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Chapter 9
Molecular Geometry
And Bonding Theories
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Chapter 09
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第二次會考 1051207 (ch5-8)
積極性補強教學：
週一、週二17：30-20：30
週三、週四17：30-21：30
海事大樓412教室
http://moodle.ntou.edu.tw/
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Contents
1.
2.
3.
4.
5.
6.
7.
8.
Molecular Shapes
The VSEPR Model
Molecular Shape and Molecular Polarity
Covalent Bonding and Orbital Overlap
Hybrid Orbitals
Multiple Bonds
Molecular Orbitals
Period 2 Diatomic Molecules
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1.

Molecular Shapes
Lewis structures is two-dimensional arrangement:

Molecular shapes three-dimensional arrangement:
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1.

*****
The VSEPR Model
Valence Shell Electron Pair Repulsion (VSEPR)
theory: A theory that allows prediction of the
shapes of molecules or polyatomic ion based on
the idea that electron domain˗ either as lone pair
(nonbonding pair) or as bonding pair ˗ repel one
another.
• Electron domain geometry: The geometrical
arrangement of electron domain in a molecule.
• Molecular geometry: The geometrical
arrangement of atoms in a molecule.
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
i)
ii)
*****
VSEPR theory proceeding
Write a best Lewis structure
Determine VSEPR notation:
ABnEm:
A: Central atoms
B: Terminal atoms
E: Lone pairs electrons
H2O for example:
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AB2E2
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iii) Determine the electron geometry
*****
 An electron group can be:
- either single bond or a multiple bond
- a (resonance) hybrid bond
- a lone pairs of electron
- a unpaired single-electron
 Repulsion force in general:
LP vs. LP > LP vs. BP > BP vs. BP
* Lone Pairs (LP), Bonding Pairs (BP)
Angle for repulsion forces: 90° > 120° > 180°
 For central (interior) atom belong to third-period or
higher element with VSEPR notation such as AB5,
AB4E, AB3E2, AB6, AB5E, AB4E2 require an expanded
octet such as 3d orbital.
 Multiple bond occupy more space than single bond
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*****
iv) Determine the molecular geometry
 Structures for the central atom without lone-pair
electrons (ABn type), electron geometry and
molecular geometry are identical.
 Structures for the central atom with lone-pair
electrons (ABnEm type) type), electron
geometry and molecular geometry are different.
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
Determine the molecular geometry of NH3
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*****
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*****
* Count only electron groups around the central atom. Each of the
following is considered one electron domain: a lone pair, a single
bond, a double bond, a triple bond, or a single electron.
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*****
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*****
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*****
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
The Five Basic Shapes
(All electrons around the central atom are bonding
group)
 Two Electron Domain (AB2): Linear
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 Three Electron Domain (AB3): Trigonal Planar
* double bond contains
more electron density
than the single bond
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 Four Electron Domain (AB4): Tetrahedral
 Five Electron Domain (AB5): Trigonal Bipyramidal
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 Six Electron Domain (AX6): Octahedral
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Example Determine the molecular geometry of NO3−.
Solution
NO3− has 5 + 3(6) + 1 = 24 valence electrons. The Lewis structure has three
resonance structures:
Use any one of the resonance structures to determine the number of electron groups
around the central atom. The nitrogen atom has three electron domain.
The electron domain geometry is trigonal planar:
The molecular geometry is also trigonal planar.
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
The Effect of Lone Pairs
(Some electrons around the central atom are lone
pairs)
 Three Electron Domain with Lone Pairs
AB2E
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 Four Electron Domain with Lone Pairs
AB3E
AB2E2
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*
Effect of Lone Pairs on Molecular Geometry
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 Five Electron Domain with Lone Pairs
AB4E
AB3E2
AB2E3
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 Six Electron Domain with Lone Pairs
*****
AB5E
AB4E2
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Sample Exercise 9.1 Use the VSEPR model to predict the molecular
geometry of (a) O3, (b) SnCl3–.
Solution
(a)
electron domains geometry:
trigonal planar
molecular geometry:
bent
electron domains geometry:
tetrahedral
molecular geometry:
trigonal-pyramidal
(b)
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Sample Exercise 9.2 Use the VSEPR model to predict the molecular
geometry of (a) SF4, (b) IF5.
Solution
(a)
electron domains geometry:
trigonal bipyramid
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molecular geometry:
seesaw-shaped
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Continued
(b)
electron domains geometry:
octahedral
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molecular geometry:
square pyramidal
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
Representing Molecular Geometries on Paper
Examples:
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
Shapes of Larger Molecules
Example: acetic acid
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*****
Sample Exercise 9.3 Eyedrops for dry eyes usually contain a water-soluble
polymer called poly(vinyl alcohol), which is based on the unstable organic
molecule vinyl alcohol:
Predict the approximate values for the H—O—C and O—C—C bond angles in
vinyl alcohol.
