Molecular Geometry
and
Bonding Theories
Brown, LeMay Ch 9
AP Chemistry
Monta Vista High School
Ch 9 PS #8, 10, 16, 20 (and draw overall dipole moments), 30, 34, 36, 41,
59, 73; Recommended #9, 11, 13, 19, 25, 31, 40, 55, 60
Rationale for VSEPR Theory
•Lewis structure is a flat drawing showing
the relative placement of atoms, bonds etc.
in a molecule, but does not tell anything
about the shape of the molecule.
•VSEPR theory helps construct molecular
shape (3-D) from the Lewis structures,
which are 2-D structures.
Valence Shell Electron Pair Repulsion Theroy
• The basis principal of VSEPR is that each group of
valence electrons (electron domains) around a
central atom tend to be as far as possible from each
other to minimize repulsions. These electron domain
repulsions around the central atom determine the molecular
geometry of a molecule.
• Electron domains: areas of valence e- density around
the central atom;
 Includes bonding e- pairs and nonbonding (lone) epairs
 A single, double, or triple bond counts as one domain
• Repulsions between two e domains are : lone pairlonepair >lone pair-bond pair> bond pair-bond pair
Valence-shell electron-pair repulsion theory
– Why is lone pair- lone pair repulsion greater than bond
pair-bond pair repulsion?
– Good Links:
Good Power point on VSEPR, Shapes of sp3, sp2, sp Carbon, VSEPR Lecture
Summary of ABE (Tables 9.1 - 9.3) on the next slide:
E = lone or non-bonding pairs
A = central atom
B = bonded atoms
Bond angles notation used here:
< xº
means ~2-3º less than predicted
<< xº
means ~4-6º less than predicted
Tables Link
# of edomains
&
# and type
of hybrid
orbitals
2
Two sp
hybrid
orbitals
e- domain
geometry
Formula
&
Molecular
geometry
X
B
A
|
X
A
|
B
Linear
AB2
Linear
Predicted
bond
angle(s)
180º
Example
(Lewis
structure with
molecular
shape)
BeF2
CO2
B
B
120º
A
|
B
BF3
3
X
Three sp2
hybrid
orbitals
X
A
|
X
AB3
Trigonal planar
B
Cl2CO
:
A
|
B
Trigonal
planar
Cl-C-Cl
<< 120º
LAB2
Bent
< 120º
NO21-
Example: CH4
H
|
H—C—H
|
H
109.5º
109.5º
109.5º
109.5º
Molecular shape =
tetrahedral
Bond angle = 109.5º
B
B
A
B
X
X
A
4
X
Four sp3
hybrid
orbitals
X
CH4
< 109.5º
A
B
X
LAB3 B
Trigonal
pyramidal
Ex: NH3 =
107º
NH3
B
A
X
B
AB4
Tetrahedral
B
:
X
or
109.5º
<<109.5º
:
A
X
:
Tetrahedral
L2AB2
B
Bent
Ex: H2O =
104.5º
H2O
PCl5
:
:
:
90º
: :
: :
:Cl: :Cl:
\ /
:Cl—P—Cl:
|
:Cl:
90º
120º
120º
90º
Molecular shape =
trigonal bipyramidal
Bond angles
equatorial = 120º
axial = 90º
B
B
A
|
B
X
X
Five
sp3d
hybrid
orbitals
A
X
X
B
AB5
Trigonal
bipyramidal
Equatorial
= 120º
Axial = 90º
PCl5
|
X
:
5
B
B-A-B
B
Trigonal
bipyramidal
B
LAB4
Seesaw
Equatorial
< 120º
Axial
< 90º
SF4
B
:
A
|
:
5
X
X
Five
sp3d
hybrid
orbitals
A
X
X
B
ClF3
B
:
A
:
Trigonal
bipyramidal
Axial
<< 90º
L2AB3
T-shaped
|
X
B
|
B
L3AB2
Linear
:
Axial =
180º
XeF2
X
X
X
B
B
X
A
A
|
|
X
X
6
B
B
B
90º
AB6
Octahedral
or
Six sp3d2
hybrid
orbitals
B
SF6
B
B
X
X
X
X
A
|
B
A
X
X
Octahedral
B
|
..
B
LAB5
Square
pyramidal
< 90º
BrF5
B
..
B
A
6
Six sp3d2
hybrid
orbitals
B
|
..
..
B
or
B
B
B
|
..
90º
B
..
or
B
XeF4
..
..
|
..
A
L2AB4
Square planar
A
B
..
B
B
A
|
..
L3AB3
T-shaped
B
<90º
B
KrCl31-
Limitations of VSEPR Theory
Even though the VSEPR model is useful in
predicting the shapes of molecules, it
does not differentiate between single,
double and triple bonds and does not
