, just as normal AOs, but the hybrid orbitals

have much more localized (smaller) negative lobes that point in the opposite direction to the “+” lobe.

• You should rote learn hybridization schemes and shapes of molecules. • σ-bond has no nodes.

• π-bond has 1 nodal plane containing the line joining the atoms. • Multiple bonds involve both σ- and π-bonds. • Photoelectron spectroscopy is used to probe the energies of orbitals in molecules

(and atoms). • VB theory fails to properly describe the details of bonding in CH4.

Summary

CM1101 27 O2 is paramagnetic (it possesses unpaired electrons) N2 is diamagnetic (all paired electrons)

Liquid N2 Liquid O2

Powerful Magnet Limitation of VB theory

http://www.youtube.com/watch?v=KcGEev8qulA 27 CM1502 AY11/12

The Schrödinger Equation

HΨ = EΨ

What is atomic orbital in reality?

Each solution to the equation (that is, each energy state of the atom) is associated with a given wave function, also called an atomic orbital.

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Basis of Molecular Orbital (MO) Theory…

Just as an atom has atomic orbitals (AOs) with a given energy and shape that are occupied by the atom’s electrons,

a molecule has molecular orbitals (MOs) with a given energy and shape that are occupied by the molecule’s electrons.

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The Central Themes of MO Theory

A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals.

Atomic wave functions are combined to obtain molecular wave functions.

Linear combinations of AOs (LCAO) is used to form the MOs.

ψ1 = 1sa(r) + 1sb(r) ψ2 = 1sa(r) - 1sb(r)

30 CM1502 AY11/12

Amplitudes of wave functions added

Amplitudes of wave functions

subtracted.

ψ2 = 1sa(r) - 1sb(r) ψ1 = 1sa(r) + 1sb(r)

If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei).

If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the nuclei).

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Bonding and antibonding molecular orbitals (MOs) in H2.

# AO combined = # MO formed

Bond order: >0 means the molecular species is stable =0 means no net stability

or σg

or σu

The BO is: ½ (nbonding – nantibonding)

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σg or σu? gerade and ungerade

• We use the inversion operation (i), and to establish the following.

• “Do the MO change sign or not upon inversion?”. • Inversion: same distance but in opposite directions from the

centre of inversion.

If there is a sign change upon applying i, we have a σu MO.

If there is no sign change upon applying i, we have a σg MO.

33 CM1502 AY11/12

MO diagram for He2+ and He2

Ener

gy

MO of He2

+

σ*1s

σ1s

AO of He+

1s

MO of He2

AO of He

1s

AO of He

1s

σ*1s

σ1s

Ener

gy

He2+ bond order = 1/2 He2 bond order = 0

AO of He

1s

34 CM1502 AY11/12

σ*2s

σ2s

2s 2s 2s 2s

σ*2s

σ2s

Li2 bond order = 1 Be2 bond order = 0

Bonding in s-block homonuclear diatomic molecules.

Ener

gy

Li2 Be2

2nd Period Homonuclear Diatomics

35 CM1502 AY11/12

z

x

y

z

x

y

Atom a Atom b

σ

1 σ and 2 π interactions

π

π

End-to-end orbital overlap → sigma (σ) bonds Side-to-side orbital overlap → pi (π) bonds

Orientations of 2p AOs

36 CM1502 AY11/12

±

LCAO of 2p orbitals

37 CM1502 AY11/12

σg

σu

πu

πg

Energy gap depends on element (Zeff and e-e repulsion)

2p

2s 2s

2p

1s 1s Way down in energy

E

1σg

1σu

Very little overlap, almost no interaction

2σg

2σu

3σg

3σu

1πu

1πg

σ2s

σ2s*

σ2p*

σ2p πp

πp* σ p overlap is much more efficient than π p (sideways) overlap.

K Shell

Building an MO Diagram

38 CM1502 AY11/12

2s

2p

2σg

2σu

3σg

3σu

1πu

1πg

2p

2s

Little interaction

Small energy gap e.g. Li

2σg

2σu

3σg

3σu

Large interaction

MO Interactions

Note that this larger interaction is sometimes referred to as “sp mixing”.

39 CM1502 AY11/12

0

500

1000

1500

2000

2500

3 4 5 6 7 8 9

Atomic Number

Ener

gy g

ap /

kJ/m

ol

2s-2p Energy Gap

CM1101

-50.00

-45.00

-40.00

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.000 1 2 3 4 5 6 7 8 9 10 11

Atomic Number

Ener

gy /

eV

1s

1s

1s AO ↓

2s,2p 2s 2s

2s

2s

2s

2s

2s

2s

2s

2p

2p

2p 2p

2p

2p

2p

2p 2p

Z E(1s) / eVLi 3 -65Be 4 -119B 5 -200C 6 -296N 7 -410O 8 -545F 9 -696Ne 10 -871

Period 1 Period 2

Only have to consider the 2s-2p energy gap for atomic no 5 to 10 i.e. B, C, N, O, F and Ne.

H He Li Be B C N O F Ne

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Relative MO energy levels for Period-2 homonuclear diatomics.

