Chemical Bonding II
Lewis Theory-VSEPR
Valence Bond Theory
Molecular Orbital Theory
Lewis Theory
of
Molecular Shape and Polarity
Structure Determines Properties!
Properties of molecular substances depend on the
structure of the molecule.
The structure includes many factors, such as:
Skeletal arrangement of the atoms
Kind of bonding between the atoms
Shape of the molecule
Molecular Geometry
We can describe the shape of a molecule with terms that relate to
geometric figures
These geometric figures have characteristic “corners”
(indicating the positions of atoms)
The geometric figures also have characteristic angles that we call
bond angles.
Lewis Theory of Molecular Shapes
VSEPR Theory
Electron “groups” repel each other.
Predicting the shapes of molecules
1) The arrangement of the electron groups will be
determined by trying to minimize repulsions between them.
2) The arrangement of atoms (“molecular shape”)
surrounding a central atom will be determined by where the
bonding electron groups are.
3) “1” and “2” are not necessarily the same
Electron Groups
A Lewis structure predicts the number of valence
electron pairs around a central atom(s).
Each lone pair of electrons constitutes one
electron group on a central atom.
Each bond constitutes one electron group,
regardless of whether it is single, double, or triple
There are three electron groups
around S:
O
S
O
one lone pair
one single bond
one double bond
Electron Group Geometry
There are five basic arrangements of electron groups
around a central atom.
For molecules that exhibit resonance, it doesn’t matter
which resonance form you use – the electron group
geometry will be the same.
Electron Group Geometries
Molecular Shapes
linear
tetrahedral
trigonal planar
trigonal
bipyramidal
octahedral
Molecular Geometry
1) The actual geometry (“molecular geometry”) of a
molecule may be different from the electron geometry.
2) When the electron groups are attached to atoms of
different size, or when the bonding to one atom is
different than the bonding to another, this will affect
the molecular geometry around the central atom.
3) Lone pairs occupy space on the central atom, but are
not “seen” as points on the molecular geometry.
Not Quite Perfect Geometry
Because the bonds and atom sizes are not
identical in formaldehyde, the observed
angles are slightly different from ideal.
The Effect of Lone Pairs
The bonding electrons
are shared by two
atoms, so some of the
negative charge is
removed from the
central atom.
The nonbonding
electrons are localized
on the central atom, so
area of negative charge
takes more space.
The Effect of Lone Pairs
Lone pair groups “occupy more space” on the central atom
than bonding electrons.
Relative sizes of repulsive force interactions:
Lone Pair – Lone Pair >
Lone Pair – Bonding Pair >
Bonding Pair – Bonding Pair
This affects the bond angles, making the bonding pair –
bonding pair angles smaller than expected.
Molecular geometries derived from
tetrahedral electron geometry.
Molecular geometries derived from trigonal
bipyramidal electron geometry.
Molecular geometries derived from
octahedral electron geometry.
Predicting the Shapes
Around Central Atoms
1. Draw the Lewis structure
2. Determine the number of electron groups around
the central atom
3. Classify each electron group as bonding or lone
pair, and count each type
4. Determine the shape and bond angles
Molecules with Multiple Central Atoms
Methanol
H
H
O
N
C
C
H
H
Glycine
O
H
Polarity of Molecules
Polarity of Molecules
For a molecule to be polar, it must
have polar bonds, and
have an unsymmetrical shape
Polarity affects the intermolecular forces of attraction
and therefore affects boiling points and solubilities
Nonbonding pairs affect molecular polarity.
Molecular Polarity
The H─Cl bond is polar. The bonding electrons are
pulled toward the Cl end of the molecule. The net result
is a polar molecule.
Adding Dipole Moments to Determine
Whether a Molecule is Polar
Some molecules are inherently polar because of the atoms which
they contain and the arrangement of these atoms in space.
H2 O
δ−
NH3
δ+
CH2O
HCl
A crude representation
of a polar molecule
Other molecules are considered nonpolar
CH4
BH3
C 2 H2
Nonpolarized
electron
clouds
CO2
What about Tetrahedral Geometry ?
