1 theories of chemical bonding chapter 10 atomic orbitals molecules
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11Theories of Chemical Theories of Chemical BondingBonding
Chapter 10Chapter 10
Atomic OrbitalsAtomic Orbitals MoleculesMolecules
22
• MOLECULAR MOLECULAR ORBITAL THEORYORBITAL THEORY — — Robert Mullikan (1896-Robert Mullikan (1896-1986)1986)
• valence electrons are valence electrons are delocalizeddelocalized
• valence electrons are valence electrons are in orbitals (called in orbitals (called molecular orbitals) molecular orbitals) spread over entire spread over entire molecule.molecule.
Two Theories of Two Theories of BondingBonding
33
Two Theories of Two Theories of BondingBonding
• VALENCE BOND THEORYVALENCE BOND THEORY — — Linus PaulingLinus Pauling
• valence electrons are localized valence electrons are localized between atoms (or are lone pairs).between atoms (or are lone pairs).
• half-filled atomic orbitals overlap half-filled atomic orbitals overlap to form bondsto form bonds..
• Two electrons of opposite spin Two electrons of opposite spin can occupy the overlapping can occupy the overlapping orbitals.orbitals.
• Bonding increases the probability Bonding increases the probability of finding electrons in between of finding electrons in between atoms.atoms.
44Sigma Bond Formation by Sigma Bond Formation by Orbital OverlapOrbital Overlap
Two s orbitals Two s orbitals overlapoverlap
55
Sigma Bond FormationSigma Bond FormationSigma Bond FormationSigma Bond Formation
Two s Two s orbitals orbitals overlapoverlap
Two p Two p orbitals orbitals overlapoverlap
66
Using VB TheoryUsing VB TheoryBonding in BFBonding in BF33
planar triangleplanar triangleangle = 120angle = 120oo
F
F F
Boron configuration
2p2s1s•• ••
••••
••
•• ••
••••
B
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Bonding in Bonding in BFBF33
Bonding in Bonding in BFBF33
• How to account for 3 bonds 120How to account for 3 bonds 120oo apart using apart using a spherical s orbital and p orbitals that are 90a spherical s orbital and p orbitals that are 90oo apart?apart?
• Pauling said to modify VB approach with Pauling said to modify VB approach with
ORBITAL HYBRIDIZATIONORBITAL HYBRIDIZATION• — — mix available orbitals to form a new mix available orbitals to form a new
set of orbitals — set of orbitals — HYBRID ORBITALSHYBRID ORBITALS — that will give the maximum overlap — that will give the maximum overlap in the correct geometry. in the correct geometry. (See Screen 10.6)(See Screen 10.6)
88
Bonding in Bonding in BFBF33
See Figure 10.9 and Screen 10.6See Figure 10.9 and Screen 10.6
rearrange electronshydridize orbs.
unused porbital
three sp 2 hybrid orbitals
2p2s
99
• The three hybrid orbitals are made The three hybrid orbitals are made from 1 s orbital and 2 p orbitals from 1 s orbital and 2 p orbitals 3 sp 3 sp22 hybrids.hybrids.
Bonding in Bonding in BFBF33
Bonding in Bonding in BFBF33
• Now we have 3, half-filled HYBRID orbitals Now we have 3, half-filled HYBRID orbitals that can be used to form B-F sigma bonds.that can be used to form B-F sigma bonds.
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An orbital from each F overlaps one of the An orbital from each F overlaps one of the spsp22 hybrids to form a B-F hybrids to form a B-F bond. bond.
Bonding in Bonding in BFBF33
Bonding in Bonding in BFBF33
B
F
F
F
B
F
F
F
B
F
F
F
B
F
F
F
1111
Bonding in CHBonding in CH44
How do we account for 4 CHow do we account for 4 C
—H sigma bonds 109—H sigma bonds 109oo
apart? apart?
Need to use 4 atomic Need to use 4 atomic
orbitals — s, porbitals — s, pxx, p, pyy, and , and
ppzz — to form 4 new — to form 4 new
hybrid orbitals pointing hybrid orbitals pointing
in the correct direction.in the correct direction.
109o109o
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4 C atom orbitals 4 C atom orbitals hybridize to form hybridize to form four equivalent spfour equivalent sp33 hybrid atomic hybrid atomic orbitals.orbitals.
4 C atom orbitals 4 C atom orbitals hybridize to form hybridize to form four equivalent spfour equivalent sp33 hybrid atomic hybrid atomic orbitals.orbitals.
