Theories of Bonding and Structure CHAPTER 10

Theories of Bonding and Structure

CHAPTER 10

Chemistry: The Molecular Nature of Matter, 6th editionBy Jesperson, Brady, & Hyslop

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CHAPTER 10: Bonding & Structure

Learning Objectives VESPR theory:

Determine molecular geometry based on molecular formula and/or lewis dot structures.

Effect of bonded atoms & non-bonded electrons on geometry Molecular polarity & overall dipole moment

Assess overall dipole moment of a molecule Identify polar and non-polar molecules

Valence Bond Theory Hybridized orbitals Multiple bonds Sigma vs pi orbitals

Molecular Orbital Theory Draw & label molecular orbital energy diagrams Bonding & antibonding orbitals Predict relative stability of molecules based on MO diagrams

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Molecular Geometry Basic Molecular Geometries

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Linear3 atoms

Trigonal Planaror

Planar Triangular

4 atoms

Tetrahedral:5 atoms

Trigonal Bipyramidal6 atoms

Octahedral:7 atoms

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VESPR Definition

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E http://chemistry-desk.blogspot.com/2011/05/prediction-of-shape-of-molecules-by.html

Valence Shell Electron Pair Repulsion ModelElectron pairs (or groups of electron pairs) in the valence shell of an atom repel each other and will position themselves so that they are far apart as

possible, thereby minimizing the repulsions.

Electron pairs can either be lone pairs or bonding pairs.

Tetrahedral arrangement of electron pairsBent geometry

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VESPR Definition


Valence Shell Electron Pair Repulsion ModelElectron pairs (or groups of electron pairs) in the valence shell of an atom repel each other and will position themselves so that they are far apart as

possible, thereby minimizing the repulsions.

Text uses “electron domain” to describe electron pairs:

Bonding domain: contains electrons that are shared between two atoms. So electrons involved in single, double, or triple are

part of the same bonding domain.

Nonbonding Domain: Valence electrons associated with one atom, such as a lone pair, or a unpaired electron.

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VESPR Basic Examples


2 bonding domains

3 bonding domains

4 bonding domains

5 bonding domains

6 bonding bonding domains

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VESPR When Lone Pairs or Multiple Bonds Present


Including lone pairs: • Take up more space around central atom • Effect overall geometry • Counted as nonbonded electron domains

Including multiple bonds (double and triple) • For purposes of determining geometry focus on the number

of atoms bonded together rather then the number of bonds in between them: ie, treat like a single bond.

• Treat as single electron bonding domain

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VESPR Electrons that are Bonding & Not Bonding


Bonding Electrons – More oval in shape – Electron density focused

between two positive nuclei.

Nonbonding Electrons– More bell or balloon shaped– Take up more space – Electron density only has positive

nuclei at one end

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VESPR 3 atoms or lone pairs


Number of Bonding Domains

3

2

Number of Nonbonding Domains

0

1

Molecular Shape

Planar Triangular(e.g. BCl3)All bond angles 120

NonlinearBent or V-shaped(e.g. SnCl2)

Bond <120

Structure

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4

3

2


0

1

2

Molecular Shape

Tetrahedron(e.g. CH4)All bond angles 109.5

Trigonal pyramidal(e.g. NH3)Bond angle less than 109.5

Nonlinear, bent(e.g. H2O)Bond angle less than109.5

Structure

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90

120

Trigonal Bipyramidal• Two atoms in axial position

– 90 to atoms in equatorial plane

• Three atoms in equatorial position– 120 bond angle to atoms

in axial position– More room here– Substitute here first

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5

4


0

1

Molecular Shape

Trigonal bipyramid(e.g. PF5)Ax-eq bond angles 90Eq-eq 120

Distorted Tetrahedron, or Seesaw(e.g. SF4)Ax-eq bond angles < 90

Structure

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5 atoms or lone pairs


• Lone pair takes up more space• Goes in equatorial plane• Pushes bonding pairs out of way• Result: distorted tetrahedron

VESPR

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3

2


2

3

Molecular Shape

T-shape(e.g. ClF3)Bond angles 90

Linear(e.g. I3

–)Bond angles 180

Structure

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6

5

Molecular Shape

Octahedron(e.g. SF6)

Square Pyramid(e.g. BrF5)

StructureNumber of Nonbonding Domains

0

1

16




4


2

Molecular Shape

Square planar(e.g. XeF4)

Structure

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VESPR Determining 3-D Structures


1. Draw Lewis Structure of Molecule– Don't need to compute formal charge– If several resonance structures exist, pick only one