Molecular Formula
➡
Structural Formula
➡
Dot Diagram
➡
Molecular Shape
➡
Intermolecular Forces
Molecular Polarity
Melting Point, Boiling Point, Solubility
Chemical Bonding
Lewis Theory-VSEPR
Valence Bond Theory
Molecular Orbital Theory
Problems with Lewis Theory
Lewis theory generally predicts trends in properties,
but does not give good numerical predictions.
Lewis theory gives good first approximations of the
bond angles in molecules, but usually cannot be
used to get actual bond angles.
Lewis theory cannot write one correct structure for
many molecules where resonance is important.
Lewis theory often does not predict the correct
magnetic behavior of molecules.
Valence Bond Theory
Linus Pauling and others applied the principles of
quantum mechanics to molecules.
They reasoned that bonds between atoms would
occur when the atomic orbitals interacted to
make new bonds.
The types of interactions depend on whether the
orbitals align along the axis between the nuclei, or
outside the axis.
Orbital Interaction
As two atoms approached, the half-filled valence
atomic orbitals on each atom would interact
to form molecular orbitals.
The molecular orbitals would be more stable than
the separate atomic orbitals because they would
contain paired electrons shared by both atoms.
Orbital Diagram for the
Formation of H2S
H
S
H
H
1s
↑
↑↓
↑↓
1s
↑
H
3s
↑
H─S bond
↑ ↑↓ S
3p
↑↓
H─S bond
Orbital Diagram for the
Formation of H2S
Predicts bond angle = 90°
Actual bond angle = 92°
“Unhybridized” C Orbitals Predict the
Wrong Bonding & Geometry
H
1s
H
1s
C
2s
2p
Valence Bond Theory – Hybridization
The number of partially filled or empty atomic orbitals
does not always predict the number of bonds or
orientation of bonds.
Ex: C = 2s22px12py12pz0 would predict two or three
bonds that are 90° apart.
For carbon what is actually observed are four bonds
that are 109.5° apart.
To adjust for these inconsistencies, it was postulated
that the valence atomic orbitals hybridize
before bonding took place.
Unhybridized C Orbitals Predict the
Wrong Bonding & Geometry
Valence Bond Theory - Main Concepts
Valence electrons of the atoms in a molecule reside in
quantum-mechanical atomic orbitals. The orbitals
can be the standard s, p, d, and f orbitals, or they may
be hybrid combinations of these.
A chemical bond results when two of these atomic
orbitals interact and there is a total of two
electrons in a new molecular orbital.
The shape of the molecule is determined by the
geometry of the interacting orbitals.
Hybridization
Hybridizing is mixing different types of orbitals in the
valence shell to make a new set of degenerate orbitals
# of new orbitals-----> 2, 3, 4, 5,
6
orbital designation---> sp, sp2, sp3, sp3d, sp3d2
The same type of atom can have different types of
hybridization:
C = sp, sp2, sp3
The particular kind of hybridization that occurs is the one
that yields the lowest overall energy for the molecule.
The sp Hybrid Orbitals in Gaseous BeCl2
Cl
Be Cl
The sp2 Hybrid Orbitals in BF3
F
B
F
F
The sp3 Hybrid Orbitals in CH4
The sp3d Hybrid Orbitals in PCl5
The sp3d2 Hybrid Orbitals in SF6
sp3 Hybridization
Atom with four electron groups around it
tetrahedral electron group geometry
~109.5° angles between hybrid orbitals
tetrahedral molecular geometry for carbon
trigonal pyramidal geometry for nitrogen
bent geometry for oxygen
Atom uses hybrid orbitals for all bonds & lone pairs
Bonding in Methane (Valence Bond Explanation)
Hybridization and VSEPR Theory
sp3 hybridization
tetrahedral
sp3 hybridization
trigonal pyramidal
sp3 hybridization
bent
sp3 Hybridized Atoms
Place electrons into hybrid and unhybridized valence orbitals as if
all the orbitals have equal energy
2s
↑↓
2s
↑↓
2s
↑ ↑ ↑
2sp3
C
↑ ↑ ↑
2sp3
N
↑ ↑↓ ↑ ↑
2sp3
O
↑ ↑
2p
↑
↑ ↑ ↑
2p
↑
↑↓ ↑ ↑
2p
↑
↑↓
sp3 hybridized atom
↑
Unhybridized atom
Bonding with Valence Bond Theory
Bonding takes place between atoms when their
atomic or hybrid orbitals interact (“overlap”).