account for bond strengths.
9.3: Molecular Polarity
Two factors must be considered in the polarity of a
molecule:
1. Are the individual bonds (joining different atoms in a
molecule) polar? Ex. HCl vs. H2. HCl is polar while H2 is
not.
d + d-
Bond polarity is most often represented by
an arrow that points toward the d- (most EN
atom), showing the shift in e- density.
H-Cl:
•
The dipole moment (m) is a vector (i.e., has a
specific direction) measuring the polarity of a
bond which contains partial charges (Q) that are
separated by a distance (r).
H-Cl:
: :: :
•
m=Qr
2. If individual bonds are polar, then do individual dipole
moments cancel out or not. A molecule is polar if its centers
of (+) and (-) charge do not cancel out- generally happens in
a distorted molecule (molecules with lone pairs of e on the
central atom.)
How to determine if a molecule is polar?
The sum of the bond dipole moments in a molecule determines
the overall polarity of the molecule.
1. Draw the true molecular geometry (3D geometry).
2. Draw each bond dipole as an arrow
3. Add the vectors, and draw the overall dipole moment. If
none, then m = 0.
4. Generally, a distorted molecule (with lone pairs on the
central atom) will have a dipole. Exception: AB2E3 type
What is the big deal about polarity?
• The polarity of a molecule will tell you a lot about
its solubility, boiling point, etc. when you
compare it to other similar molecules. Water, for
example, is a very light molecule (lighter than
oxygen gas or nitrogen gas) and you might expect
it would be a gas based on its molecular weight,
however the polarity of water makes the
molecules "stick together" very well. Hence water
is present as liquid.
• Polar substances are soluble in water (which is
polar) and non polar substances are soluble in
non polar solvents such as benzene and oil.
Ex: Draw molecular geometires, bond dipole moments, and overall
dipole moments. Also, name the e- domain geometry and the
molecular geometry.
CO2
CCl4
BF3
NH3
H2O
PH3
Rationale For Valence Bond Theory
• VB theory provides a basis for covalent bond
formation based upon overlapping of atomic
orbitals to share electrons.
• This theory successfully predicts bond
strengths based upon orbital overlap (such as
H2 bond being weaker than N2 bond)- sigma
vs. pi bond strength
Covalent Bonding and Orbital Overlap: Valence Bond Theory
The basic principle of VB theory is that a covalent bond forms
when the orbitals of two atoms overlap. Three central themes
of VB theory derive from this principle:
1. Opposing spins of e pairs: In accordance with Pauli’s
exclusion principle, an orbital can have max of two e with
opposite spins.
2. Maximum overlap of bonding orbitals: The bond strength
depends upon the attraction of nuclei for the shared e, so the
greater the overlap, the stronger the bond.
3. End to end overlap of the atomic orbitals form a sigma
bond and allows the free rotation of the parts of the
molecule. Side-to-side overlap forms a pi bond, which restricts
rotation. A multiple bond consists of one sigma bond and rest
pi bonds.
Sigma and Pi bonds
Sigma (s) bond:
• Covalent bond that results from axial overlap of orbitals between atoms in
a molecule
• Lie directly on internuclear axis
• “Single” bonds, could form between s-s orbital or s-p orbital or p-p orbital
