Valence Bond Theory
and
Molecular Orbital Theory
Shapes of Atomic Orbitals for Electrons
 Four different kinds of orbitals for electrons
denoted s, p, d, and f
 s and p orbitals most important in organic and
biological chemistry
 s orbitals: spherical, nucleus at center
 p orbitals: dumbbell-shaped, nucleus at middle
 d orbitals: elongated dumbbell-shaped, nucleus at
center
2
The Nature of Chemical Bonds:
 Covalent bond forms when two atoms approach each
other closely so that a singly occupied orbital on one
atom overlaps a singly occupied orbital on the other
atom
 Two models to describe covalent bonding.
Valence bond theory, Molecular orbital theory
Central Themes of Valence Bond Theory
Basic Principle of Valence Bond Theory: a covalent
bond forms when the orbitals from two atoms
overlap and a pair of electrons occupies the region
between the nuclei.
1) Opposing spins of the electron pair. The
region of space formed by the overlapping
orbitals has a maximum capacity of two
electrons that must have opposite spins.
2) Maximum overlap of bonding orbitals. The
bond strength depends on the attraction of
nuclei for the shared electrons, so the greater
the orbital overlap, the stronger the bond.
Central Themes of Valence Bond Theory
3) Hybridization of atomic orbitals.
bonding in simple diatomic molecules:
Example1: HF (direct overlap of the s and p orbitals of
isolated ground state atoms).
Example 2: CH4 (4 hydrogen atoms are bonded to a
central carbon atom)- hybridization happens to obtain
the correct bond angles.
Pauling proposed that the valence atomic orbitals in
the molecule are different from those in the
isolated atoms. We call this Hybridization!
Fig. 11.1
What Is A Hybrid Orbital?
 are a type of atomic orbital that results when two or more atomic orbitals
of an isolated atom mix (the number of hybrid orbitals on a covalently
bonded atom is equal to the number of atomic orbitals used to form the
hybrid orbitals)
 are used to describe the orbitals in covalently bonded atoms (hybrid
orbitals do not exist in isolated atoms),
 have shapes and orientations that are very different from those of atomic
orbitals in isolated atoms
 in a set are equivalent, and form identical bonds (when the bonds are to a
set of identical atoms), and
 are usually involved in sigma bonds in polyatomic molecules; pi bonds
usually involve the overlap of unhybridized orbitals.
In Hybridization there is ‘mixing’ or
‘blending’ of atomic orbitals to
accommodate
the
spatial
requirements in a molecule.
Hybridization occurs to minimize
electron pair repulsions when atoms
are brought together to form
molecules.
Types of Hybrid Orbitals
1. sp3 Orbitals and the Structure of Methane
 Carbon has 4 valence electrons (2s2 2p2)
 In CH4, all C–H bonds are identical (tetrahedral)
 sp3 hybrid orbitals: s orbital and three p orbitals
combine to form four equivalent, unsymmetrical,
tetrahedral orbitals (sppp = sp3), Pauling (1931)
11
Carbon: 2s22px12py1 one electron in each of four sp3
The Structure of Methane
 sp3 orbitals on C overlap with 1s orbitals on 4 H atoms
to form four identical C-H bonds
 Each C–H bond has a strength of 436 (438) kJ/mol and
length of 109 pm
 Bond angle: each H–C–H is 109.5°, the tetrahedral
angle.
13
The sp3 Hybrid Orbitals in NH3 and H2O
Fig. 11.5
Hybridization of Nitrogen and Oxygen
 Elements other than C can have hybridized orbitals
 H–N–H bond angle in ammonia (NH3) 107.3°
 C-N-H bond angle is 110.3 °
 N’s orbitals (sppp) hybridize to form four sp3 orbitals
 One sp3 orbital is occupied by two nonbonding
electrons, and three sp3 orbitals have one electron each,
forming bonds to H and CH3.
15
sp3 Orbitals and the Structure of Ethane
 Two C’s bond to each other by s overlap of an sp3




orbital from each
Three sp3 orbitals on each C overlap with H 1s orbitals
to form six C–H bonds
C–H bond strength in ethane 423 kJ/mol
C–C bond is 154 pm long and strength is 376 kJ/mol
All bond angles of ethane are tetrahedral
16
2. sp2 Orbitals and the Structure of
Ethylene
 sp2 hybrid orbitals: 2s orbital combines with two 2p
orbitals, giving 3 orbitals (spp = sp2). This results in a
double bond.