Bonding in a Tetrahedron — Bonding in a Tetrahedron — Formation of Hybrid Atomic Formation of Hybrid Atomic
OrbitalsOrbitals
1313Bonding in a Tetrahedron — Bonding in a Tetrahedron — Formation of Hybrid Atomic Formation of Hybrid Atomic
OrbitalsOrbitals
4 orbitals in C 4 orbitals in C hybridize to form hybridize to form four equivalent spfour equivalent sp33 hybrid atomic hybrid atomic orbitals.orbitals.
4 orbitals in C 4 orbitals in C hybridize to form hybridize to form four equivalent spfour equivalent sp33 hybrid atomic hybrid atomic orbitals.orbitals.
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Bonding in CHBonding in CH44
Figure 10.6Figure 10.6
1515
Orbital HybridizationOrbital HybridizationFigure 10.5Figure 10.5
Orbital HybridizationOrbital HybridizationFigure 10.5Figure 10.5
BONDSBONDS SHAPESHAPE HYBRID HYBRID
REMAINREMAIN
22 linearlinear sp sp 2 p’s2 p’s
33 trigonaltrigonal sp sp22 1 p1 pplanarplanar
44 tetrahedral sptetrahedral sp33 nonenone
1616
1717
O
CO H
H
H
NH
Hsp3
sp3
sp3
sp2
••
••••C
Bonding in Bonding in GlycineGlycine
1818
O
CO H
H
H
NH
Hsp3
sp3
sp3
sp2
••
••••C
Bonding in Bonding in GlycineGlycine
1919
O
CO H
H
H
NH
Hsp3
sp3
sp3
sp2
••
••••C
Bonding in Bonding in GlycineGlycine
2020
O
CO H
H
H
NH
Hsp3
sp3
sp3
sp2
••
••••C
Bonding in Bonding in GlycineGlycine
2121
Bonding in Bonding in GlycineGlycine
O
CO H
H
H
NH
Hsp3
sp3
sp3
sp2
••
••••C
2222
C
H
H
H
H
sp2120Þ C
Multiple BondsMultiple BondsConsider ethylene, CConsider ethylene, C22HH44
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Sigma Bonds in CSigma Bonds in C22HH44
C
H
H
H
H
sp2120Þ C
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π Bonding in Cπ Bonding in C22HH44
The unused p orbital on The unused p orbital on each C atom contains an each C atom contains an electron and this p orbital electron and this p orbital overlaps the p orbital on overlaps the p orbital on the neighboring atom to the neighboring atom to form the π bond. form the π bond. (See Fig. (See Fig. 10.9)10.9)
p orb.for šbond
3 sp 2
hybrid orbitals
2p2s
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π Bonding in Cπ Bonding in C22HH44
The unused p orbital on each C atom contains The unused p orbital on each C atom contains an electron and this p orbital overlaps the p an electron and this p orbital overlaps the p orbital on the neighboring atom to form the orbital on the neighboring atom to form the π bond. π bond. (See Fig. 10.9)(See Fig. 10.9)
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Multiple BondingMultiple Bondingin Cin C22HH44
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and π Bonding inand π Bonding in CC22HH44
Figure 10.11Figure 10.11
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and π Bonding inand π Bonding in CHCH22OO
Figure 10.12Figure 10.12
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and π Bonding inand π Bonding in CC22HH22
Figure 10.13Figure 10.13
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Consequences of Multiple Consequences of Multiple BondingBonding
Figure 10.14Figure 10.14
There is restricted rotation around C=C bond.There is restricted rotation around C=C bond.
3131
Consequences of Multiple Consequences of Multiple BondingBonding
See Butene.Map in ENER_MAP in CAChe models.See Butene.Map in ENER_MAP in CAChe models.
Restricted rotation around C=C bond.Restricted rotation around C=C bond.
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Double Bonds and Double Bonds and VisionVision
See Screen 10.13, Molecular Orbitals and VisionSee Screen 10.13, Molecular Orbitals and VisionSee also Chapter Focus 10, page 380See also Chapter Focus 10, page 380
See a See a recent publication on the underlying molecular rearrangementson the underlying molecular rearrangements
3333
• Valence electrons are delocalizedValence electrons are delocalized• Valence electrons are in orbitals (called Valence electrons are in orbitals (called
molecular orbitals) spread over entire molecular orbitals) spread over entire molecule.molecule.