2. Count electron pair domains– Lone pairs and bond pairs around central atom– Multiple bonds count as one set (or one effective pair)

3. Arrange electron pair domains to minimize repulsions• Lone pairs

– Require more space than bonding pairs– May slightly distort bond angles from those predicted.– In trigonal bipyramid lone pairs are equatorial – In octahedron lone pairs are axial

4. Name molecular structure by position of atoms—only bonding electrons

Molecular Polarity Polar Molecules


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• Have net dipole moment– Negative end– Positive end

• Polar molecules attract each other.– Positive end of polar molecule attracted to

negative end of next molecule.– Strength of this attraction depends on

molecule's dipole moment– Dipole moment can be determined

experimentally• Polarity of molecule can be predicted by taking

vector sum of bond dipoles• Bond dipoles are usually shown as crossed

arrows, where arrowhead indicates negative end

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Molecular Polarity Molecular Shape & Polarity

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6Ehttp://wps.prenhall.com/wps/media/objects/3081/3155729/blb0903.html

• Many physical properties (melting and boiling points) affected by molecular polarity

• For molecule to be polar:– Must have polar bonds

• Many molecules with polar bonds are nonpolar - Possible because certain

arrangements of bond dipoles cancel

- For molecules with more than two atoms, must consider the combined effects of all polar bonds

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Molecular Polarity Symmetrical Nonpolar Molecules


• Symmetrical molecules – Nonpolar because bond dipoles cancel

• All five shapes are symmetrical when all domains attached to them are composed of identical atoms

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Molecular Polarity Symmetrical Nonpolar Molecules


Cancellation of Bond Dipoles In Symmetrical Trigonal Bipyramidal and Octahedral Molecules

• All electron pairs around central atom are bonding pairs and • All terminal groups (atoms) are same• The individual bond dipoles cancel

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Molecule is usually polar if – All atoms attached to central atom are NOT same Or, – There are one or more lone pairs on central atom

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Water and ammonia both have non-bonding domains Bond dipoles do not cancel Molecules are polar

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Molecular Polarity Polar Molecules: Exception


Exception to these general rules for identifying polar molecules:

Nonbonding domains (lone pairs) are symmetrically placed around central atom

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ProblemSet A

1. For the following molecules: a. Draw a lewis dot structure.b. Determine the molecular geometry at each central atom.c. Identify the bond angles.d. Identify all polar bonds: δ+ / δ-e. Assess the polarity of the molecule & indicate the overall

dipole moment if one exists

AsF5 AsF3 SeO2

GaH3

ICl2- SiO4-4

TeF6

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VB Theory Review: Modern Atomic Theory of Bonding


Modern Atomic Theory of Bonding is based on wave mechanics and gave us:

– Electrons and shapes of orbitals– Four quantum numbers– Heisenberg uncertainty principle

• Electron probabilities– Pauli Exclusion Principle

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VB Theory Valence Bond Theory & Molecular Orbital Theory


Valence Bond Theory• Individual atoms, each have their own orbitals and orbitals

overlap to form bonds• Extent of overlap of atomic orbitals is related to bond strength

Molecular Orbital Theory • Views molecule as collection of positively charged nuclei

having a set of molecular orbitals that are filled with electrons (similar to filling atomic orbitals with electrons)

• Doesn't worry about how atoms come together to form molecule

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VB Theory Valence Bond Theory & Molecular Orbital Theory


Both Theories:• Try to explain structure of molecules, strengths of

chemical bonds, bond orders, etc.• Can be extended and refined and often give same

results

Valence Bond Theory Bond between two atoms formed when pair of electrons with paired (opposite) spins is shared by two overlapping atomic orbitals

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VB Theory H2


H2 bonds form because 1s atomic valence orbital from each H atom overlaps

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VB Theory F2


• F2 bonds form because atomic valence orbitals overlap• Here 2p overlaps with 2p• Same for all halogens, but different np orbitals

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VB Theory HF


HF involves overlaps between 1s orbital on H and 2p orbital of F

1s 2p

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VB Theory H2S


Predicted 90˚ bond angle is very close to experimental value of 92˚.

