Valence bond theory Molecular orbital theorysfcheng/inchem94/Chapter 3 bonding... · Slide 3 of 60...

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Slide 1 of 60 Chapter 3 (continued) Covalent Bonding: Orbitals Valence bond theory Molecular orbital theory

Transcript of Valence bond theory Molecular orbital theorysfcheng/inchem94/Chapter 3 bonding... · Slide 3 of 60...

Page 1: Valence bond theory Molecular orbital theorysfcheng/inchem94/Chapter 3 bonding... · Slide 3 of 60 Atomic Orbital Overlap • Valence Bond (VB) Theory states that a covalent bond

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Chapter 3 (continued)

Covalent Bonding: Orbitals

Valence bond theory

Molecular orbital theory

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Bonding In H2

21

2

21

2

21

221 zyx ∂

∂+

∂∂

+∂∂

=∇

ψψ E=Η̂

abbaba RrrrrrU

111111

221112

+−−−−=

( )22211121

212

2

,,,,,)(8

ˆ zyxzyxUm

h+∇+∇−=Η

π

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Atomic Orbital Overlap

• Valence Bond (VB) Theory states that a covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms. This overlap region has a high electron charge density.

• The valence bond theory attempts to find the best approximation of optimal orbital overlap for all the bonds in a molecule.

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0.7433.78+ effective nuclear charge

0.744.747Empirical

0.7494.02

0.8693.14

0.90.25

R (? )E (eV)wavefunction

)2()1( ba ϕϕψ =

)1()2()2()1( baba ϕϕϕϕψ +=

)1()2()2()1( baba ϕϕϕϕψ +=

)]1()2()2()1([

)1()2()2()1(

bbaa

baba

ϕϕϕϕλϕϕϕϕψ

+++=

Theoretical treatment

ionic

covalent

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Bonding In H2S

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Several Important Points

• Most of the electrons in a molecule remain in the same orbital locations that they occupied in the separated atoms.

• Bonding electrons are localized in the region of atomic orbital overlap.

• For orbitals with directional lobes, maximum overlap occurs when atomic orbitals overlap end to end.

• The molecular geometry depends on the geometric relationships among the atomic orbitals of the central atom that participate in bonding.

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sp3 Hybridization Scheme

Hybridization

109.50

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Bonding in Methane

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Bonding in Ammonia

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The sp2 Hybridization Scheme

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The sp Hybridization Scheme

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Hybrid Orbitals Involvingd Subshells

• This hybridization allows for expanded valence shellcompounds.

• A 3s electron can be promoted to a 3d subshell which gives rise to a set of five sp3d hybrid orbitals. These molecules have a trigonal bipyramidal molecular geometry.

• One 3s electron and one 3p electron can be promoted to two 3d subshells which gives rise to a set of six sp3d2

hybrid orbitals. These molecules have an octahedralmolecular geometry.

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The sp3d and sp3d2 Hybrid Orbitals

sp3d

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Hybrid Orbitals and TheirGeometric Orientations

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Hybrid Orbitals andMultiple Covalent Bonds

• Covalent bonds formed by the end-to-end overlap of orbitals, regardless of orbital type, are called sigma (σ) bonds. All single bonds are sigma bonds.No nodal plane along inter-nuclear axis

• A bond formed by parallel, or side-by-side, orbital overlap is called a pi (π) bond.One nodal plane along inter-nuclear axis

sp2-hybrid

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Descriptions of Ethylene

Rotational barrier for double bond

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Valence Bond Theory of the Bonding in Acetylene

sp-hybrid

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Characteristics ofMolecular Orbitals

• Molecular orbitals (MOs) are mathematical equations that describe the regions in a molecule where there is a high probability of finding electrons.

• Bonding molecular orbitals (σ, π) are at a lower energy level than the separate atomic orbitals and have a high electron probability, or electron charge density.

• Antibonding molecular orbitals (σ*, π*) are at a higher energy level than the separate atomic orbitalsand places a high electron probability away from the region between the bonded atoms.

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The 1s Orbital

Ψ (r,θ,φ) = R(r) Υ0,0(θ,φ)

Υ0,0(θ,φ) = 1/2π1/2

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+ +

Constructive Interference

ba ϕϕψ +=

ψ

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+

-

Destructive Interference

ba ϕϕψ −=

ψ

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Molecular Orbitals and Bondingin the H2 Molecule

++

+ -

)2()1()2()1()2()1()2()1(

)]2()2()][1()1([

)2()1(

baabbbaa

baba

total

ϕϕϕϕϕϕϕϕϕϕϕϕ

ψψ

+++=++=

ionic covalent

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Bond order = ½ ( # of bonding electrons - # of anti-bonding electrons )

Electron configuration of H2 : (σ1s)2

B.O. of H2 = ½ (2 - 0) = 1

Bond energy = 435 kJ/mol

Bond length = 74 pm

ab

ab

SH

E−

=∆1

ab

ab

SH

E+

=∆1

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H2-H2

+

He2

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--0(σ1s)2(σ1s*)2He2

108238½(σ1s)2(σ1s*)1H2-

106269½(σ1s)1H2+

744351(σ1s)2H2

Bond length (pm)

