1. There are two major theories for describing chemical bonding between atoms: valence bond theory and molecular orbital theory. 2. Valence bond theory describes bonding as the overlap of atomic orbitals to form shared pairs of electrons between atoms. For H2, the 1s orbitals of the two hydrogen atoms overlap to form a sigma bond with shared electron density between the nuclei. 3. Molecular orbital theory uses atomic orbitals to construct molecular orbitals delocalized over the whole molecule. For H2, combining the 1s atomic orbitals yields a lower energy bonding molecular orbital and a higher energy antibonding molecular orbital, with two electrons filling the bonding orbital to form the stable H2 molecule.

1. 1.121.12
Electron Waves andElectron Waves and
Chemical BondsChemical Bonds

2. Valence Bond TheoryValence Bond Theory
Molecular Orbital TheoryMolecular Orbital Theory
The Lewis model of chemical bonding predatesThe Lewis model of chemical bonding predates
the idea that electrons have wave properties.the idea that electrons have wave properties.
There are two other widely used theories ofThere are two other widely used theories of
bonding that are based on the wave nature of anbonding that are based on the wave nature of an
electron.electron.
Models for Chemical BondingModels for Chemical Bonding

3. Examine how the electrostatic forces changeExamine how the electrostatic forces change
as two hydrogen atoms are brought together.as two hydrogen atoms are brought together.
These electrostatic forces are:These electrostatic forces are:
attractions between the electrons andattractions between the electrons and
the nucleithe nuclei
repulsions between the two nucleirepulsions between the two nuclei
repulsions between the two electronsrepulsions between the two electrons
++ ee––
++ ee––
Formation of HFormation of H22 from Two Hydrogen Atomsfrom Two Hydrogen Atoms

4. PotentialPotential
energyenergy
H• + H•H• + H•
Internuclear distanceInternuclear distance
HH HH
weak net attraction atweak net attraction at
long distanceslong distances
Figure 1.14Figure 1.14

5. PotentialPotential
energyenergy
H• + H•H• + H•
Internuclear distanceInternuclear distance
HH HH
HH HH
HH HH
attractive forces increaseattractive forces increase
faster than repulsive forcesfaster than repulsive forces
as atoms approach each otheras atoms approach each other
Figure 1.14Figure 1.14

6. PotentialPotential
energyenergy
H• + H•H• + H•
HH22
Internuclear distanceInternuclear distance
74 pm74 pm
HH HH
HH HH
HH HH
-436 kJ/mol-436 kJ/mol
maximum net attractionmaximum net attraction
(minimum potential energy)(minimum potential energy)
at 74 pm internuclear distanceat 74 pm internuclear distance
Figure 1.14Figure 1.14

7. 11ss 11ssH H
2 H atoms: each electron "feels"2 H atoms: each electron "feels"
attractive force of one protonattractive force of one proton
HH22 molecule: each electron "feels"molecule: each electron "feels"
attractive force of both protonsattractive force of both protons
H H
Figure 1.14Figure 1.14

8. PotentialPotential
energyenergy
H• + H•H• + H•
HH22
Internuclear distanceInternuclear distance
74 pm74 pm
HH HH
HH HH
HH HH
-436 kJ/mol-436 kJ/mol
repulsive forces increaserepulsive forces increase
faster than attractive forcesfaster than attractive forces
at distances closer than 74 pmat distances closer than 74 pm
Figure 1.14Figure 1.14

9. Valence Bond TheoryValence Bond Theory
constructive interference between twoconstructive interference between two
electron waves is basis of shared-electronelectron waves is basis of shared-electron
bondbond
Molecular Orbital TheoryMolecular Orbital Theory
derive wave functions of moleculesderive wave functions of molecules
by combining wave functions of atomsby combining wave functions of atoms
Models for Chemical BondingModels for Chemical Bonding

10. 1.131.13
Bonding in HBonding in H22::
The Valence Bond ModelThe Valence Bond Model

11. Electron pair can be shared when half-filledElectron pair can be shared when half-filled
orbital of one atom overlaps in phase withorbital of one atom overlaps in phase with
half-filled orbital of another.half-filled orbital of another.
Valence Bond ModelValence Bond Model

