2-43

Heteronuclear Molecules

• The relative energy of the bonding orbitals determines themagnitude of the covalent bond energy (∆Ecov):

2-44

Energy Level D

iagram of C

O

2-45

Hydrogen Fluoride

• In H-F the 1s orbital of H is energetically well above the 1sand 2s orbitals of F–> it interacts only with the 2pz orbital (all remainingelectrons are in non-bonding orbitals!)

2-46

Lithium Fluoride

• As the polarity difference between two atoms increases, theorbital energy difference also increases–> electrons shift towards the more electronegative atom

• Limiting case: Ionic compounds

Ionic crystal:Ions are held together in a3-dimensional lattice bycombination of electrostaticand covalent interactions

2-47

Homonuclear Bond Energies

Note: Values can vary considerably depending on compounds involved

• Bond becomes weaker with increasing atom size• But: First row elements of group 15, 16 and 17 form weaker bonds than

2nd row elements (repulsion between lone pairs more pronounced)• Group 1&2: Destabilizing δ+ charges when mutually bonded

• Energy of C–C to N–N sharply decreased due to presence of lone pairs

2-48

Heteronuclear Bond Energies

• Heteronuclear bond energies much higher (stronger bonds) than homonuclearenergies (due to electronegativity differences)

• Group 2 bonds stronger than group 1 (ionic bond: lattice energies proportional to ioncharges)

• B–F stronger than Al–F due to π interaction

• Si–F stronger than C–F: large difference in electronegativity, π interaction with vacantd orbitals of Si

2-49

Multiple Bond Energies

• N2 triple is very strong (only the CO triple bond is stronger)• N=N is more than twice the bond energy of a N–N single bond

But: P=P is less than twice the bond energy of the P–P bond–> π bond interaction for 2nd and 3rd row elements weaker (due to larger and more diffuse porbitals)–> P–P single bond considerably stronger than N–N (or O–O) (less repulsion of lone pairelectrons)

2-50

Molecular Orbitals of Polyatomic Molecules

• Concept of linear combination can be also applied to polyatomicmolecules–> the resulting MOs are delocalized over the entire molecule

• Symmetry analysis by group theory predicts those linearcombinations, which lead to bonding, anti-bonding or non-bonding MOs

• The energy of the resulting MOs is measured via photoelectronspectroscopy or estimated with quantum chemical calculations

2-51

Beryllium Dihydride (BeH2)

• VSEPR analysis: linear geometry

• Set of AOs:Be: H:Note: the 2px and 2py orbitals yield non-bonding interactions

• Form group orbitals with 1s orbitals of H and H’:

Ψ Ψ ΨA s sH H= +1 1( ) ( ' )

Ψ Ψ ΨB s sH H= −1 1( ) ( ' )

2-52

Group Orbitals Interact with Be AOs:

ΨA interacts with the 2s orbital of Be to form a bonding (σs) andanti-bonding (σs*) orbital:

ΨB interacts with the 2pz orbital of Be to form a bonding (σp)and anti-bonding (σp*) orbital:

2-53

Energy Level Diagram

Group orbitals

ΨA

ΨB

energy

2-54

• VSEPR analysis: bent geometry

• Set of AOs:O: H:

• Note: the 2py orbital results a non-bonding interactions

• Form goup orbitals with 1s orbitals of H and H’:

MOs of Water (H2O)

Ψ Ψ ΨA s sH H= +1 1( ) ( ' )

Ψ Ψ ΨB s sH H= −1 1( ) ( ' )

2-55

The Two ΨA Group Orbital Interactions:

ΨA interacts with two AOs of Oxygen: The 2s and 2pz orbital:

–> this results in one bonding, one anti-bonding and onenon-bonding (approximately) orbital:

ΨA2pz

2s

Oxygen AOs

(Group Orbital)

σs,z*

σs,z

σs,z nb

2-56

The ΨB Group Orbital Interaction:

ΨB interacts with the 2px orbital of oxygen to form a bonding (σs)and anti-bonding (σs*) orbital:

ΨB2px

2-57

To Give the Final Energy Level Diagram...

ΨA

ΨB

energy

Group orbitals

2-58

Diagram

with M

O shapes

2-59

Hybridization

• Molecular Orbital Theory:–> Electrons are delocalized over entire molecule (including core shellelectrons!)