To interact, the orbitals must either be aligned
along the axis between the atoms, or
The orbitals must be parallel to each other and
perpendicular to the interatomic axis.
Types of Bonds
Sigma (σ) bond - when the interacting atomic orbitals
point along the axis connecting the two bonding nuclei
Pi (π) bond - when the bonding atomic orbitals are parallel
to each other and perpendicular to the axis connecting the
two bonding nuclei
The interaction between parallel orbitals is not as strong as
between orbitals that point at each other;
Therefore, σ bonds are stronger than π bonds.
Types of Bonds
Carbon Hybridizations
Unhybridized
↑↓
↑
↑↓
↑
↑↓
2s
↑
↑
↑
↑
↑
2p
↑
↑
2 sp3
sp2 hybridized
↑
↑ ↑
2sp2
sp hybridized
↑
↑
2p
2s
Unhybridized
sp3 hybridized
2p
2s
Unhybridized
↑
2sp
↑
2p
↑
↑
2p
Different Carbon Hybridizations Lead
to Different Molecular Geometries
sp3
sp2
electron density
sp
sp2 Hybridization
Atom with three electron groups around it
trigonal electron group planar system
~120° bond angles - flat
C = trigonal planar molecular geometry
N = bent molecular geometry
O = linear geometry
Atom uses hybrid orbitals for σ bonds and lone pairs
Atom uses a nonhybridized p orbital for a π bond
sp2 Hybridized Atoms
Orbital Diagrams
Unhybridized atom
↑↓
2s
↑↓
2s
↑ ↑ ↑
2p
↑↓ ↑ ↑
2p
↑
↑ ↑
2sp2
↑
↑ ↑
2sp2
↑
2s
↑ ↑
2p
↑
↑↓
sp2 hybridized atom
↑ ↑↓ ↑
2sp2
↑
2p
↑
2p
↑
2p
C
N
O
H
Ethene, CH2CH2
H
C
C
H
↑
↑
↑
σ
σ
↑
C
↑
sp2
1s H 1s H
σ
pC
↑
↑
↑
sp2 C
↑
σ
σ
↑
pC
π
↑
↑
H
1s H 1s H
Bonding in Ethene, C2H4
π
π
Bond Rotation
Rotation around a σ bond does not require breaking the
interaction between atomic orbitals.
Rotation around a π bond requires the breaking of the
interaction between atomic orbitals.
Restricted Rotation Around
π-bonded Atoms in C2H2Cl2
no
net
dipole
sp hybridization
Atom with two electron groups
linear shape
180° bond angle
Atoms use hybrid orbitals for σ bonds or lone pairs
Atom use nonhybridized p orbitals for π bonds
sp Hybridized Atoms
Orbital Diagrams
Unhybridized atom
2s
↑↓
2s
↑ ↑
2p
↑ ↑
2sp
↑ ↑ ↑
2p
↑
↑
↑↓
sp hybridized atom
↑
2sp
↑ ↑
2p
↑ ↑
2p
C
C
N
HCCH (C2H2) Orbitals
↑
pC
↑
sσ
↑
σ
↑
C
↑
H
pC
↑
↑
sσ
↑
↑
sp C
↑
2π
C
H
1s H
1s H
sp C
Bonding in C2H2
Bonding in C2H2
sp3d hybridization
Atom with five electron groups around it
trigonal bipyramidal electron geometry
Seesaw, T–Shape, Linear
120° & 90° bond angles
Uses empty d orbitals from valence shell
d orbitals can be used to make π bonds
sp3d hybridization
sp3d hybridization
Unhybridized atom
↑↓
3s
↑↓
↑ ↑ ↑
3p
3s
↑↓ ↑ ↑
3p
↑↓
↑↓ ↑↓ ↑
4s
4p
sp3d hybridized atom
↑
3d
↑ ↑ ↑
3sp3d
↑↓ ↑
3d
↑ ↑
↑
P
↑
S
3sp3d
↑↓ ↑↓ ↑ ↑ ↑
4d
4sp3d
(non-hybridizing d orbitals not shown)
Br
3
sp d
hybridization
F
F
F
F
F
F
As
F
Br
S
F
F
F
F
F
sp3d2 hybridization
Atom with six electron groups around it
octahedral electron geometry
Square Pyramid, Square Planar
90° bond angles
Use empty d orbitals from valence shell.
