1 theories of chemical bonding chapter 10 atomic orbitals molecules

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

77

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


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.



• 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.

1010

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.



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

1212

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.

1414

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

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


1919

O

CO H

H

H

NH

Hsp3

sp3

sp3

sp2

••

••••C


2020

O

CO H

H

H

NH

Hsp3

sp3

sp3

sp2

••

••••C


2121


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

2323

Sigma Bonds in CSigma Bonds in C22HH44

C

H

H

H

H

sp2120Þ C

2424

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

2525

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)

2626

Multiple BondingMultiple Bondingin Cin C22HH44

2727

and π Bonding inand π Bonding in CC22HH44


2828

and π Bonding inand π Bonding in CHCH22OO


2929

and π Bonding inand π Bonding in CC22HH22


3030

Consequences of Multiple Consequences of Multiple BondingBonding


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.

3232

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

3434

The Paramagnetism of OThe Paramagnetism of O22

3535


• 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



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

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


• 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


• 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


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.



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.



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.

1 theories of chemical bonding chapter 10 atomic orbitals molecules

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p orbitals

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molecular orbitals

available orbitals

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