Bond energy (kJ/mol)

B.O.Electron configuration

Species

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Lewis Structure

Hetero-nuclear Diatomic Molecule

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Electron configuration of Li2 : KK(σ1s)2

B.O. of Li2 = ½ (2 - 0) = 1

Bond length = 267 pm

2nd Period Homo-nuclear Diatomic Molecules

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Molecular Orbitals Formed byCombining 2p Atomic Orbitals

++ +

____

_ + +__

1 node ⊥ inter-nuclear axis

+ +_ _

+_

1 node along inter-nuclear axis

_ +

+__

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Diamagnetic Paramagnetic

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Molecular Spectroscopy

UV-Vis

IRMicrowave

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KE = h? - BE

The Photoelectric Effect

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• X-ray Photoelectron Spectroscopy (XPS) - using soft x-ray (200-2000 eV) radiation to

examine core-levels.

• Ultraviolet Photoelectron Spectroscopy (UPS) - using vacuum UV (10-45 eV) radiation to examine

valence levels.

Photoelectron spectroscopy- a single photon in/ electron out process

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Light sources: a Helium lamp emitting at 21.2 eV (He I radiation)or 40.8 eV (He II radiation)

Ultraviolet Photoelectron Spectroscopy(UPS)

Koopmans’Theorem

For a closed-shell molecule, the ionization energy of an electron in a particular orbital is approximately equal to the orbital energy.

I.E. = Eorbital = B.E.

such as H2 ? H2+ + e-

.... ,....

EKhvEIorEIhvEK−=

−=

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Vibrational Fine Structure in PES

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Vibrational energy states

)v'(....

)21

v()21

v()v( 2

+∆+=−⇒

+−+=

vib

eee

EEIEKhv

xhvhvE

where ΔEvib+(v’) = E+(v = v’) - E+(v = 0) is the extra (i.e., energy above

v = 0) vibrational energy of the ion.Lines corresponding to different vibrational energy levels of H2

+ , v = 0, 1, 2, 3, . . .,

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Figure 4.4: He(I) UPS spectrum of HCl gas.

1. Loss of a bonding electron decreases the bond order, increasing the bond length in the resulting cation compared to the parent molecule.

2. Loss of a nonbonding electron has no effect on bond order or bond length.

3. Loss of an antibonding electron increases the bond order, decreasing the bond length of the cation compared to the parent molecule.

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ΔN = N+ – J”where N+ and J”represent the rotational quantum numbers of the ion and the neutral, respectively.

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Vibrational frequencies from UPS spectra of CO and N2

1706CO+ (B)

1549CO+ (A)

2200 ? weakly antibondingCO+ (X)2157COυ (cm-1)molecule

1936N2+ (A)

2331N2

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Paramagnetic

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Paramagnetism of Oxygen

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Molecular Orbitals of Homo-nuclear Diatomic Molecules of 2nd Period

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Bonding in Benzene

The σ-Bonding Framework

sp2

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The π-Molecular Orbitals of Benzene

E

+

++ _

_

node

node

π-M.O. of benzene

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3 nodes

2 nodes

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Conjugated Double Bonds

E

π-M.O.

Bonding

Anti-bonding

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Band Theory

• This is a quantum-mechanical treatment of bonding in metals.

• The spacing between energy levels is so minute in metals that the levels essentially merge into a band.

• When the band is occupied by valence electrons, it is called a valence band.

• A partially filled or low lying empty band of energy levels, which is required for electrical conductivity, is a conduction band.

• Band theory provides a good explanation of metallic luster and metallic colors.

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bonding

Anti-bonding

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The 2s Band in Lithium Metal

Bonding

Anti-bonding

e- e-Valence band

Conduction band

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Band Overlap in Magnesium

Valence band

Conduction band

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Band Structure of Insulatorsand Semiconductors

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Density of states in (a) metal, (b) semimetal (e.g. graphite).

(a) (b)

Density of state= dn/dE

n = number of states

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Conductivity of Graphite

insulator

e- -conductor

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Fermi distribution (a) at T= 0, and (b) at T> 0. The population decays exponentially at energies well above the Fermi level.

Population,1

1/)( +

= − kTEeP µ

Fermi level - the highest occupied orbital at T= 0

(a) (b)

where, µ = chemical potential

When E= µ, P= 1/2

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Fermi distribution at T> 0 for (a) Intrinsic semiconductor, (b)Fermi distribution and the band gap

(a) (b)population

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Extrinsic semiconductor: (a) n-type, e.g. P doped Si(b) p-type, e.g. Ga doped Si.

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Conductivity (σ) & Energy Gap (Eg)

kT

Ee

g

kTE g

2ln ln 0

2/0

−=

= −

σσ

σσ

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