d orbitals can be used to make π bonds.
sp3d2 hybridization
sp3d2 Hybridized Atoms
Orbital Diagrams
Unhybridized atom
↑↓
↑↓ ↑ ↑
3s
3p
↑↓
↑↓ ↑↓ ↑
4s
4p
sp3d2 hybridized atom
↑ ↑ ↑ ↑ ↑ ↑
3d
3sp3d2
↑↓ ↑ ↑ ↑ ↑
4d
S
↑
Br
4sp3d2
↑↓ ↑↓
↑↓ ↑↓
↑↓ ↑↓
↑↓
↑ ↑↑↑ ↑↑ ↑↑ ↑↑ ↑ Xe
↑↓ ↑↓
↑↓ ↑↓
↑ ↑
3d 2
33d224d
4p
4p
4s
4s
4p
4s
4sp
4d
4sp
4d
5s
5p
5d
5sp d
sp3d2 hybridization
F
F
F
F
F
F
F
F
F
Br
S
F
F
F
F
Xe
F
F
Predicting Hybridization and
Bonding Scheme
1. Start by drawing the Lewis structure
2. Use VSEPR Theory to predict the electron group
geometry around each central atom.
3. Select the hybridization scheme that matches the
electron group geometry.
4. Sketch the atomic and hybrid orbitals on the atoms
in the molecule, showing overlap of the appropriate
orbitals
5. Label the bonds as σ or π
Predict the hybridization and
bonding scheme for CH2CH2
1.! Start by drawing the Lewis
structure
2.! Use VSEPR Theory to
predict the electron group
geometry around each
central atom
The molecule has two interior
atoms. Since each atom has
three electron groups (one
double bond and two single
bonds), the electron geometry
about each atom is trigonal
planar.
Predict the hybridization and
bonding scheme for CH2CH2
3. Select the hybridization
scheme that matches
the electron group
geometry
C1 = trigonal planar
C1 = sp2
C2 = trigonal planar
C2 = sp2
4.! Sketch the atomic and
hybrid orbitals on the
atoms in the molecule,
showing overlap of the
appropriate orbitals
continued…
Predict the hybridization and
bonding scheme for CH2CH2
5.! Label the bonds as σ or π
π
H
H
C
C
H
H
σ
Predict the hybridization and
bonding scheme for CH3CHO
1.! Start by drawing the Lewis
structure
2.! Use VSEPR Theory to
predict the electron group
geometry around each
central atom
2
1
C2 = 4 electron areas
C2= tetrahedral
C1 = 3 electron areas
C1 = trigonal planar
Predict the hybridization and
bonding scheme for CH3CHO
3. Select the hybridization
scheme that matches
the electron group
geometry
4.! Sketch the atomic and
hybrid orbitals on the
atoms in the molecule,
showing overlap of the
appropriate orbitals
2
1
C2 = tetrahedral
C2 = sp3
C1 = trigonal planar
C1 = sp2
Predict the hybridization and
bonding scheme for CH3CHO
2
1
5.! Label the bonds as σ or π
π
H
H
O
C
C
H
H
σ
Chemical Bonding
Lewis Theory-VSEPR
Valence Bond Theory
Molecular Orbital Theory
Problems with Valence Bond
Theory
VB theory predicts properties better than Lewis theory
bonding schemes, bond strengths, lengths, rigidity
There are still properties it doesn’t predict perfectly
magnetic behavior of certain molecules
strength of bonds
VB theory presumes the electrons are localized in orbitals
doesn’t account for delocalization
Molecular Orbital Theory
In MO theory, we apply Schrödinger’s wave equation to
the molecule to calculate a set of molecular orbitals.
The equation solution is estimated .
We start with good guesses as to what the orbitals should look
like, then test the estimate until the energy is minimized
The electrons belong to the whole molecule
orbitals are delocalized
LCAO
The simple guess starts with atomic orbitals of the
atoms adding together to make molecular orbitals,
the Linear Combination of Atomic Orbitals.
The waves can combine either constructively or
destructively.