by axial overlapping
Ex: F2
Pi (p) bond:
• Covalent bond that results from side-by-side overlap of orbitals between
atoms in a molecule.
• Are “above & below” and “left & right” of the inter nuclear axis and
therefore have less total orbital overlap, so they are weaker than s bonds.
Forms between two p orbitals (py or pz)
• Make up the 2nd and 3rd bonds in double & triple bonds.
Ex: O2
N2
Covalent Bonding and Orbital Overlap
• Valence-bond theory: overlap of orbitals between atoms results in a
shared valence e- pair (i.e., bonding pair)
a.
Figure : Formation of bond in H2
Energy
(kJ/mol)
0
-436
d
a
b
c
0.74 Å
H-H distance
As 2 H atoms approach, the 2 valence ein the 1s orbitals begin to overlap,
becoming more stable.
b. As H-H distance approaches 0.74 Å,
energy lowers b/c of electrostatic
attraction between the nuclei & the
incoming e-.
c.
When H-H distance = 0.74 Å, energy is at
its lowest because electrostatic
attractions & repulsions are balanced.
(This is the actual H-H bond distance.
d. When H-H distance < 0.74 Å, energy
increases b/c of electrostatic repulsion
between 2 nuclei & between the 2 e-.
Limitations of VB Theory
• Valence bond (VB) theory assumes that all
bonds formed between two atoms are
localized bonds and are formed by the
donation of an electron from each atom. This
is actually an invalid assumption because
many atoms bond using delocalized electrons.
Rationale for Hybrid Orbital Theory
Good youtube video
• Hybrid orbital theory is seen as an extension
of VB theory, where atomic orbitals
“hybridize” to form new hybrid orbitals. This
hybrid orbital theory helps explains the
bonding in terms of quantum mechanical
model of atom (s,p,d,f orbitals).
9.5: Hybrid Orbital Theory
Movie on Hybrid Orbitals
Explains the molecular geometries in terms of
s,p,d,f orbitals.
VSEPR explains that e domains must be
farthest from each other around central atom,
but fails to explain these in terms of orbitals as
defined in wave mechanical model of atom.
Hybrid orbital theory of Linus Pauling
proposed that the valence atomic orbitals in
the molecule are very different from those in
the isolated atoms.
The process of orbital mixing is called
hybridization, and the new atomic orbitals are
called hybrid orbitals. Animation on Hybrid Orbitals,
Hybridization Movie
Hybrid Orbital Theory
• Two key points about the number and types of
hybrid orbitals are that
1. The number of hybrid orbitals obtained
equals the number of atomic orbitals mixed.
2. The type of hybrid orbitals obtained varies
with the types of atomic orbitals mixed.
“sp” hybrid orbitals
•
BeF2 (g): observed as a linear molecule with 2 equal-length Be-F
bonds. Valence bond theory predicts that each bond is an overlap
of one Be 2s e- and one 2p e- of F. However, Be’s 2s e- are already
paired. So…
To form 2 equal bonds with 2 F atoms:
1.
In Be, one 2s e- is promoted to an empty 2p orbital.
2.
The occupied s and p orbitals are hybridized (“mixed”), producing two
equivalent “sp” orbitals.
3.
As the two “sp” hybrid orbitals of Be overlap with two p orbitals of F,
stronger bonds result than would be expected from a normal Be s and F p
overlap. (This makes up for energy needed to promote the Be eoriginally.)
Energy →
Be (ground state) → Be (promoted) → Be (sp hybrid)
2p
2s
F F

