Lecture 24 - PowerPoint Presentation

Slide1

Lecture 24Valence bond theory

(c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign.

This material has

been developed and made available online by work supported jointly by University of Illinois, the National Science Foundation under Grant CHE-1118616 (CAREER), and the Camille & Henry Dreyfus Foundation, Inc. through the Camille Dreyfus Teacher-Scholar program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsoring agencies

.Slide2

Valence bond theory

There

are two

major approximate

theories of chemical

bonds:

valence bond

(VB) theory

and molecular orbital

(MO) theory.

While computationally less widely used than MO, VB has a special appeal to organic chemists studying reaction mechanisms and remains useful and important.

The concepts of

sp

n

hybridization

and

lone pairs

are introduced.Slide3

Orbital approximation

In

polyelectron

atoms, we

used the

orbital

approximation

– forced separation of variables – where we

filled

hydrogenic

orbitals with

electrons to construct atomic wave functions.

For polyatomic

molecules, can we also use orbital approximation? Can we use

hydrogenic

atomic orbitals

to construct molecular wave functions?Slide4

Singlet and triplet He (review)

In the

orbital approximation

for (1

s

)

1

(2s)1 He, there are four different ways of filling two electrons:

Anti-symmetric

Anti-symmetric

Anti-symmetric

Singlet

Triplet

more stableSlide5

VB theory for H

2

Let us construct the molecular wave function of H

2

using its two 1

s

orbitals

A and B.Slide6

VB theory for H

2

singlet

more stable

triplet

e

n

n

e

e

n

n

eSlide7

Covalent bond

Enhanced electron probability density between nuclei (shielding nucleus-nucleus repulsion). The greater the overlap of two AO’s the stronger the bond.

Two singlet-coupled (

α

1

β

2−

β

1

α

2) electrons for one bond (

Lewis structure).Slide8

σ

and π bonds

A

π

bond is weaker than

σ

bond because of a less orbital overlap in

π

.

σ

bond

π

bondSlide9

N

2

N is (1

s

)

2

(2

s)2(2p

x)1(2p

y)1(2pz)

1N2 forms one σ bond

and two π bonds. Altogether three-fold covalent bonds (triple bonds).Slide10

H

2

O

O

is

(1

s

)2(2s)

2(2px)2

(2py)1(2pz)

1.The two unpaired electrons in 2p

orbitals can each form a σ bond with H (1s)1.

This explains the HOH angle of near 90º. Slide11

NH3

N is (1

s

)

2

(2

s

)2(2px

)1(2py)1

(2pz)1.The

three unpaired electrons in 2p orbitals can each form a σ bond

with H (1s)1.This explains the pyramidal structure with the HNH angle of near 90

º. Slide12

Promotion and hybridization

C

(1

s

)

2

(

2s)2(2px)1(2

py)1 is known to form

four equivalent bonds as in CH4.

1

s

2

s

2

p

valence

1

s

2

s

2

p

valence

Promotion

– we invest a

small energy in C

for a

bigger energy gain (4 bonds instead of 2) in CH

4

Still not equivalentSlide13

sp

3

hybridization

From one

s

and three

p

orbitals, we form four

equivalent bonds by linearly combing them:

x

y

z

These are orthonormalSlide14

CH

4

With the

sp

3

hybridization, C

is (1

s)2(sp

3)1(sp3

)1(sp3)1(

sp3)1. The

four unpaired electrons in the four sp3 orbitals can each form a σ

bond with H (1s

)1.This explains the tetrahedron structure of CH4 with the HCH angle of

precisely 109.47º.Slide15

sp2 hybridization

From one

s

and

two

p

orbitals, we form three equivalent bonds by linearly combing them:

x

y

These are orthonormalSlide16

CH

2

=CH

2

With the

sp

2

hybridization, C is (1s)

2(2pz)1 (

sp2)1(sp2)

1(sp2)1

. Three unpaired electrons in three sp2 orbitals can each form a

σ bond with H(

1s)1 or C(sp2)

1. C(2pz)1

additionally forms a π bond.This explains the planar structure of ethylene with the HCH and CCH angles

of near 120º.Slide17

sp1 hybridization

From one

s

and

one

p

orbital,

we form two equivalent bonds by linearly combing them:

These are orthonormalSlide18

CHΞCH

With the

sp

1

hybridization, C is (1

s

)2(2pz)1

(2py)1(

sp1)1(sp1)

1. Two unpaired electrons in two

sp1 orbitals can each form a σ bond with H(1

s)1 or C(sp1)

1. C(2pz)1

and (2py)1

form two π bonds.This explains the linear structure

of acetylene.

Cf. H2OSlide19

Lone pairs

Revisit H

2

O

.

O

is

(1s)2(2s)2

(2px)2(2

py)1(2pz)1

.Two unpaired electrons each form a covalent bond: O(2py

)1H(1s)1 and O(2pz

)1H(1s)1

Two valence electrons that do not participate in chemical bond are called a lone pair: O(2s

)2 and O(2px)2.

Lone pairs are part of electron density not shielding nucleus-nucleus repulsion and thus not being stabilized by nuclear charges. They are naked electron pairs that repel other lone pairs or bonding electron pairs.Slide20

Lone pairs in H

2

O

Two different views of H

2

O:

nonhybridized

versus sp3

hybridized

The observed HOH angle is 104.5º, closer to the sp3 picture, suggesting that lone-pair repulsion plays a significant role.

sp

3 picture suggests HOH angle ~

109.5º

Nonhybridization

suggests HOH angle ~ 90º

sp3 lone pairsp3 lone pair

2s lone pair

2pz lone pairSlide21

Lone pairs in NH

3

Two different views of NH

3

:

nonhybridized

versus

sp3 hybridized

The

observed HNH angle is 107º, much closer to the sp3 picture, suggesting that a dominating role of lone-pair repulsion.

sp

3 picture suggests

HNH angle ~ 109.5º

Nonhybridization

suggests HNH angle ~ 90º

sp3 lone pair2

s lone pairSlide22

Lone pairs in H

2

X

The larger the central atom in the

isovalence

H

2

X series, the more widely spread valence p and

s orbitals and the less lone-pair repulsions. H2Te has no need to promote and hybridize

(HTeH angle of 89.5º), whereas H2O gains

much by promoting and hybridizing into sp3 and separating the lone pairs widely.

H

2

X

HXH angle

H

2O

104.5

H

2

S

92.2

H

2

Se

91.0

H

2

Te

89.5Slide23

Homework challenge #7

C

is

(1

s

)

2

(2s)2(2px)

1(2py)1

. Is methylene CH2 bent (nonhybridized p, sp

2, sp3) or linear (sp

1)?Find the answer in the following paper and report.“Methylene: A Paradigm for Computational Quantum Chemistry” by Henry F. Schaefer III,

Science, volume 231, page 1100, 7 March 1986.Slide24

Summary

VB theory

is

an orbital approximation

for molecules. The orbitals used are

hydrogenic

atomic orbitals.VB theory explains the Lewis structure (two singlet-coupled electrons – α

and β spins – per bond).This explains σ and

π bond, promotion and spn hybridization

, lone pairs.Lone-pair repulsion is important in determining molecular structures.