MO energy levels for O2, F2, and Ne2

MO energy levels for B2, C2, and N2

without 2s-2p mixing

with 2s-2p mixing

41 CM1502 AY11/12

MO occupancy and molecular properties for B2 through Ne2

Problem: Use an MO diagram to

predict whether F2

2+ and F2

2- exist

or otherwise. 42 CM1502 AY11/12

Heteronuclear Diatomics, • When two dissimilar atoms bind, the AO energies are

different. – E.g., 2s AO energy of Li, is very different to the 2s AO energy

of F. • The degree of interaction between two AO in LCAO is

given by 2 factors. – The difference in energy between the AOs before they are

allowed to interact. – The degree to which they overlap with each other.

• The AOs no longer combine equally, so instead of having – ψ1 = φ1 + φ2 we have ψ1 = c1φ1 + c2φ2 – ψ2 = φ1 - φ2 we have ψ2 = c1’φ1 - c2’φ2

43 CM1502 AY11/12

• ε1s(H) = -13.6 eV (from IE) • ε2p(F) = -17.4 eV (from IE), and ε2s(F) is very

low in energy. • The energy difference between the 1s AO

on H and the 2s AO of F (at around -40 eV) is so great that these two AO’s hardly interact.

• The 1s AO on H overlaps with the 2pz AO of F, but the energy difference is relatively large between these two AO’s (17.4-13.6=3.8eV) so they interact only moderately.

Hydrogen Fluoride

44 CM1502 AY11/12

-50.00

-45.00

-40.00

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.000 1 2 3 4 5 6 7 8 9 10 11

Atomic Number

En

erg

y / e

V

1s

1s

1s AO ↓

2s,2p 2s 2s

2s

2s 2s

2s

2s

2s

2s

2p

2p 2p 2p

2p 2p

2p 2p 2p

Z E(1s) / eVLi 3 -65Be 4 -119B 5 -200C 6 -296N 7 -410O 8 -545F 9 -696Ne 10 -871

Note: that the 2p AOs of F have been split for clarity, they are actually degenerate, as are the n2p MOs.

HF Energy Level Diagram and MOs

2σ

3σ

4σ

45 CM1502 AY11/12

• MO theory is able to explain the significant polarity of HF.

• The MOs in HF localize electron density on F. – 2σ (σ2s/n2s) MO is much like the 2s AO of F.

– 3σ (σ2p) MO is much like the 2pz AO on F.

– 1π (n2p) MO are the 2py and 2px AOs on F.

– Occupying these MOs places a significant part of H’s 1s

electron onto F.

Ionic Character Explained

46 CM1502 AY11/12

CO

2s, σ

2pz, σ; 2px,y, π

2s, σ

2pz, σ; 2px,y, π

n2s 3σ

Both σ symmetry - can not cross each other Interact strongly, consequently they mix well

Was nonbonding, becomes bonding

Was bonding, becomes nonbonding

4σ 1π π2p

π2p*

5σ

6σ

2π

σp*

CO has 10 valence electrons CO has BO of ½ (6 – 0) = 3 Electronic configuration: KK(n2s)2(σsp)2(π2p)4(nsp)2

O

C σsp

nsp

47 CM1502 AY11/12

Photoelectrons in Molecules

• Photoelectron spectroscopy can be used to determine the energies of MOs as well.

• We can find the energies of MOs in exactly the same way as we did for the atoms.

• Consider CO → CO+ – KK(n2s)2(σsp,p)2(π2p)4(n2p)2 → KK(n2s)2(σsp,p)2(π2p)4(n2p)1 (IE = 14.01 eV) – KK(n2s)2(σsp,p)2(π2p)4(n2p)2 → KK(n2s)2(σsp,p)2(π2p)3(n2p)2 (IE = 16.91 eV) – KK(n2s)2(σsp,p)2(π2p)4(n2p)2 → KK(n2s)2(σsp,p)1(π2p)4(n2p)2 (IE = 19.72 eV) – Etc.

• If we irradiated a sample of CO with photons of energy 20.0 eV, what would we observe? – Three sets of photoelectrons. – Their KEs, in eV, would be: (20.0-14.01), (20.0-16.91) and (20.0-19.72).

• Using higher energy photons, we can probe the energies of the lower lying MOs.

48 CM1502 AY11/12

49

VB vs MO Theory VB Theory MO Theory

Localized orbital model Delocalized orbital model

Used for investigating properties of a ground-state molecule such as: molecular structure and geometry bond dissociation energy

Used for investigating properties of a molecule such as: energies of orbitals ionizations or excited states arising from electronic transitions (spectroscopy) magnetism

49 CM1502 AY11/12

Summary

• Orbitals can interact with each other significantly if – They overlap significantly (can only occur if their symmetries are the

same) AND… – their energies are similar.

• MO theory can be used to predict the existence or otherwise of molecules, the bond order in molecules, and the degree of ionic character in a bond (as well as many other things, e.g., UV-vis spectra, IR spectra, NMR spectra, MW spectra and much more).

• Ionization can take place from each occupied orbital. • If the photon energy is high enough, ionization can occur from

orbitals other than the HOAO or HOMO.

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