• First Principle:First Principle: The total # of molecular The total # of molecular orbitals equals the number of atomic orbitals equals the number of atomic orbitals contributed by the atoms that orbitals contributed by the atoms that have combined.have combined.
• Second Principle:Second Principle: The bonding The bonding molecular orbitals are lower in energy molecular orbitals are lower in energy than the parents orbitals and the than the parents orbitals and the anibonding orbitals are higher in energy.anibonding orbitals are higher in energy.
• Third Principle:Third Principle: The electrons of the The electrons of the molecule are assigned to orbitals of molecule are assigned to orbitals of successively higher energy according to successively higher energy according to the Pauli exclusion principle and Hund’s the Pauli exclusion principle and Hund’s rule.rule.
Molecular Orbital TheoryMolecular Orbital Theory
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The Paramagnetism of OThe Paramagnetism of O22
3535
Molecular Orbital TheoryMolecular Orbital Theory
• Bonding and antibonding sigma MO’s are formed from 1s Bonding and antibonding sigma MO’s are formed from 1s orbitals on adjacent orbitals.orbitals on adjacent orbitals.
3636
Molecular Orbital TheoryMolecular Orbital Theory
Figure 10.17Figure 10.17
1. # MO’s = # atomic 1. # MO’s = # atomic
orbitals used.orbitals used.
2. Bonding MO is 2. Bonding MO is
lower in energy than lower in energy than
atomic orbitals. atomic orbitals.
Antibonding MO is Antibonding MO is
higher.higher.
3. Electrons assigned 3. Electrons assigned
to MO’s of higher and to MO’s of higher and
higher energy.higher energy.
3737
Dihelium MoleculeDihelium MoleculeBond order = 1/2 [# e- in bonding MOs Bond order = 1/2 [# e- in bonding MOs
- # e- in antibonding MOs]- # e- in antibonding MOs]
3838
Sigma Bonding from p OrbitalsSigma Bonding from p Orbitals
3939
π Bonding from p Orbitalsπ Bonding from p Orbitals
Sideways overlap of atomic 2p orbitals that lie in the same direction in space give π bonding and antibonding MOs.
4040
& π Bonding from p Orbitals& π Bonding from p Orbitals
4141
4242
MO Theory of Metals & MO Theory of Metals & SemiconductorsSemiconductors
• Can explain Can explain – LusterLuster
– Electrical and thermal conductivityElectrical and thermal conductivity
– MalleabilityMalleability
• All explanations come down to All explanations come down to electron mobilityelectron mobility
4343
MO Theory of Metals & MO Theory of Metals & SemiconductorsSemiconductors
• Electrical conductivityElectrical conductivity– MetalsMetals — conductivity decreases with temperature — conductivity decreases with temperature
– SemiconductorsSemiconductors — increases with T — increases with T
– InsulatorInsulator — very low conductivity — very low conductivity
4444
MO Theory of Metals & MO Theory of Metals & SemiconductorsSemiconductors
• Band theory-The central idea underlying the description of the electronic structure of solids is that valence electrons donated by atoms are spread over the entire structure.
4545Silicon and MOsSilicon and MOs
This gives 2 bond This gives 2 bond per Si atomper Si atom
2000 MOs
2000 MOs
Have 1000 Si atomsHave 1000 Si atoms
4000 e- or 2000 pairs4000 e- or 2000 pairs
2 pairs per Si atom2 pairs per Si atom
Band is completely filledBand is completely filled
4646
Heat of AtomizationHeat of Atomization
• ∆H of vaporization (or atomization)
is a good measure of bonding in
solids.
• M(s) ---> M(g)
• Energy change = ∆Hvap
• High ∆H values for transition metals
indicate d orbital participation.
4747
Heat of VaporizationHeat of Vaporization
4848
Fermi LevelFermi Level• The HOMO at T = 0 is
the Fermi level.• At temp > 0, electrons
near Fermi level can be promoted to nearby empty levels.
• These promoted e- are mobile and move under electric field.
• Promotion gives e- in higher levels and “hole” in lower levels. Therefore, 2 mobile e-.
Band gapFermi levelIn metals
antibonding and bonding levels merge and band gap vanishes
4949
Electrical ConductivityElectrical Conductivity
Conduction band
Filled levels
+
e-Empty levels
Add energy
Valence band
5050
Electrical ConductivityElectrical Conductivity
• Metal conductivity Metal conductivity DECREASESDECREASES with increase in T. with increase in T.