 sp2 orbitals are in a plane with 120° angles
 Remaining p orbital is perpendicular to the plane
17
Bonds From
2
sp
Hybrid Orbitals
 Two sp2-hybridized orbitals overlap to form a s bond
 p orbitals overlap side-to-side to formation a pi () bond
 sp2–sp2 s bond and 2p–2p  bond result in sharing four
electrons and formation of C-C double bond
 Electrons in the s bond are centered between nuclei
 Electrons in the  bond occupy regions are on either side of a
line between nuclei
18
Structure of Ethylene
 H atoms form s bonds with four sp2 orbitals
 H–C–H and H–C–C bond angles of about 120°
 C–C double bond in ethylene shorter and stronger than
single bond in ethane
 Ethylene C=C bond length 134 pm (C–C 154 pm)
19
Fig. 11.3
3. sp Orbitals and the Structure of Acetylene
 C-C a triple bond sharing six electrons
 Carbon 2s orbital hybridizes with a single p orbital
giving two sp hybrids
 two p orbitals remain unchanged
 sp orbitals are linear, 180° apart on x-axis
 Two p orbitals are perpendicular on the y-axis and the
z-axis
21
Orbitals of Acetylene
 Two sp hybrid orbitals from each C form sp–sp s bond
 pz orbitals from each C form a pz–pz  bond by sideways
overlap and py orbitals overlap similarly
22
Bonding in Acetylene
 Sharing of six electrons forms C C
 Two sp orbitals form s bonds with hydrogens
23
4. The sp3d Hybrid Orbitals in PCl5
Fig. 11.6
5. The sp3d2 Hybrid Orbitals in SF6
Sulfur Hexafluoride --
Fig. 11.7
SF6
Molecular Orbital Theory
 A molecular orbital (MO): where electrons are most likely
to be found (specific energy and general shape) in a molecule
 Additive combination (bonding) MO is lower in energy
 Subtractive combination (antibonding) MO is higher energy
27
Molecular Orbitals in Ethylene
 The  bonding MO is from combining p orbital lobes
with the same algebraic sign
 The  antibonding MO is from combining lobes with
opposite signs
 Only bonding MO is occupied
28
Valence Bond Theory vs. MO
Theory
 VB Theory begins with two steps:
 hybridization (where necessary to get atomic orbitals that
“point at each other”)
 combination of hybrid orbitals to make bonds with
electron density localized between the two bonding atoms
 Key differences between MO and VB theory:
 MO theory has electrons distributed over molecule
 VB theory localizes an electron pair between two atoms
 MO theory combines AOs on DIFFERENT atoms to make
MOs (LCAO)
 VB theory combines AOs on the SAME atom to make
hybridized atomic orbitals (hybridization)
 In MO theory, the symmetry (or antisymmetry) must be
retained in each orbital.
 In VB theory, all orbitals must be looked at once to see
retention of the molecule’s symmetry.
29
Sigma and Pi Bonds
 Difference between sigma and pi bond
Sigma bond(σ)
 Formed by head to head overlap of AO’s
 The 2 AO’s that overlap are symmetrical about the x axis
joining the 2 nuclei.
 Has free rotation
 Lower energy
 Only one bond can exist between two atoms( a single
covalent bond)
Pi bond(π)
 Formed by side-to-side overlap of AO’s
 No free rotation
 Has higher energy
 One or two bonds can exist between two atoms
 Have nodal plane on the molecular axis and no longer
symmetrical about the molecular axis.
Formation of Sigma Molecular Orbitals:
1. Overlapping of two 1s atomic orbital
Example: H2
+
bonding
antibonding
2. Overlapping of two px atomic orbital
bonding
antibonding
+
3. Overlapping of an s and px atomic orbitals
bonding
+
antibonding
4. Overlapping of px and dz2 or dx2-y2
bonding
antibonding
Formation of Pi Molecular Orbitals:
1. Overlapping of two py atomic orbitals
+
bonding
antibonding
2. Overlapping of two pz atomic orbitals
+
bonding
antibonding
3. Overlapping of py or pz with dxz or dxy
+
bonding
antibonding
Fig. 11.10
Fig. 11.11
Comparison between sigma and pi electrons in
ethylene and acetylene
1. Pi electron are made exposed to the environment
than the sigma electrons.
2. Pi electrons are more reactive than sigma electrons.
3. The looseness of the pi electrons in C2H2 is less than
in C2H4. This is the result of the greater s character in
sp hybrids as compared with the s character in sp2
hydrid.
4. Pi electrons in C2H2 are attracted more strongly
towards the nucleus than the pi electrons in C2H4.
5. The pi bonds in C2H2 are more susceptible to attack
by other chemical entities than in C2H4.
Valence Bond Theory: Overlap of Atomic Orbitals
s bond - overlap of s orbitals
1s
s bond - overlap of
+
F:
H-F
s orbital and p orbital
2p
1 s bond - head/head
N2
N:
overlap of p orbitals
2s
2p
2  bonds - sidewise
Bonds with hybridization of atomic orbitals:
overlap of p orbitals
H-H
sp3 hybridization
CH4
H:
2s
2p
C:
1s
sp3
C atom:
4 s bonds - overlap of
H-s orbitals and sp3 orbitals
Of C
A single sp3 orbital, each with single electron
sp2 hybridization
H2CO C:
2s
H
2p
H
O
H
O
p
sp2
H
C
C atom
3 s bond;
1  bond
A single sp2 orbital, each with single electron
sp hybridization
CO2
O
C
C:
2s
2p
O
O
sp
p
C
O
C atom:
2 s bonds
2  bond
A single sp orbital, each with single electron
Dinitrogren: 2 Models
N N
without hybridization – with just p electrons
N2
N:
2s
2p
with sp hybridization – with all valence electrons
N:
N2
2s
2p
p
sp
1st sp orbital
one with
nonbonded
pair
2p
sp2
p
-geometry around O is trigonal planar
- requires 3 equivalent orbitals from the O
- hence, sp2 hybridization
N
1 s bonds
2  bond
O
H
2s
2nd sp orbital
N
O atom in H2CO (previous slide)
O:
1 s bond - head/head
overlap of p orbitals
2  bonds - sidewise
overlap of p orbitals
H
O atom
Can form 1 s bond;
Can form 1  bond
Has 2 nonbonded pairs