• Assume that unpaired electrons in S and H are free to form paired bond

• We may assume that H—S bond forms between s and p orbital

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VB Theory Need to Change Approach to Explain Bonding in CH4


Example: CH4 C 1s 22s 22p 2 and H 1s 1

• In methane, CH4 – All four bonds are the same– Bond angles are all 109.5°

• Carbon atoms have– All paired electrons except two unpaired 2p– p orbitals are 90° apart– Atomic orbitals predict CH2 with 90° angles

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VB Theory Hybridization


• Mixing of atomic orbitals to allow formation of bonds that have realistic bond angles.– Realistic description of bonds often requires combining

or blending two or more atomic orbitals• Hybridization just rearranging of electron probabilities

Why do it? • To get maximum possible overlap• Best (strongest) bond formed

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VB Theory Hybrid Orbitals


• Blended orbitals result from hybridization process• Hybrid orbitals have

– New shapes– New directional properties– Each hybrid orbital combines properties of parent atomic

orbitals

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• Symbols for hybrid orbitals combine the symbols of the orbitals used to form them– Use s + p form two sp hybrid orbitals– Use s + p + p form three sp 2 hybrid orbitals

• One atomic orbital is used for each hybrid orbital formed

• Sum of exponents in hybrid orbital notation must add up to number of atomic orbitals used

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Mixing or hybridizing s and p orbital of same atom results in two sp hybrid orbitals

Two sp hybrid orbitals point in opposite directions

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VB Theory Ex: sp Hybridized Orbitals: BeH2


• Now have two sp hybrid orbitals • Oriented in correct direction for

bonding• 180 bond angles

– As VSEPR predicts and– Experiment verifies

• Bonding = – Overlap of H 1s atomic

orbitals with sp hybrid orbitals on Be

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Hybrid Atomic Orbitals Used Electron Geometry

sp s + p LinearBond angles 180°

sp2 s + p + p Trigonal planarBond angles 120°

sp3 s + p + p + p TetrahedralBond angles 109.5°

sp3d s + p + p + p + d Trigonal BipyramidalBond angles 90° and 120°

sp3d2 s + p + p + p + d + d OctahedralBond angles 90°

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VB Theory Bonding in BCl3


• Overlap of each half- filled 3p orbital on Cl with each half-filled sp2 hybrid on B

Forms three equivalent bonds

Trigonal planar shape 120 bond angle

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VB Theory


Overlap of each half- filled 1s orbital on H with each half-filled sp3 hybrid on carbon

Forms four equivalent bonds Tetrahedral geometry 109.5 bond angle

Bonding in CH4

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VB Theory Hybrid sp Orbitals

Two sp hybrids

Three sp2 hybrids

Four sp3 hybrids

Linear

Planar Triangular

Tetrahedral

All angles 120

All angles 109.5


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VB Theory Expanded Octet Hybridization


Hybridization When Central Atom has More Than Octet• If there are more than four equivalent bonds on central atom, then must add

d orbitals to make hybrid orbitalsWhy? • One s and three p orbitals means that four equivalent orbitals is the most you

can get using s and p orbitals alone

So, only atoms in third row of the periodic table and below can exceed their octet• These are the only atoms that have empty d orbitals of same n level as

s and p that can be used to form hybrid orbitals• One d orbital is added for each pair of electrons in excess of standard

octet

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VB Theory Expanded Octet Hybridization


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VB Theory Hybridization in Molecules with Lone Pairs


CH4 sp3 tetrahedral geometry 109.5° bond angleNH3

107° bond angleH2O

104.5° bond angle• Angles suggest that NH3 and H2O both use sp3 hybrid orbitals in

bonding• Not all hybrid orbitals used for bonding e–

– Lone pairs can occupy hybrid orbitals• Lone pairs must always be counted to determine geometry

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VB Theory Ex: H2O Hybridization


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VB Theory Multiple Bonds


• So where do extra electron pairs in multiple bonds go?– Not in hybrid orbitals– Remember VSEPR, multiple bonds have no

effect on geometry• Why don’t they effect geometry?

Two types of bond result from orbital overlap• Sigma () bond

– Accounts for first bond• Pi () bond

– Accounts for second and third bonds

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VB Theory Sigma () Bonds


• Head on overlap of orbitals• Concentrate electron density concentrated most

heavily between nuclei of two atoms• Lie along imaginary line joining their nuclei

s + s

p + p

sp + sp

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VB Theory Pi () Bonds


• Sideways overlap of unhybridized p orbitals • Electron density divided into two regions

– Lie on opposite sides of imaginary line connecting two atoms

• Electron density above and below bond.