Solution
H—O—C angle is slightly less than 109.5゜.
O—C—C angle is slightly greater than 120゜.
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

*****
Memo for VSEPR
Without lone-pair electrons
VSEPR
Notation
AB2
AB3
AB4
Electron
Geometry
Linear
Trigonal planar
Tetrahedral
Molecular
Geometry
Linear
Trigonal planar
Tetrahedral
AB5
AB6
Trigonal bipyramidal
Octahedral
Trigonal bipyramidal
Octahedral
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
With lone-pair electrons
*****
VSEPR
Notation
AB2E
AB3E
AB2E2
AB4E
Electron
Geometry
Trigonal planar
Tetrahedral
Tetrahedral
Trigonal bipyramidal
Molecular
Geometry
Bent
Trigonal pyramidal
Bent
Seesaw
AB3E2
AB2E3
AB5E
AB4E2
Trigonal bipyramidal
Trigonal bipyramidal
Octahedral
Octahedral
T-shaped
Linear
Square pyramidal
Square planar
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3. Molecular Shape and Molecular Polarity
 Bond dipole versus Molecular dipole
 Bond dipole: A separation of positive and negative
charge in an individual bond.
 Molecular dipole:
• For diatomic molecule: molecular dipole is
identical to bond dipole.
• For a molecule consisted by three or more
atoms, molecular dipole is estimated by the
vector sum of individual bond dipole
moment (overall dipole moment).
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 Polar molecule versus Nonpolar molecule
 Polar molecule: A molecule in which the
molecular dipole is nonzero.
 Nonpolar molecule: A molecule in which the
molecular dipole is zero.
 Molecular polarity prediction
• Draw the Lewis structure for the molecule and
determine its molecular geometry.
• Determine if the molecule contains polar bonds
by electronegativity values.
• Determine if the polar bonds add together to form
a overall dipole moment.
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
*****
Examples
CO2
Molecular geometry: linear
Overall dipole moment: m = 0 D
Nonpolar molecule
H2 O
Molecular geometry: bent
Overall dipole moment: m = 1.85 D
Polar molecule
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X. VB versus MO
 Quantum-Mechanical Approximation Technique
 Perturbation theory (used in valence bond
theory): A complex system (such as a molecule)
is viewed as a simpler system (such as two atoms)
that is slightly altered or perturbed by some
additional force or interaction (such as the
interaction between the two atoms).
 Variational method (used in molecular orbital
theory): The energy of a trial function (educated
function) within the Schrodinger equation is
minimized.
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
Schrodinger equation revisited
H = E
• H (Hamiltonian operator), a set of mathematical
operations that represent the total energy (kinetic
and potential) of the electron within the atom.
• E is the actual energy of the electron.
•  is the wave function , a mathematical function
that describes the wavelike nature of the electron.
 Perturbation theory: Approach by small
changes to a known system in which Hamiltonian
operator is modified.
 Variational method: Approach by combining
systems of comparable weighting in which wave
function is modified.
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
Valence bond theory versus molecular orbital
theory
 Valence bond theory (VB): An advanced model
of chemical bonding in which electrons reside in
quantum-mechanical orbitals localized on
individual atoms that are a hybridized blend of
standard atomic orbitals; chemical bonds result
from an overlap of these orbitals.
 Molecular orbital theory (MO): An advanced
model of chemical bonding in which electrons
reside in molecular orbitals delocalized over the
entire molecule. In the simplest version, the
molecular orbitals are simply linear combinations
of atomic orbitals.
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4. Covalent Bonding and Orbital Overlap
 Valence bond theory describes that covalent bonds are
formed when atomic orbitals on different atoms overlap.
 Simple Atomic Orbitals (AO’s) Overlap
• A covalent bond is formed by the
pairing of two electrons with
opposing spins in the region of
overlap of atomic orbitals between two
atoms.
• This overlap region has a high
electron charge density.
• The overall energy of the system is
lowered.
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 Formation of the H2 molecule as atomic orbitals
overlap.
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 Acceptable simple Atomic Orbitals (AO’s) Overlap
Bonding in H2S for example
• Predicted H˗S˗H angle is 90o, actual H˗S˗H angle is 92o,
therefore, the simple AO overlap is acceptable for H2S
molecule.
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 Unacceptable simple Atomic Orbitals (AO’s)
Overlap
C
Example: CH4
• Ground-state
electron
configuration of C
for example, it
should form only
2 bonds
• Actually, the
central atom of
H2S, H2O, NH3,
and CH4, are sp3
hybridization
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*****
5. Hybrid Orbitals
 Hybridization: A mathematical procedure in which
standard atomic orbitals are combined to form new,
hybrid orbitals.
