Chapter 10

Chemistry-140 Lecture 26

Chapter 10:

Bonding & Molecular Structure:

Orbital Hybridization, Molecular Orbitals

 Chapter Highlights

 intro to VB & MO theory

 orbital overlap

 orbital hybridization

 multiple bonding ( p bonds)

 bond order

 MO theory


Two Approaches to Chemical Bonding



Valence Bond (VB) Theory: (Linus Pauling, 1954) assumes covalent bonding is due to overlap of atomic orbitals which create a region of shared electron density between the nuclei



Molecular Orbital (MO) Theory: (Robert Mulliken, 1966) assumes valence electrons are in molecular orbitals which extend over several atoms


Valence Bond Theory: Orbital Overlap

 Orbital overlap: If two H-atoms approach each other closely enough their 1s orbitals can partially occupy the same region of space….


VB Theory: Orbital Overlap

H-atoms

H

A

:1s

A

H

B

:1s

B

H

2 molecule

1s

A

1s

B

Overlap Region


Energy Profile of a Covalent Bond


Orbital Overlap

 The valence bond orbital between two atoms is a region of

high probability of finding the electron.



There is an optimum distance between the two nuclei, called the bond length: the distance of separation at which the total energy is minimized.



The imaginary line that passes through both nuclei is called the internuclear axis



Sigma ( s

) bond:

A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the

internuclear axis.


Sigma ( s

) Bonds


What Orbitals Do We Use to Make the

Tetrahedral Molecule CH

4

?

C: [He]2s 2 2p 2

H: 1s 1


Hybrid Orbitals



Hybridization: The process of mathematically mixing two or more atomic orbitals, on a single atom.

 Hybrid orbital: The result of this blending of orbitals. The number of hybrid orbitals formed is always the same as the number of atomic orbitals used

Chemistry-140 Lecture 26 sp 3 Hybridization

H



CH

4 has four equivalent C-H bonds

H

H

1s 2s 2p

C ground state

H promoted state


 sp 3 hybrid orbitals: are formed from the mixing of one

s-orbital and three p-orbitals. The arrangement of the four sp 3 hybrid orbitals is tetrahedral, with a

109.5° angle between the hybrid orbitals

1s 2sp 3

sp 3 Hybridization



F



BF

3 has three equivalent B-F bonds

1s 2s 2p

B

F ground state

F promoted state



s-orbital and two p-orbitals. The arrangement of the three sp 2 hybrid orbitals is trigonal planar, with a

120° angle between the hybrid orbitals

1s 2sp 2 2p

Chemistry-140 Lecture 26 November 8th, 1996


1s

F

Chemistry-140 Lecture 26 sp Hybridization

Be F



BeF

2 has two equivalent Be-F bonds

2s 2p ground state promoted state




sp hybrid orbitals: are formed from the mixing of one

s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals

1s 2sp 2p

sp Hybridization




Chapter 10:





Chapter Highlights

 intro to VB & MO theory

 orbital overlap

 orbital hybridization

 multiple bonding ( p bonds)

 bond order

 MO theory


F



BF

3 has three equivalent B-F bonds

1s 2s 2p

B

F ground state

F promoted state



s-orbital and two p-orbitals. The arrangement of the three sp 2 hybrid orbitals is trigonal planar, with a

120° angle between the hybrid orbitals

1s 2sp 2 2p

sp 2 Hybridization

1s

F


Be F



BeF

2 has two equivalent Be-F bonds

2s 2p ground state promoted state




sp hybrid orbitals: are formed from the mixing of one

s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals

1s 2sp 2p

sp Hybridization






Sigma ( s

) bond:

A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the

internuclear axis.


Sigma ( s

) Bonds


Multiple Bonds



In almost all cases, single bonds are s

-bonds

 BUT: To explain double and triple bonds we need another kind of bond.

H H

C C H C C

C

2

H

2 acetylene

H

H

C

2

H

4 ethylene

H

Chemistry-140 Lecture 28 p

-Orbital Overlap

 p

-bonds: those in which the electron density is above and

below the internuclear axis. The internuclear axis is a region of zero electron density.


Ethylene (sp 2 hybridization)



10 of 12 valence electrons are used to form the C-H (four) and

C-C (one) s

-bonds. The extra p-orbitals are perpendicular to the plane of the molecule and contain a single electron

1s 2s 2p ground state promoted state

1s 2sp 2 2p sp 2 hybridization





H(1s)



C(sp 2 ) s

-bonds

C(p) p

-bond


Acetylene (sp hybridization)



6 of 10 valence electrons are used to form the C-H (two) and C-

C (one) s

-bonds. The TWO extra p-orbitals are perpendicular to the axis of the molecule and contain a single electron each

1s 2s 2p ground state promoted state

1s 2sp 2p

sp hybridization






Consequences of Multiple Bonding

Cl

C

This cannot occur for a multiple p

-bond system and isomers may result

H cis

Free rotation occurs around the axis of a single s

-bond trans


Bond Order and Hybridization in Resonance Structures

O O

O O O O

TWO p

-electrons over THREE atoms. O-O bond order is 1.5!!