Orbital “shapes”
One s + one p
→
Two sp orbitals
(to bond with 2 F’s)

A central atom in a Lewis structure with exactly 2 e- domains has sp hybrid
orbitals.
“sp2” hybrid orbitals
• BF3 (g): observed as trigonal planar molecule with 3 equal-length B-F
bonds. However, 2 valence e- in B are paired, and are the s and p enot at the observed 120º angle.
B (ground) → B (promoted) → B (sp2 hybrid)
2p
2s

One s + two p
→
Three sp2 orbitals
F F F
(to bond with 3 F’s)

A central atom with exactly 3 e- domains has sp2 hybrid orbitals.
•
3” hybrid orbitals
“sp
CH (g): observed as tetrahedral
4
C (ground) → C (promoted) → C (sp3 hybrid)
2p
2s

One s + three p
→
Four sp3 orbitals
H H H H
(to bond with 4 H’s)

A central atom with exactly 4 e- domains has sp3 hybrid orbitals.
3d” hybrid orbitals (or dsp3)
“sp
PCl (g): observed as trigonal bipyramidal; forms 5 bonds of equal energy (* but
•
5
not equal length: equatorial are slightly longer)
P (ground) → P (promoted) →
P (sp3d hybrid)
3d
3p
3s

One s + three p + one d
Cl Cl Cl Cl Cl
→
Five sp3d orbitals
(to bond with 5 Cl’s)

A central atom with exactly 5 e- domains has sp3d hybrid orbitals.
“sp3d2” hybrid orbitals (or d2sp3)
•
SF6 (g): observed as octahedral; forms 6 equal-length bonds

One s + three p + two d

A central atom with exactly 6 e- domains has sp3d2 hybrids.
→
Six sp3d2 orbitals
Non-bonding e- pairs
•
Lone pairs occupy hybrid orbitals , too
Ex: H2O (g): observed as bent; but3 e- domain is tetrahedral
O (ground)
→
O (sp hybrid)
2 bonding pairs
2p
2s

2 non-bonding pairs
(lone pairs)
H H
Four sp3 orbitals (2 bonding, 2 non-bonding)
9.6: Multiple Bonds
Draw Lewis structures. For C’s: label hybridization, molecular geometry, and
unique bond angles
C2H6
C2H4
C2H2
C6H6
Sigma (s) bonds in C2H4
Ex: ethene; C-C s-bonds and C-H s-bonds result
from axial overlap of H s-orbitals and C sp2orbitals
Pi (p) bonds in C2H4
p orbital bonds side-by-side
= p bond
2p
C
2s
sp2 hybrids bond
axially
= s bonds
• Each C has 4 valence e-:
– 3 e- for 3 s-bonds
– 1 e- for 1 p-bond, which results from side-by-side
overlap of one non-hybridized p-orbital from each C
Sigma (s) bonds in C2H2
Ex: ethyne (a.k.a. acetylene) C-C s-bond and C-H sbonds result from axial overlap of
H s-orbitals and C sp-orbital
Pi (p) bonds in C2H2
p orbital bonds side-by-side
= p bonds
2p
C sp hybrids bond axially = s
bonds
2s
p

