orbitals & bonding

8/12/2019 Orbitals & Bonding

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Atomic Orbitals

Valence Bond Theory

Molecular Orbital Theory

Hybridization


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Introduction

Lewis Dot and VSEPR have been useful models toexplain quite a bit about chemical bonding.

We have seen areas where they are not satisfactory.

They dont explain the charges on certain molecules orions very well.

They dont explain bonding in some species.

They dont give us bond energies; the single mostimportant factor in many chemical reactions and chemical

properties.

Valence Bond theory of Localized Orbitalsvastlyimproves on these inadequacies.


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Valence Bond Theory (AOs)

Localized orbitals can be atomic orbitals (AO) and/or molecular orbitals (MO).

AOs only associated with a single atom.

s, p, d, , lonepairs, hybrid orbitals are all AOs.

MOs associated with two or more atoms

Bonds are MOs

Well focus on AOs first. Our goal is to develop a set of basis functionsthat describe the spaceoccupied by the

electrons in an atom and then use those functions (orbitals) to make bonds.

The spherical harmonics functions: s,p,d, are one such set of basis functions (or basic

orbitals).


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Hybrid Orbitals (VB)

Problems with spd orbitals as the basis set. Bond angles not always 90 (p-orbitals have 90 angles)

Intermediate angles would require difficult to visualize combinationsof spdf orbitals to define, say, a bond angle of 120.

So, we define a new set of basis functions

Made from the original basis. These describe the same space as spdf orbitals

Easier to visualize how they participate in bonding.

We call this new set of basis functions Hybrid orbitals Different combinations of spdf orbitals can be used to create different types of

hybrid orbitals. An s and a p combine to make two sp orbitals

An s and two p orbitals create three sp2orbitals

s + p + p + psp3+ sp3+ sp3+ sp3, etc.


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2s 2p

Overlap produces

nodes where negative

interference exactly cancels

the component orbitals

Nodal surface

2p2s

Nodal surface

2p + 2s

Sign change

2sp 2sp

Start with 2 AOs, end with 2 AOs.

sp Hybridization


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2s2px 2py

2sp2 2sp2 2sp2

Started with 3 AOs

Ended with 3 AOs

sp2Hybridization


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sp3Hybridization

s + p + p + p (4 orbitals)

These functions define a sphere centred on the atom.

Divide the sphere in to 4 equal parts

Gives 4 sp3 orbitals in a tetrahedral arrangement.

Each orbital looks like this


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Summary (VB)

# Hybrid Orbitals

(# domains in VSEPR)Hybridization Geometry

2 sp Linear

3 sp2 Trigonal planar

4 sp3 Tetrahedral

5 sp3

d Trigonal bipyramidal6 sp3d2 Octahedral

These atomic orbitals, now matching the geometry of the molecule in question,

are then used to create bonds by overlap with AOs from the other atoms in themolecule. This overly simplified approach to bonding, called Valence Bond

Theory, generally creates molecules with shapes that match those developed by

the Valence Shell Electron Shell Repulsion theory.


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Multiple bonding using sigma and pi bonds.(VB)

Using localized orbitals VB approach we can explain multiple bonds.

First bond of a multiple set is always a sigma bond. Second and third bonds of a multiple set are pi bonds.

Consider C2H4.

Sigma bonds first.

Created from three sp2orbitalson each of the C atoms.

Now the pi bonds. Created from the unhybridized

p orbital on the C atom.

So the overall effect is:


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Triple bonds using sigma and pi bonds (VB)

Consider C2H2.

Lewis structure shows a triple bond between the two Carbons.

Sigma bonds are created from two sp orbitals on each C atom.

Pi bonds are created from the unhybridized p orbitals (2 each) on the C

atoms.


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Molecular Orbital Theory

VB theory is limited in its validity because it required that allorbitals be localized. On an atom (AOs).

Between two atoms(localized MOs, a.k.a., bonds.)

MO theory: Molecular Orbitals are not localized

MOs are created using bits of every AOl on the whole molecule.Each MO is a Linear Combination of Atomic Orbitals (LCAO).

Allows for more flexibility.

Generally, calculations using this theory require computer programs.

Basis set: use the simplest set (spdf atomic orbitals).

Computer determines the best combination of these AOs (LCAO) tocreate each of the MOs.


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Molecular Orbital Theory Now, lets use our AOs to make MOs.

Simplest case: H2.

1s 1s

1s + 1s = s1s bond

Phase change

1s - 1s = s1s* antibond

Energy

0.0

Bond order = #bonds #antibonds = 1 Electron configuration (s1s)2


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Molecular orbitals

Now consider: He2.