O-O distance & energy an average of a single & a double bond


Identifying Orbital Hybridization Schemes

Question

Complete this Lewis structure and assign hybridization schemes to all the non-hydrogen atoms. How many electrons are there in p

-orbitals in this compound?

H

O

H C C O H

H

Answer


Identifying Orbital Hybridization Schemes sp 2

H

O

H C C O sp 3

H sp 2 sp 3

H

Since there is only ONE p

-bond, the number of electrons in p

-bonds is TWO!


Chapter 10:





Chapter Highlights

 intro to VB & MO theory

 orbital overlap



 orbital hybridization multiple bonding ( p bonds)

 bond order



MO theory


An Introduction to Molecular Orbitals

 Molecular Orbitals: Valence electrons are in molecular orbitals, MO’s extending over the whole molecule.



Emphasizes the uniqueness of each molecule rather than being the sum of its atoms (VB theory)

Why Bother!!!

O

2 is paramagnetic!! That's a good reason!!


Molecular Orbitals From Atomic Orbitals



TWO atomic orbitals H

A

(1s) and H

B

(1s) combine mathematically (a linear combination) to produce TWO molecular orbitals H

2

( s

1s

) and H

2

( s

1s

*

).

s

1s

= Bonding MO s

1s

* = Antibonding MO


Molecular Orbitals From Atomic Orbitals



Bonding MO ( s

1s

): From addition of the two atomic orbitals. Leads to an increased probability that the electrons are found in this region. Electrons and orbital are concentrated between the nuclei.



Antibonding MO ( s

1s

*

): From subtraction of the two atomic orbitals. Leads to a reduced probability that the electrons are found in this region. Without significant electron density between the nuclei, they are repelled.


Molecular Orbital Description of H

2

H

A

(1s) H

B

(1s)

H

A

(1s) H

B

(1s) sigma*

antibonding MO with node sigma

bonding MO


A Molecular Orbital Diagram for H

2


Some Basic Principles of MO Theory



A first principle: The number of molecular orbitals (MO) produced is always equal to the number of atomic orbitals

(AO) used in the combination.



A second principle: Bonding MO’s are always lower in energy and antibonding MO’s higher in energy than their parent AO’s.



A third principle:

Electrons are assigned to MO’s with successively higher energies; obeying the Pauli exclusion principle and Hund’s rule.


Bond Order in MO Theory

Recall: Bond order was defined as the number of bonding electron pairs linking two atoms.

In MO Theory:

Bond order = 1/2 [( number of electrons in bonding MO’s )

- ( number of electrons in antibonding MO’s )]


Bond Order From an MO Diagram

H

2

: ( s

1s

) 2 ( s

1s

*)

Bond order for H

2

= 1

He

2

: ( s

1s

) 2 ( s

1s

*)

Bond order for He

2

2

= 0


A Molecular Orbital Diagram for Li

2


Formation of s

(2p) and s

(2p)* MO’s


Formation of p

(2p) and p

(2p)* MO’s


MO’s Derived From the 2p Orbitals


MO Diagram for First Row Diatomics X

2


MO Diagram for N

2

(Highest Occupied MO) (Lowest Unoccupied MO)

HOMO LUMO


Electron Configuration and

Bond Order for the N

2

Molecule

N

2

: ( s

1s

) 2 ( s

1s

*) 2 ( s

2s

) 2 ( s

2s

*) 2 ( p

2p

) 4 ( s

2p

) 2 ( p

2p

*)( s

2p

*)

N

2

: [core] ( s

2s

) 2 ( s

2s

*) 2 ( p

2p

) 4 ( s

2p

) 2

Bond order for N

2

= 1/2 (8 - 2) = 3


MO Diagram for O

2


Electron Configuration and

Bond Order for the O

2

Molecule

O

2

: ( s

1s

) 2 ( s

1s

*) 2 ( s

2s

) 2 ( s

2s

*) 2 ( p

2p

) 4 ( s

2p

) 2 ( p

2p

*) 2 ( s

2p

*)

O

2

: [core] ( s

2s

) 2 ( s

2s

*) 2 ( p

2p

) 4 ( s

2p

) 2 ( p

2p

*) 2

Bond order for O

2

= 1/2 (8 - 4) = 2

MO Theory predicts that O

2

has TWO unpaired electrons and is therefore PARAMAGNETIC!!


Textbook Questions From Chapter # 10

Review concepts:

Hybrid orbitals:

Molecular orbital theory:

General questions:

Conceptual questions:

1, 2, 3, 4, 5

16, 18, 20, 24

30, 34

36, 40, 43, 45, 53

61

Chapter 10

MO Theory predicts that O

has TWO unpaired electrons and is therefore PARAMAGNETIC!!

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Chapter 10

MO Theory predicts that O

has TWO unpaired electrons and is therefore PARAMAGNETIC!!

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