• Hybrid Orbital Description:–> Valence bond approach–> Bonds described as localized interactions of TWO electrons

Bonding between two atoms can be also described as overlap of twohybrid orbitals, which represent the correct valence geometries

– A hybrid orbital is a linear combination of AOs of a SINGLE atom

– Different linear combinations will result different geometries

2-60

Hybrid O

rbitals

2-61

Linear Geometry

• Beryllium Hydride

promotion

Linear combination of one 2s and one 2p orbitals results two sphybrid orbitals:

sp s pz( ) ( )112

2 2= + sp s pz( ) ( )212

2 2= −

2-62

Linear Geometry

• Ethyne (HCCH)

• The two remaining p orbitals contain one electron each–> Delocalization of these two electrons results two orbitalswith π symmetry (with 90° angle between each other):

2-63

Trigonal Geometry

• Boron Trihydride:

• The remaining 2pz orbital is perpendicular to the the threehybrid orbitals and is not occupied

2-64

Trigonal Geometry

• Ethene (H2CCH2):

• The remaining two 2px orbitals is perpendicular to the the threehybrid orbitals and contain one electron each–> Delocalization results one additional orbital with π symmetry

2-65

Tetrahedral Geometry

• Methane (CH4)

• The 2s and three 2p orbitals of carbon result four sp3 hybridorbitals

2-66

How useful are hybrid orbitals?

• Provides a qualitative picture of the bonding around an atom

• Purely mathematical concept

• Hybridization arguments are not predictive, just descriptive!

• MO theory is predictive, but complicated to use

2-67

Frontier Orbitals

• Many properties of molecules can be interpreted through theuse of the molecular orbital model, and in particular bylooking at the frontier orbitals:– the HOMO (highest occupied molecular orbital)

–> Donor orbital– the LUMO (lowest unoccupied molecular orbital)

–> Acceptor orbital

• The energy difference between the HOMO and LUMOcorresponds to the lowest excitation energy

2-68

Conjugated Systems

• When two or more double (or triple) bonds are close to one another, thevalence π electrons tend to “mingle together”

–> the MO model with its emphasis on delocalization explains this effectbetter than the localized valence bond approach:

• Ethene:

π

π*

H

H H

H

2-69

Conjugated Sytems

• Butadiene:

π

π

π*

π*

1 node

2 nodes

3 nodes

no node

H

H

H

H

H

H

Carbon: sp2 hybridized

2-70

Energy Levels

• With increasing number of orbitals, the energy levels getcloser and closer–> the energy difference between HOMO and LUMO isdecreasing–> excitation by a small electric potential or by light will moveelectrons into the LUMO orbitals, ready to convey a current(if a potential difference is imposed)–> semiconducting properties

2-71

Cyclic Structures

2-72

August Kekulé had a dream...

• Benzene was isolated 1823 from distillation of whale oil byMichael Faraday (named ‘bicarburet of hydrogen’)

• The structure was an unsolved puzzleuntil 1865, when Kekulé dreamed of“carbon-chain snakes” and finallyproposed the correct structure

Some older “versions” of benzene:

2-73

Resonance Structures of Benzene

• There are two possible resonance structure for benzene:

–> each carbon has sp2 hybridization, the remaining 6p-orbitals combine to give 6 delocalized MO π orbitals

2-74

MO Energy Diagram

π

π

π*

π*

1 node

2 nodes

3 nodes

no node

π

π*

Energy

2-75

Large Conjugated Sytems

• Graphite consists of layers of fused 6-membered carbon rings (sp2 hybridized) with aninterlayer spacing of 335 pm (sum of carbon radii)

• The remaining unhybridized p-orbitals participate in extensive π bonding, with electron densitydelocalized over the layers

• Bond distance: 142 pm = bond order of 1.333

• At very high pressure graphite canbe converted to diamonds, anotherallotrope of carbon

• All carbon atoms are sp3 hybridized,there are no delocalized electrons–> diamond is an insulator

2-76

Buckminster Fullerene

• In 1985 another allotrope of carbon (C60) was discovered via pulsed laservaporization of graphite

• It was named after the architect Buckminster Fuller

• All 60 carbons are sp2 hybridized, leaving 60 p-orbitals to give 60 MOs(spread over both sides of the surface)

2-77

Natural Products

• Many colored compounds in nature consist of large, delocalized π-systems

• The HOMO-LUMO energy difference in these molecules is small enough toabsorb light in the visible region

N

NN

N

O

O

H3CO

O

O

H

H3C

Mg

Chlorophyll (green)

beta-carotene (orange)

Note: The color of a material is complementaryto the absorbed light–> beta carotene is orange, and therefore itabsorbs strongly in the blue and violet region ofthe spectrum

2-78

Photosynthesis

• The green color of plants is due to absorption of light bychlorophyll pigments–> the absorbed energy is used to convert CO2 to carbohydrates(sugars), oxygen is produced as a “side product”