No electron density along bond axis

bond consists of both regions

Both regions = one bond

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VB Theory Pi () Bonds


• Can never occur alone– Must have bond

• Can form from unhybridized p orbitals on adjacent atoms after forming bonds

• bonds allow atoms to form double and triple bonds

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VB Theory Multiple Bonds Ex: Ethene (C2H4)


• Each carbon is – sp

2 hybridized (violet)– has one unhybridized p

orbital (red)

• C=C double bond is– one bond (sp

2 – sp 2 )

– one bond (p – p)

p—p overlap forms a C—C bond

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VB Theory Conformations


• C—C single bond has free rotation around the C—C bond

• Conformations– Different relative

orientations on molecule upon rotation

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VB Theory Conformations Ex: Pentane, C5H12


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VB Theory Properties of -Bonds


• Can’t rotate about double bond

• bond must first be broken before rotation can occur

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Ex: Bonding in Formaldehyde


• C and O each – sp 2 hybridized

(violet)– Has one

unhybridized p orbital (red)

C=O double bond is one bond (sp2 – sp2) one bond

(p – p)

Unshared pairs of electrons on oxygen in sp2 orbitals

sp2—sp2 overlap to form C—O bond

VB Theory

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Bonding in Ethyne, C2H2


Each carbon is sp hybridized (violet) Has two unhybridized p

orbitals, px and py (red)

CC triple bond one bond

sp – sp two bonds

px – px

py – py

VB Theory

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VB Theory Ex: Bonding in N2


Each nitrogen sp hybridized (violet) Has two unhybridized p orbitals,

px and py (red)NN triple bond one bond

sp – sp two bonds

px – px

py – py

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ProblemSet B

2. What is the hybridization of oxygen in OCl2? 3. For the species and XeF4O, determine the following:

a. electron domain geometry (geometry including non-bonding pairs)

b. molecular geometryc. Hybridization around central atomd. Polarity

4. How many and bonds are there in CH2CHCHCH2, and what is the hybridization around the carbon atoms?

5. Draw & list the bonding orbitals for HCN.

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ProblemSet B

2. sp3

3. XeF4O: octahedral, square pyramid, sp3d2, polar

4. 9, 2, sp2

5. HCN: C will be create a σ bond to H and N with sp2 hybridized orbitals and use 2 p orbitals to participate in 2 π bonds with N. N will participate in the σ bond with C with an sp2 hybridized orbital, the other will hold the N lone pair, and then N will use 2 p orbitals to π bond with C.

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MO Theory Molecular Orbital Theory


1. Molecular orbitals are associated with entire molecule as opposed to one atom

2. Allows us to accurately predict magnetic properties of molecules

3. Energies of molecular orbitals determined by combining electron waves of atomic orbitals

Molecular Orbital Theory Views molecule as collection of positively charged nuclei having a set of molecular orbitals that are filled with electrons (similar

to filling atomic orbitals with electrons)Doesn't worry about how atoms come together to form

molecule

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MO Theory Bonding Molecular Orbitals


• Come from various combinations of atomic orbital wave functions

• For H2, two 1s wave functions, one from each atom, combine to make two molecular orbital wave functions

1sA + 1sB Combined Bonding MO

Constructive interference of waves Energy of bonding MO lower than atomic orbitals

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MO Theory * Antibonding Molecular Orbitals


• Destructive interference of the 1s waves• Energy of the bonding molecular orbital is higher

than energy of parent atomic orbitals

• Number of atomic orbitals used must equal number of molecular orbitals

• Other possible combination of two 1s orbitals: 1sA – 1sB

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Summary of MO from 1s Atomic Orbital


• Bonding molecular orbital– Electron density builds up between nuclei– Electrons in bonding MOs tend to stabilize molecule

• Antibonding molecular orbital– Cancellation of electron waves reduces electron density

between nuclei– Electrons in antibonding MOs tend to destabilize molecule

MO Theory

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MO Theory MO Diagram for H2


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MO Theory Rules for Filling in MO Energy Diagrams


1. Electrons fill lowest-energy orbitals that are available– Aufbau principle applies

2. No more than two electrons, with spin paired, can occupy any orbital

– Pauli exclusion principle applies3. Electrons spread out as much as possible, with spins unpaired,

over orbitals of same energy– Hund’s rules apply

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MO Theory Bond Order


• Measure of number of electron pairs shared between two atoms

• H2 bond order = 1• A bond order of 1 corresponds to a single bond

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MO Theory MO Diagram for He2


• Four electrons, so both and * molecular orbitals are filled

• Bond order

• There is no net bonding• He2 does not form

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2p Molecular Orbitals


MO Theory

MO Theory 2nd Row Periodic Table MO Diagrams


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Li2 N2 2p Lower in energy than 2p