1s 1s

1s + 1s = s1s bond

Phase change

1s - 1s = s1s* antibond

Energy

0.0

Bond order = #bonds #antibonds = 0 Electron configuration (s1s)2(s1s*)2


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Types of MOs s MOs are bonding orbitals with electron density concentrated

along the axis connecting the bonded nuclei

s*MOs are anti-bonding orbitals along the axis but with a

planar node perpendicular to the axis between the two atoms.

pMOs are bonding orbitals with electron densities alongopposite sides of the axis but not on it.

p*MOs are anti-bonding orbitals (node perpendicular to theaxis) with electron densities alongside the axis but not on it.


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Shapes of MOs: s(bonds)

From s orbitals: ss

From p orbitals

(end-to-end) sp


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Shapes of MOs: s*(antibonds)

From s orbitals: ss*

From p orbitals

(end-to-end) sp*


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Shapes of MOs: p(bonds)

From p orbitals: pp

From d orbitals:

From p & d orbitals

sp

2p + 2p=pp

3d + 3d=pd

3p + 3d=ppd


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Molecular Orbitals

Generally, MOs are made of part of all the orbitals in

all the atoms of the molecule so the diagrams we just

viewed are actually overly simplified versions of real

MOs. MOs are generally labeled in ways like the previous

simplified examples:

A bonding MO that is predominantly located on the axis

between two atoms but also has (very small) contributionsfrom other orbitals located elsewhere on the molecule are

still called sbonds, etc.


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MOs in a diatomic molecule

Molecular orbitals now contain parts of all the AOs but arelabeled by those that predominate.

AOs(atom 1) MOs AOs(atom 2)

sp

ss*

pp

pp*

sp*


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B2

AOs (B 1) MOs AOs (B 2)

sp

ss*

pp

pp*

sp*We start with 3

electrons from each

B to contribute to the

MOs.

Now, place these

electrons into the

MOs according to

the Aufbau and

Hund principles.

Note the unpaired

electrons in the ppbonding orbitals.

B2is paramagnetic

Bond Order = # bonds # antibonds = [1 + + ] 1 = 1

(s2s)2(s*2s)2(p2p)2


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C2

AOs (C 1) MOs AOs (C 2)

sp

ss*

pp

pp*

sp*We start with 4

electrons from each

C to contribute to

the MOs.

Now, place these

electrons into the

MOs according to

the Aufbau and

Hund principles.

No unpaired

electrons. So C2isdiamagnetic

Bond Order = # bonds # antibonds = [1 + 1 + 1] 1 = 2

(s2s)2(s*2s)2(p2p)4


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N2

AOs (N 1) MOs AOs (N 2)

sp

ss*

pp

pp*

sp*We start with 5

electrons from each

N to contribute to

the MOs.

Now, place these

electrons into the

MOs according to

the Aufbau and

Hund principles.

No unpaired

electrons. So N2isdiamagnetic

Bond Order = # bonds # antibonds = [1 + 1 + 1 + 1] 1 = 3

(s2s)2(s*2s)2(p2p)4(s2p)2


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O2

AOs (O 1) MOs AOs (O 2)

sp

ss*

pp

pp*

sp*We start with 6

electrons from each

O to contribute to

the MOs.

Now, place these

electrons into the

MOs according to

the Aufbau and

Hund principles.

Unpaired electrons

in the two pp*orbitals. So O2is

paramagnetic

Bond Order = # bonds # antibonds = [1 + 1 + 1 + 1] [1 + + ] = 2

(s2s)2(s*2s)2(p2p)4(s2p)2(p*2p)2


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NO

AOs (N) MOs AOs (O)

sp

ss*

pp

pp*

sp*We start with 5

electrons from N

and 6 from O to

contribute to the

MOs.

Now, place these

electrons into the

MOs according to

the Aufbau and

Hund principles.

Unpaired electron inone pp*orbital. SoNO is paramagnetic

Bond Order = # bonds # antibonds = [1 + 1 + 1 + 1] [1 + ] = 2

(s2s)2(s*2s)2(p2p)4(s2p)2(p*2p)1


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Mononuclear diatomics

Li2 Be2 B2 C2 N2 O2 F2


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Combining p orbitals


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Ozone


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Suggested Homework

Reading: Petrucci sections 11.1-11.6

Problems: chapter 11: 1, 5, 11, 13, 20, 23, 27,

29, 30, 32, 35, 39, 41, 43,

orbitals & bonding

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