• Contrary to expectation. Would expect increased Contrary to expectation. Would expect increased electron promotion.electron promotion.
• Ability of e- to travel smoothly through the solid in a Ability of e- to travel smoothly through the solid in a conduction band depends on uniformity of atom conduction band depends on uniformity of atom arrangement.arrangement.
• An atom vibrating vigorously at a site is equivalent An atom vibrating vigorously at a site is equivalent to an impurity that disrupts the orbitals. to an impurity that disrupts the orbitals.
• Thus, higher T means lower conductivity.Thus, higher T means lower conductivity.
Filled levels
+
e-Empty levels
Add energy
5151
InsulatorsInsulators
• Very few e- from the valence band have sufficient energy to move to the conduction band.
Valence Valence band is fullband is full
6 eV in diamond6 eV in diamond
5252
SemiconductorsSemiconductors• Group 4A elementsGroup 4A elements
– C (diamond) is an insulatorC (diamond) is an insulator
– Si, Ge, and gray Sn are Si, Ge, and gray Sn are semiconductorssemiconductors
» all of the above have the all of the above have the diamond structure, which diamond structure, which appears especially appears especially favorable to semiconductor favorable to semiconductor behaviorbehavior
– White Sn and Pb are metalsWhite Sn and Pb are metals
5353
SemiconductorsSemiconductors• Many inorganic compounds are
semiconductors.
• Best known are “III-V” compounds
• GaAs = “Ge”
• InSb = “Sn”
• Have ZnS or zinc blende structure.
5454
Band Theory & SemiconductorsBand Theory & Semiconductors
• Semiconductors have a band structure similar to Semiconductors have a band structure similar to
insulators but band gap is small insulators but band gap is small
• Band gap = 0.5 to 3.0 eVBand gap = 0.5 to 3.0 eV
• At least a few electrons have sufficient thermal energy At least a few electrons have sufficient thermal energy
to be promoted to an empty band.to be promoted to an empty band.
5555
Band Theory & SemiconductorsBand Theory & Semiconductors
• Semiconductors have a band structure similar to insulators but have a small band gap
• Electrons can be promoted thermally.
• The higher the temperature the more electrons are promoted.
Valence bandValence band
Conduction bandConduction band
e-e- e-e- e-e-
+ + +
Small band gap
5656
Intrinsic SemiconductorsIntrinsic SemiconductorsGroup 4A Band gap (eV)
C 6.0
Si 1.1
Ge 0.7
Gray Sn (>13 ˚C) 0.1
White Sn (<13 ˚C) 0
Lead 0
Valence bandValence band
Conduction Conduction bandband
e-e- e-e- e-e-
+ + +
Small band gap
These are called INTRINSIC semiconductors
5757
Extrinsic SemiconductorsExtrinsic Semiconductors
• Conductivity controlled by a tracetrace of dopant such as Ga (or Al) or As
• The dopant atom takes the place of a Si atom.
• Dopant atom has one fewer electrons than Si (= Ga or Al) or one more electron than Si (= As).
5858Add Group 3A AtomAdd Group 3A Atom
--> p-type Semiconductor--> p-type Semiconductor
• If Ga conc. is small, acceptor levels are “discrete” — not extended over the lattice.
• Positive holes left in valence band can move.
• Si + Ga (or Al) is a positive hole or p-type p-type semiconductorsemiconductor.
5959
p-Type Semiconductorp-Type Semiconductor
• Acceptor level is slightly higher in energy than Fermi level.
• Electrons readily promoted into acceptor level.
Valence bandValence band
Conduction bandConduction band
e-e- e-e- e-e-
+ + +
1.1 eVAcceptor level
6060
n-Type Semiconductorn-Type Semiconductor• Add As — has 5e- and so
adds extra e-.
• Donor level has electrons.
• Electrons promoted from donor level to conduction band.
• Negative electrons are charge carriers and so called n-type.
Valence bandValence band
Conduction bandConduction band
e-e- e-e- e-e-
1.1 eVDonor level
6161
SummarySummary
• Conductivity of extrinsic >> intrinsic Conductivity of extrinsic >> intrinsic semiconductors.semiconductors.
• Conductivity of extrinsic semiconductors can Conductivity of extrinsic semiconductors can be accurately controlled.be accurately controlled.
• Intrinsic semiconductors are very dependent Intrinsic semiconductors are very dependent on T and on stray impurities.on T and on stray impurities.