Molecular Orbitals
When wave functions combine constructively, the
resulting molecular orbital has less energy than the
original atomic orbitals
it is called a Bonding Molecular Orbital
σ, π
most of the electron density between the nuclei
Amplitudes of wave functions added
Molecular Orbitals
When wave functions combine destructively, the
resulting molecular orbital has more energy than the
original atomic orbitals
it is called an Antibonding Molecular Orbital
σ*, π*
most of the electron density outside the nuclei
nodes between nuclei
Amplitudes of wave functions
subtracted.
Interaction of 1s Orbitals
Molecular Orbital Theory
Electrons in bonding MOs are stabilizing
lower energy than the atomic orbitals
Electrons in antibonding MOs are destabilizing
higher in energy than atomic orbitals
electron density located outside the internuclear axis
electrons in antibonding orbitals cancel stability gained by
electrons in bonding orbitals
Contours and energies of the bonding and
antibonding molecular orbitals (MOs) in H2.
Energy Comparisons of Atomic
Orbitals to Molecular Orbitals
Increasing
energy
Molecular Orbitals and Properties
Bond Order = difference between number of electrons in
bonding and antibonding orbitals
only need to consider valence electrons
may be a fraction
higher bond order = stronger and shorter bonds
If bond order = O, then bond is unstable compared to
individual atoms and no bond will form
A substance will be paramagnetic if there are unpaired
electrons in molecular orbitals
A Molecular Orbital Diagram - H2
antibonding MO
σ*
H·
1s
atomic
orbital
1s
atomic
orbital
σ
bonding MO
·H
A Molecular Orbital Diagram - H2
LUMO
lowest unoccupied
molecular orbital
σ*
H·
1s
atomic
orbital
1s
atomic
orbital
σ
HOMO
highest occupied
molecular orbital
·H
A Molecular Orbital Diagram - H2
σ*
H·
1s
atomic
orbital
1s
atomic
orbital
σ
=1
Because more electrons are in
bonding orbitals than are in antibonding orbitals,
there is a net bonding interaction.
·H
A Molecular Orbital Diagram - He2
σ*
He:
1s
atomic
orbital
1s
atomic
orbital
σ
=0
Because as many electrons are in
bonding orbitals as in antibonding orbitals,
no net bonding interaction.
He:
A Molecular Orbital Diagram - Li2
σ*
Li·
2s
atomic
orbital
2s
atomic
orbital
σ
σ*
1s
atomic
orbital
σ
1s
atomic
orbital
·Li
A Molecular Orbital Diagram - Li2
σ*
Li·
2s
atomic
orbital
2s
atomic
orbital
σ
=1
Because more electrons are in
bonding orbitals than are in antibonding orbitals,
there is a net bonding interaction.
·Li
Interaction
of p
Orbitals
Contour representations of the molecular orbitals formed by the 2p orbitals on two atoms.
Each time we combine two atomic orbitals, we obtain two molecular orbitals: one bonding
and one antibonding. In (a) the p orbitals overlap "head-to-head" to form and * molecular
orbitals. In (b) and (c) they overlap "sideways" to form and * molecular orbitals.
Molecular Orbitals - B2, C2, N2, O2, F2, Ne2,
A Molecular Orbital Diagram - O2
Oxygen
Atomic
Orbitals
2p
σ
!
!
π
Oxygen
Atomic
Orbitals
2p
O2 MO’s
π!
Because more electrons
are in bonding orbitals
than are in antibonding
orbitals, there is a net
bonding interaction.
σ!
σ
2s
BO = ½(8 be – 4 abe)
BO = 2
!
Because there are
unpaired electrons in the
antibonding orbitals,
O2 is predicted to be
paramagnetic
2s
σ"
Dioxygen ( O2 ) is Paramagnetic
Using MO Theory to Explain Bond Properties
As the following data show, removing an electron from
N2 forms an ion with a weaker, longer bond than in the
parent molecules, whereas the ion formed from O2 has
a stronger, shorter bond:
These facts can be explained by examining diagrams that
show the sequence and occupancy of MOs.
Using MO Theory to Explain Bond Properties
N2
bonding e- lost
N 2+
O2
σ
2p
σ
2p
π
2p
π
2p
σ2p
σ2p
π2p
π2p
σ
σ
2s
σ2s
1/2(8-2)=3
O2+
antibonding
e- lost
2s
σ2s
1/2(7-2)=2.5
1/2(8-4)=2
Bond orders
1/2(8-3)=2.5