•
•
•
Hybridizing is mixing different types of orbitals in the
valence shell to make a new set of degenerate orbitals
such as sp, sp2, sp3, sp3d, sp3d2.
Hybrid orbitals minimize the energy of the molecule
by maximizing the orbital overlap in a bond.
Those central atoms are available hybridized,
however, those terminal atoms are supposed to be
unhybridized.
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
General statements regarding hybridization *****
• Hybridization is employed for central atom
only, thus, the hybrid orbital describes the
electron geometry for central atom.
• Number of hybrid orbitals = Number of
standard atomic orbitals combined = Number of
σ bond + Number of lone pairs.
• Number of hybridization obitals of a central
atom = 2 → sp; = 3 → sp2; = 4 → sp3; = 5 →
sp3d; = 6 → sp3d2.
• Hybrid orbitals may overlap with standard
atomic orbitals or with other hybrid orbitals to
form σ bond.
• Molecular geometry is described by the relative
atomic position around central atom.
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
sp3 hybridization (C for example)
one s orbital with three p orbitals combine to
form four sp3 hybrid orbitals (degenerate).
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*****
Examples of sp3 hybridization (for central atom)
Central Moleatom
cule
Standard
orbitals
Hybrid
Orbital
σ
C
H
H C H
H
2s
O
σ
σ
sp3
2p
lone
N
σ
Geometry
σ
σ
σ
..
H N H
H
H
2s
2p
sp3
lone lone σ
.. .
O.
H
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2s
σ
sp3
2p
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
sp2 hybridization (B for example)
one s orbital with two p orbitals combine to form
three sp2 hybrid orbitals
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Examples of sp2 hybridization (for central atom)
Central
atom
Molecule
Standard
orbitals
B
C
F B F
F
H
H
2s
2p
H
H
2s
σ
σ
2p
sp2
σ
C C
Unhybridized
Orbital
Hybrid
Orbital
σ
2p
σ
σ
σ
π
2p
sp2
lone
*****
σ
π
.. ..
N
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H N N H
2s
2p
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sp2
2p
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
sp hybridization (Be for example)
one s orbital with one p orbitals combine to form
two sp hybrid orbitals
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*****
Examples of sp hybridization (for central atom)
Central
atom
Molecule
Standard
orbitals
Hybrid
Orbital
σ
Be
Cl Be Cl
2s
2p
C
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H C C H
2s
2p
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σ
sp
σ
Unhybridized
Orbital
σ
sp
2p
π
π
2p
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 Hypervalent Molecules
(elements of period 3 and beyond may have more than
octet electrons around central atom)
 sp3d hybridization, AsF5 for example
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Continued
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 sp3d2 hybridization, SF6 for example
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Continued
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
Procedure for Hybridization and Bonding
Scheme
*****
1. Write the Lewis structure for the molecule.
2. Use VSEPR theory to predict the electron
geometry about the central atom.
3. Select the correct hybridization for the central
atom based on the electron geometry.
4. Sketch the molecule, beginning with the central
atom and its orbitals. Show overlap with the
appropriate orbitals on the terminal atoms.
5. Label all bonds using the σ or π notation
followed by the type of overlapping orbitals.
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*****

Example for hybridization/electron geometry types
versus molecular geometry
Number of
σ + lone
Hybridization
VSEPR
notation
Electron
geometry
Molecular
geometry
Example
2
sp
AX2
Linear
linear
Cl-Be-Cl
3
sp2
AX3
AX2E
Trigonal planar
Trigonal planar
Angular
BCl3
SO2
4
sp3
AX4
AX3E
AX2E2
Tetrahedral
Tetrahedral
Trigonal pyramidal
Angular
CH4
NH3
H2O
5
sp3d
AX5
AX4E
AX3E2
AX2E3
Trigonal bipyramidal
Trigonal bipyramidal
Seesaw
T-shaped
Linear
PBr5
SF4
ClF3
XeF2
6
sp3d2
AX6
AX5E
AX4E2
Octahedral
Octahedral
Square pyramidal
Square planar
SF6
BrF5
XeF4
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6.
*****
Multiple Bonds
 σ (sigma) bond: The first covalent bond formed
by end-to-end overlap of standard or
hybridized orbitals between the bonded atoms:
s + s, s + p, p + p (end-to-end), s + hybrid orbital
p + hybrid orbital, hybrid orbital + hybrid orbital
 π (Pi) bond: The second (and third, if present)
bond in a multiple bond, results from side-by-side
overlap of unhybridized p orbitals:
p + p (side-by-side)
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
σ bonding and π bonding
* The electron density on internuclear axis, π bond
less than σ bond. Therefore, π bond makes
weaker overlap than σ bond.