O2, F2 and Higher 2p Lower in energy than 2p

Can ignore filled 1s bonding & antibonding and focus on valence electrons

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MO Theory MO Diagram for Li2


2p Lower in Energy than 2p

LiLiLi2

Diamagnetic as no unpaired spinsBond order = (2 – 0)/2

= 1

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MO Theory MO Energy Diagram for F2


F electron configuration = [He]2s22p5 Bond order = (8 – 6)/2

= 1

F – F single bond stable molecule

Diamagnetic as no unpaired spins

FFF2

2p Lower in Energy than 2p

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MO Theory Heteronuclear Diatomic Molecules


• If Li through N 2p below 2p • If O, F and higher atomic number, then 2p below 2p Example

– BC both are to left of N • so 2p below 2p

– OF both are to right of N • so 2p below 2p

– What about NF?• Each one away from O so average is O and 2p below 2p

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MO Theory B-C and N-F


2p lower 2p lower

BC NFNumber of valence e = 3 + 4 = 7 Number of valence e = 5 + 7 = 12

Bond Order = (5 – 2)/2 = 1.5 Bond Order = (8 – 4)/2 = 2

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MO Theory N-O


• Bond Order for NO tricky• N predicts 2p lower

• O predicts 2p lower• Have to look at experiment • Shows that 2p is lower

2p lower

Number of valence e = 5 + 6 = 11

Bond Order = (8 – 3)/2 = 2.5

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MO Theory N-O+ and N-O–


NO+ NO• Same diagram• Different number

of e–

• NO+ has 11 – 1 = 10 valence e

Bond order = (8 – 2)/2 = 3

• NO has11 + 1 = 12 valence e

Bond order = (8 – 4)/2 = 2

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MO Theory Relative Stability of N-O, N-O+ and N-O–


• Recall that as bond order increases, bond length decreases, and bond energy increases

Molecule or ion

Bond Order

Bond Length (pm)

Bond Energy (kJ/mol)

NO+ 3 106 1025

NO 2.5 115 630

NO 2 130 400

So NO+ is most stable form Highest bond order, shortest and strongest bond

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ProblemSet C

6. What is the MO Energy Diagram for B2? How many unpaired electrons does B2 have?

7. What is the bond order & number of unpaired electrons in

8. Draw the MO Energy Diagram for BN.

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Bonding VB vs MO Theory


• Neither VB or MO theory is entirely correct– Neither explains all aspects of bonding– Each has its strengths and weaknesses

• MO theory correctly predicts unpaired electrons in O2 while Lewis structures do not

• MO theory is a difficult because even simple molecules have complex energy level diagrams

• MO theory is a difficult because molecules with three or more atoms require extensive calculations

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Bonding VB vs MO Theory


Successes of VB Theory• Based on simple Lewis structures and related geometric figures• Three dimensional structures based on electron domains without massive

calculations• Simple hybrid orbitals invoked where experimental evidence shows the need• Integer bond orders are often correct

Successes of MO Theory• MO theory is particularly successful in explaining paramagnetism of B2 and O2

– One electron each in 2px and 2py (for B2)

– One electron each in *2px and *2py (for O2)

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Resonance VB Theory Treatment of Resonance


• Formate anion, HCOO–

• C has three electron domains (all bonding pairs) so – sp2 hybridized; trigonal planar

• Each O has three electron domains (one bonding pair and two lone pairs) – so sp2 hybridized; trigonal planar

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Resonance VB Theory Treatment of Resonance


• Have two resonance structures• Have lone pair on each O atom in unhybridized p

orbitals as well as empty p orbital on C• Lewis theory says

– Lone pair on one O – Use lone pair of other O to form (pi) bond– Must have two Lewis structures

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Resonance MO Theory Treatment of Resonance


Bonding MO delocalized over all three atoms

This is also our resonance hybrid picture This is the best view of what actually occurs and can be

obtained from both VB and MO theory

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Resonance MO / VB Theory Treatment of Resonance:Benzene


• Six C atoms, each sp2 hybridized (3 bonds)• Each C also have one unhybridized p orbital (6 total)• So six MOs, 3 bonding and three antibonding• So three bonds

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Resonance MO / VB Theory Treatment of Resonance: Benzene


• Can write benzene as two resonance structures• But actual structure is composite of these two• Electrons are delocalized • Have three pairs of electrons delocalized over six C atoms • Extra stability is resonance energy• Functionally, resonance and delocalization energy are the same

thing

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Theories of Bonding and Structure CHAPTER 10