12. 11ss 11ssH H
in-phase overlap of two half-filledin-phase overlap of two half-filled
hydrogen 1s orbitalshydrogen 1s orbitals
σσ bond of Hbond of H22
H H
Valence Bond ModelValence Bond Model

13. σσ Bond: orbitals overlap alongBond: orbitals overlap along
internuclear axisinternuclear axis
Cross section of orbital perpendicular toCross section of orbital perpendicular to
internuclear axis is a circle.internuclear axis is a circle.
H H
Valence Bond ModelValence Bond Model

14. Figure 1.17(Figure 1.17(aa) The 1) The 1ss orbitals of two separated hydrogenorbitals of two separated hydrogen
atoms are far apart. Essentially no interaction. Eachatoms are far apart. Essentially no interaction. Each
electron is associated with a single proton.electron is associated with a single proton.
Valence Bond Model of HValence Bond Model of H22

15. Figure 1.17(Figure 1.17(bb) As the hydrogen atoms approach each other,) As the hydrogen atoms approach each other,
their 1their 1ss orbitals begin to overlap and each electron begins toorbitals begin to overlap and each electron begins to
feel the attractive force of both protons.feel the attractive force of both protons.
Valence Bond Model of HValence Bond Model of H22

16. Figure 1.17(Figure 1.17(cc) The hydrogen atoms are close enough so) The hydrogen atoms are close enough so
that appreciable overlap of the the two 1that appreciable overlap of the the two 1ss orbitals occurs.orbitals occurs.
The concentration of electron density in the region betweenThe concentration of electron density in the region between
the two protons is more readily apparent.the two protons is more readily apparent.
Valence Bond Model of HValence Bond Model of H22

17. Figure 1.17(Figure 1.17(dd) A molecule of H) A molecule of H22. The two hydrogen 1. The two hydrogen 1ss
orbitals have been replaced by a new orbital thatorbitals have been replaced by a new orbital that
encompasses both hydrogens and contains both electrons.encompasses both hydrogens and contains both electrons.
Valence Bond Model of HValence Bond Model of H22

18. 1.141.14
Bonding in HBonding in H22::
The Molecular Orbital ModelThe Molecular Orbital Model

19. Electrons in a molecule occupy molecularElectrons in a molecule occupy molecular
orbitals (MOs) just as electrons in an atomorbitals (MOs) just as electrons in an atom
occupy atomic orbitals (AOs).occupy atomic orbitals (AOs).
Two electrons per MO, just as two electronsTwo electrons per MO, just as two electrons
per AO.per AO.
Express MOs as combinations of AOs.Express MOs as combinations of AOs.
Main IdeasMain Ideas

20. Two AOs yield two MOsTwo AOs yield two MOs
Bonding combinationBonding combination Antibonding combinationAntibonding combination
ψψMOMO == ψψ(H)(H)1s1s ++ ψψ(H')(H')1s1s ψψ''MOMO == ψψ(H)(H)1s1s -- ψψ(H')(H')1s1s
Linear combination of atomic orbitals methodLinear combination of atomic orbitals method
expresses wave functions of molecular orbitalsexpresses wave functions of molecular orbitals
as sums and differences of wave functionsas sums and differences of wave functions
of atomic orbitals.of atomic orbitals.
MO Picture of Bonding in HMO Picture of Bonding in H22

21. 11ss 11ss
AOAOAOAO
Fig. 1.19: Energy-Level Diagram for HFig. 1.19: Energy-Level Diagram for H22 MOsMOs

22. bondingbonding
antibondingantibonding
σσ
σσ**
MOMO
MOMO
Fig. 1.19: Energy-Level Diagram for HFig. 1.19: Energy-Level Diagram for H22 MOsMOs

23. bondingbonding
antibondingantibonding
σσ
σσ**
MOMO
MOMO
Fig. 1.19: Energy-Level Diagram for HFig. 1.19: Energy-Level Diagram for H22 MOsMOs

24. bondingbonding
antibondingantibonding
σσ
σσ**
MOMO
MOMO
Fig. 1.19: Energy-Level Diagram for HFig. 1.19: Energy-Level Diagram for H22 MOsMOs