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 ( bonds)

bond order

MO theory

Chemistry-140 Lecture 26

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

Two Approaches to Chemical Bonding


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

HA:1sA

Overlap Region

HB:1sB

1sA 1sB

H-atoms

H2 molecule


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 () Bonds

Sigma () bond:

A bond in which

the electron density

is circularly

symmetrical about

the internuclear

axis. The orbital

overlap is along the

internuclear axis.


C: [He]2s22p2

What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ?

H: 1s1


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

Hybrid Orbitals


CH4 has four equivalent C-H bonds

sp3 Hybridization

1s 2s 2p

ground state

promoted state

CH

HH

H


sp3 hybrid orbitals: are formed from the mixing of one

s-orbital and three p-orbitals. The arrangement of

the four sp3 hybrid orbitals is tetrahedral, with a

109.5° angle between the hybrid orbitals

sp3 Hybridization

1s 2sp3


sp3 Hybridization


BF3 has three equivalent B-F bonds

sp2 Hybridization

1s 2s 2p

ground state

promoted state

B

F

F

F



s-orbital and two p-orbitals. The arrangement of the

three sp2 hybrid orbitals is trigonal planar, with a

120° angle between the hybrid orbitals

sp2 Hybridization

1s 2sp2 2p


Chemistry-140 Lecture 26 November 8th, 1996

sp2 HybridizationChemistry-140 Lecture 26

BeF2 has two equivalent Be-F bonds

sp Hybridization

1s 2s 2p

ground state

promoted state

F Be F


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

sp Hybridization

1s 2sp 2p


sp Hybridization


Chapter 10:Bonding & Molecular Structure:


Chapter Highlights


orbital overlap



bond order

MO theory


BF3 has three equivalent B-F bonds

sp2 Hybridization

1s 2s 2p

ground state

promoted state

B

F

F

F



s-orbital and two p-orbitals. The arrangement of the

three sp2 hybrid orbitals is trigonal planar, with a

120° angle between the hybrid orbitals

sp2 Hybridization

1s 2sp2 2p


Chemistry-140 Lecture 26 November 8th, 1996

sp2 Hybridization


BeF2 has two equivalent Be-F bonds

sp Hybridization

1s 2s 2p

ground state

promoted state

F Be F


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

sp Hybridization

1s 2sp 2p


sp Hybridization


Sigma () Bonds

Sigma () bond:

A bond in which

the electron density

is circularly

symmetrical about

the internuclear

axis. The orbital

overlap is along the

internuclear axis.


Multiple Bonds

In almost all cases, single bonds are -bonds

BUT: To explain double and triple bonds we need another

kind of bond.

CC

H H

HH

C2H4 ethylene

C2H2 acetylene

CC HH


-Orbital Overlap

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

below the internuclear axis. The internuclear axis is a

region of zero electron density.


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

C-C (one) -bonds. The extra p-orbitals are perpendicular to

the plane of the molecule and contain a single electron

Ethylene (sp2 hybridization)

ground state

promoted state

sp2 hybridization

1s 2sp2 2p

1s 2s 2p



H(1s)C(sp2)

C(p)

-bonds

-bond


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

C (one) -bonds. The TWO extra p-orbitals are perpendicular

to the axis of the molecule and contain a single electron each

Acetylene (sp hybridization)

ground state

promoted state

sp hybridization

1s 2s 2p

1s 2sp 2p


Acetylene (sp hybridization)


Consequences of Multiple Bonding

Cl

H

C

Free rotation occurs aroundthe axis of a single -bond

This cannot occur for a multiple -bond

system and isomers may result

cis trans


Bond Order and Hybridization in Resonance Structures

TWO -electrons over THREE atoms. O-O bond order is 1.5!!O-O distance & energy an average of a single & a double bond

O

O O

O

O O


Identifying Orbital Hybridization Schemes

H C C O

H

H

O

H

Question

Complete this Lewis structure and assign hybridization

schemes to all the non-hydrogen atoms. How many electrons

are there in -orbitals in this compound?


Identifying Orbital Hybridization Schemes

Answer

H C C O

H

H

O

H

sp3

sp3sp2

sp2

Since there is only ONE -bond, the

number of electrons in -bonds is TWO!


Chapter 10:Bonding & Molecular Structure:


Chapter Highlights


orbital overlap



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!!!

O2 is paramagnetic!! That's a good reason!!

O O =


TWO atomic orbitals HA(1s) and HB(1s) combine

mathematically (a linear combination) to produce TWO

molecular orbitals H2 (1s) and H2(1s*).

1s* = Antibonding MO 1s* = Antibonding MO

1s = Bonding MO1s = Bonding MO

Molecular Orbitals From Atomic Orbitals


Bonding MO (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 (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 Orbitals From Atomic Orbitals


HA(1s) HB(1s)

HA(1s) HB(1s)

sigma*antibonding MO

with node

sigmabonding MO

Molecular Orbital Description of H2


A Molecular Orbital Diagram for H2


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.

Some Basic Principles of MO Theory


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

H2: (1s)2 (1s*)

Bond order for H2 = 1He2: (1s)2

(1s*)2

Bond order for He2 = 0


A Molecular Orbital Diagram for Li2


Formation of (2p) and (2p)* MO’s


MO’s Derived From the 2p Orbitals


MO Diagram for First Row Diatomics X2


MO Diagram for N2 (Highest Occupied MO)

HOMO(Lowest Unoccupied MO)

LUMO


N2:(1s)2(1s*)2(2s)2(2s*)2(2p)4(2p)2(2p*)(2p*)

Bond order for N2 = 1/2 (8 - 2) = 3

Electron Configuration and

Bond Order for the N2 Molecule

N2:[core](2s)2(2s*)2(2p)4(2p)2


MO Diagram for O2


O2:(1s)2(1s*)2(2s)2(2s*)2(2p)4(2p)2(2p*)2(2p*)

Bond order for O2 = 1/2 (8 - 4) = 2

Electron Configuration and

Bond Order for the O2 Molecule

O2:[core](2s)2(2s*)2(2p)4(2p)2(2p*)2

MO Theory predicts that OMO Theory predicts that O22

has TWO unpaired electronshas TWO unpaired electronsand is therefore PARAMAGNETIC!!and is therefore PARAMAGNETIC!!


Textbook Questions From Chapter # 10Review concepts: 1, 2, 3, 4, 5

Hybrid orbitals: 16, 18, 20, 24

Molecular orbital theory: 30, 34

General questions: 36, 40, 43, 45, 53

Conceptual questions: 61

Textbook Questions From Chapter # 10Review concepts: 1, 2, 3, 4, 5

Hybrid orbitals: 16, 18, 20, 24

Molecular orbital theory: 30, 34

General questions: 36, 40, 43, 45, 53

Conceptual questions: 61


chemistry-140 lecture 26

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