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
Single Bond and Multiple Bonds
-
Single bonds:
Double bond:
Triple bond:
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one σ bond
one σ bond and one π bond
one σ bond and two π bonds
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 VB theory of bonding in ethylene (H2C=CH2)
example of sp2 hybridization and a double bond
• Lewis structure
• A π-bond has two
lobes (above and
below plane), but
is one bond,
side-by-side
overlap of 2p–2p
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Continued
• All six atoms in
C2H4 lie in the
same plane
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 VB theory of bonding in Acetylene (HCCH)
example of sp hybridization and a triple bond
• Lewis structure
• Two π-bonds
from 2p–2p
overlap
forming a
cylinder of πelectron
density
around the
two carbon
atoms
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Continued
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 VB theory of bonding in Formaldehyde (H2C=O)
example of sp2 hybridization and a double bond
• Lewis structure
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Continued
lonelone σ
π
σ
π
σ σ
• Valence bond
model
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 Resonance Structures, Delocalization, and π
Bonding
 Localized or Delocalized Electrons
• Localized electrons: Bonding electrons (σ or π)
that are specifically shared between two atoms.
• Delocalized electrons: Electrons that are spread
over a number of atoms in a molecule or a crystal
rather than localized on a single atom or a pair of
atoms.
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 Delocalized π bonds in benzene
Benzene, total of 30 valence
electrons, 24 valence form the σ
bonds, 6 C(sp2)-C(sp2) and 6 C(sp2)H(1s)
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The remaining six valence electrons
occupy these six pπ orbitals
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Continued
benzene has a six-electron π system
delocalized among the six carbon
atoms.
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 Delocalized π bonds in NO3-
NO3-, total of 24 valence electrons,
12 as nonbonding pairs and 6 σ
bonds (3 C(sp2)-N(sp2) bonds)
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Continued
Delocalized the six-electron π
system in NO3-.
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8. Molecular Orbital Theory: Electron Delocalization
Chemical Bond
 Molecular Orbital (MO): A model of chemical
bonding in which electrons reside in molecular
orbitals delocalized over the entire molecule.
• The molecular orbitals are linear combinations of
atomic orbitals (LCAO).
• Because the orbitals are wave functions, the waves
can combine either constructively or
destructively.
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 MOs formed by combining two 1s AOs
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*****
 LCAO–MO Theory:
• The total number of MOs formed from a particular
set of AOs always equals the number of AOs in the
set.
• When two AOs combine to form two MOs, one MO
is lower in energy (the bonding MO) and the other is
higher in energy (the antibonding MO).
• When assigning the electrons of a molecule to MOs,
fill the lowest energy MOs first with a maximum of
two spin-paired electrons per orbital.
• When assigning electrons to two MOs of the same
energy, follow Hund’s rule—fill the orbitals singly
first, with parallel spins, before pairing.
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 Applications of MOs
• Estimate the bond order:
Bond Order (BO) =
(Σ bonding e– － Σ antibonding e–)/2
• Predict the existence of molecule
• Estimating bond length and bond energy
• Predicting magnetic properties
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
*****
1st Period Homonuclear Diatomic MOs
H2 and He2 for example:
σ1s*
AOs of H
(two 1s AOs)
σ1s
MOs of H2
BO = (2−0)/2 = 1
H2 molecule does exist
Diamagnetic
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Chapter 09
σ1s*
AOs of He
(two 1s AOs)
σ1s
MOs of He2
BO = (2−2)/2 = 0
He2 molecule does not exist
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8. Period 2 Diatomic Molecules
 MOs formed by combining two set 2p AOs
 σ2p and σ2p*:
end-to-end
overlap of
AOs
 π2p and π2p*:
side-by-side
overlap of
AOs
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
2nd Period Homonuclear Diatomic MOs
* Effects of 2s–2p Mixing: Increasing energy difference,
decreasing the degree of mixing.
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*****
Continued
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 Predicting magnetic properties by MOs
Lewis structure  Experiment
For O2:
showed O2 is
..
..
paramagnetic
.. O O ..
 MO prove O2
have unpaired
electrons
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

2nd Period Heteronuclear Diatomic MOs
NO for example
• Oxygen is more electronegative
than nitrogen, so its atomic
orbitals are lower in energy than
nitrogen’s atomic orbitals.
• The lower energy atomic orbital
makes a greater contribution to
the bonding molecular orbital
and the higher energy atomic
orbital makes a greater
contribution to the antibonding
molecular orbital.
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End of Chapter 09
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