Lecture 24
Valence 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.
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 spn hybridization and lone
pairs are introduced.
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?
Singlet and triplet He (review)

In the orbital approximation for (1s)1(2s)1
He, there are four different ways of filling two
electrons:
Anti-symmetric
Antisymm
etric
{
}
{
}
Y ( r ,r ) » {j ( r )j ( r ) - j ( r )j ( r )} {a (1)b (2) + b (1)a (2)}
Y ( r1 ,r2 ) » j1s ( r1 )j 2s ( r2 ) - j1s ( r2 )j 2s ( r1 ) a (1)a (2) Triplet
Y ( r ,r ) » j ( r )j ( r ) - j ( r )j ( r ) b (1)b (2) more stable
1
2
1s
1
2s
2
1s
2
2s
1
1
2
1s
1
2s
2
1s
2
2s
1
{
}
Y ( r1 ,r2 ) » j1s ( r1 )j 2s ( r2 ) + j1s ( r2 )j 2s ( r1 ) {a (1)b (2) - b (1)a (2)}
Singlet
Anti-symmetric
VB theory for H2

Let us construct the molecular wave function
of H2 using its two 1s orbitals A and B.
A(1) B(2) (1)  (2)
VB theory for H2
singlet
[ A(1)B(2) + B(1)A(2)][a (1)b (2) - b (1)a (2)]
more stable
e
n
n
e
ì a (1)a (2)
ï
éë A(1)B(2) - B(1) A(2) ùû í b (1)b (2)
ï a (1)b (2) + b (1)a (2)
î
triplet
e
n
n
e
Covalent bond
A(1)B(2)  B(1) A(2) (1) (2)   (2) (1)
(1) Enhanced electron probability density between nuclei
(shielding nucleus-nucleus repulsion). The greater the
overlap of two AO’s the stronger the bond.
(2) Two singlet-coupled (α1β2−β1α2) electrons for one
bond (Lewis structure).
σ and π bonds

A π bond is weaker than σ bond because of
a less orbital overlap in π.
σ bond
π bond
N2


N is (1s)2(2s)2(2px)1(2py)1(2pz)1
N2 forms one σ bond and two π bonds.
Altogether three-fold covalent bonds
(triple bonds).
H2 O



O is
(1s)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.
NH3



N is
(1s)2(2s)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 90º.
Promotion and hybridization

C (1s)2(2s)2(2px)1(2py)1 is known to form four
equivalent bonds as in CH4.
valence
2p
valence
2s
2s
1s
1s
2p
Still not equivalent
Promotion – we invest a small energy in C for a
bigger energy gain (4 bonds instead of 2) in CH4
sp3 hybridization

From one s and three p orbitals, we form four
equivalent bonds by linearly combing them:
h1 =
1
2
h2 =
1
2
h3 =
1
2
h4 =
1
2
(s + p + p + p )
(s - p - p + p )
(s - p + p - p )
(s + p - p - p )
x
y
z
x
y
z
x
y
z
x
y
These are orthonormal
z
z
y
x
CH4



With the sp3 hybridization, C is
(1s)2(sp3)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.
sp2 hybridization

From one s and two p orbitals, we form three
equivalent bonds by linearly combing them:
h1 =
1
3
h2 =
1
3
h3 =
1
3
(s +
(s +
(s -
2 py
)
y
3
2
px -
1
2
3
2
px -
1
2
pz
These are orthonormal
)
p )
py
y
x
CH2=CH2



With the sp2 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.
sp1 hybridization

From one s and one p orbital, we form two
equivalent bonds by linearly combing them:
h1 =
h2 =
( s + px )
1
( s - px )
2
1
2
py
pz
These are orthonormal
CHΞCH



With the sp1 hybridization, C is (1s)2(2pz)1
(2py)1(sp1)1(sp1)1.
Two unpaired electrons in two sp1 orbitals can
each form a σ bond with H(1s)1 or C(sp1)1.
C(2pz)1 and (2py)1 form two π bonds.
This explains the linear structure of acetylene.
Cf. H2O
Lone pairs




Revisit H2O. O is (1s)2(2s)2(2px)2(2py)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.
Lone pairs in H2O

Two different views of H2O: nonhybridized
versus sp3 hybridized
2s lone pair
2pz lone pair
sp3 lone pair
sp3 lone pair
sp3 picture suggests
HOH angle ~ 109.5º

Nonhybridization suggests
HOH angle ~ 90º
The observed HOH angle is 104.5º, closer to
the sp3 picture, suggesting that lone-pair
repulsion plays a significant role.
Lone pairs in NH3

Two different views of NH3: nonhybridized
versus sp3 hybridized
2s lone pair
sp3
lone pair
sp3 picture suggests
HNH angle ~ 109.5º

Nonhybridization suggests
HNH angle ~ 90º
The observed HNH angle is 107º, much
closer to the sp3 picture, suggesting that a
dominating role of lone-pair repulsion.
Lone pairs in H2X

The larger the central atom in
the isovalence H2X 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 2X
HXH angle
H 2O
104.5
H 2S
92.2
H2Se
91.0
H2Te
89.5
Homework challenge #7


C is (1s)2(2s)2(2px)1(2py)1. Is methylene CH2
bent (nonhybridized p, sp2, sp3) or linear
(sp1)?
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.
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.