Each C has 4 valence e-:
– 2 e- for 2 s-bonds
– 2 e- for 2 p-bonds, which result from side-by-side overlap of two non-hybridized p-orbitals
from each carbon
Sigma (s) bonds in C6H6
Ex: benzene; C-C s-bonds and C-H s-bonds result
from axial overlap of H s-orbitals and C sp2orbitals
http://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/intro3.htm#strc8c
Localized v. Delocalized Bonds
• Delocalized bonds are present in compounds
showing resonance structures, while electrons are
localized in most other bonds.
Localized vs. Delocalized p Bonds
(localized)
(delocalized – MINIMUM OF 4 c’S)
Delocalized p bonds in C6H6
•
•
C-C p-bonds result from overlap of one non-hybridized p-orbitals from each C
Delocalization of e- in p-bonds results in a “double-donut” shaped e- cloud above
and below the molecular carbon plane.
Limitations of Hybrid Orbital Theory
Hybrid orbital theory assumes that all
bonds are formed with localized
electrons, which is not true. MO
(Molecular Orbital) theory explains
bonding in terms of delocalized orbitals
as well.
9.7: Molecular Orbital (MO) theory
So far we have used valence-bond theory (covalent
bonds form from overlapping orbitals between
atoms) with hybrid orbital theory and VSEPR theory
to connect Lewis structures to observed molecular
geometries. However, VB theory does not explain
the magnetic or spectral properties of a molecule.
MO theory is similar to atomic orbital (AO) theory
(s, p, d, f orbitals) and helps to further explain
some observed phenomena, like unpredicted
magnetic properties in molecules like those in O2.
AO are associated with the individual atoms, but
MO are associated with the whole molecule.
*AO & MO in H2
Atomic orbitals
s*1s
E
1s
Anti-bonding orbital
Molecular orbitals
1s
s1s
Bonding orbital
Combination of two 1s AO from each H forms two MO
in H2 molecule.
Bonding MO: form between nuclei and are stable
Antibonding MO: marked with *; form “behind” nuclei
and are less stable.
*Types of MO
• Sigma (s) MO: form from combinations of:
– Two 1s or 2s orbitals from different atoms; written as s1s
or s2s.
– Two 2pz orbitals from different atoms (axial overlap);
written as s2pz.(Some sources say 2 px orbitals?)
• Pi (p) MO: form from combinations of:
– Two 2px or 2py orbitals from different atoms; written
as p2px or s2py.
– Do not appear until B2 molecule
MO s from Atomic p-Orbital
Combinations
 P orbitals can interact with each other forming either
sigma molecular orbitals, s2p , in a end-to-end overlap
or pi molecular obrbitals, p2p, in a side-to-side overlap.
 The order of energy for MO s derived from 2p orbitals
is s2p < p2p < p2p*< s2p*
 There are three perpendicular p orbitals, so two sigma p
orbitals (one bonding and one antibonding) and four pi
p orbitals (two bonding and two antibonding) are
formed.
 This energy order gives the expected MO diagram for
most of the p-block elements for homonuclear
diatomic molecules.
MO s for B, C and N
 The energy order of p orbitals results from the assumption that
since s and p orbitals have differences in energy, they do not
interact with each other. (or mix)
 However, when 2p atomic orbitals are half filled, such as in B, C and
N, the repulsions between e are little and the energy of these p
orbitals is not much different than the s atomic orbital, which leads
to s and p orbital mixing. This mixing lowers the energy of the 2s
bonding and antibonding orbitals and increases the energy of sigma
2p (bonding and antibonding) orbitals.The pi 2p orbitals are not
affected. This mixing gives a different energy order:
 s2s < s2s*< p2p<s2p < p2p*< s2p
*MO diagrams for “< O2”
• Resulting MO for
diatomic molecules
with < 16 e- (B2, C2,
N2, etc.)

N atom
N atom
Bond order =
½ (# bonding e- # antibonding e-)
B.O. (N2) = ½ (10 – 4) =
6 / 2 = 3 (triple bond)
 N2 has no unpaired
electrons which makes it
diamagnetic.
*MO diagrams for “≥ O2”
Resulting MO for
diatomic molecules
with ≥ 16 e- (like O2, F2,
Ne2, etc.)

O atom
O atom
Bond order =
½ (# bonding e- # antibonding e-)
B.O. (O2) = ½ (10 – 6) =
= 2 (double bond)
 O2 has unpaired
electrons which makes it
paramagnetic.
Liquid N2 and liquid O2
• From U. Illinois:
http://www.chem.uiuc.edu/clcwebsite/liquido2.html
N2
O2
Magnetism
In an element or compound:
 Diamagnetism: all e- paired; no magnetic properties
 Paramagnetism: at least 1 unpaired e– * Drawn into exterior magnetic field since spins of atoms become aligned;
unlikely to retain alignment when field is removed
Ex:
N
O
Sc
Mn
O2
 * Ferromagnetism: occurs primarily in Fe, Co, Ni
– Drawn into exterior magnetic field since spins of atoms become aligned;
very likely to retain alignment when field is removed (i.e., “a permanent
magnet”)
– Nd2Fe14B is very ferromagnetic