Bonding in Molecules

1
Bonding in Molecules Covalent Bonding
The term covalent implies sharing of electrons
between atoms.
Valence electrons and valence shell orbitals

• Only valence electrons are used for bonding
  ns, np, nd
• Core electrons are held too tightly (too low
  in energy)
• Filled nd orbitals are considered core electrons

Valence state electron configurations and
Promotion Energies
- The promotion energy is the energy required to
promote electrons from the ground state to a
valence state, which is one type of excited
state configuration that is used for bonding.
C
E.g. C
2s1
2p3
2s2
2p2
ground state
valence state
2
Localized Bonding Models
Localized implies that electrons are confined to
a particular bond or atom.
The Lewis approach to bonding Pairs of electrons
are localized in bonds or as non-bonding lone
pairs on atoms. Each bond is formed by a pair
of electrons shared by two atoms.
G.N. Lewis
Octet rule most main group atoms will tend to
end up with an ns2 np6 electron
configuration. This is mostly true for the
molecules of organic chemistry not necessarily
for inorganic compounds.
3
Rules for drawing Lewis diagrams

• a. Pick the central atom.
• - Atoms that are present only once in the
  formula, especially heavy elements and metals,
  tend to be at the center of the structure.
• - Oxygen is often terminal and hydrogen almost
  always is.
• - Often the formula is written with the central
  atom first.
• (Sometimes there may be more than one central
  atom.)
• Write out the valence shell electron
  configurations for the neutral central atom and
  the "terminal" atoms in their ground states.
• c. If there is a negative charge distribute it
  among the terminal atoms in the first instance.
  Bear in mind that all the terminal atoms must
  make at least one covalent bond with the central
  atom, so do not create any noble gas
  configurations on them. Positive charge is best
  initially assigned by removing electrons from the
  central atom.
• The total number of unpaired electrons on the
  terminal atoms will have to match the number of
  unpaired electrons on the central atom to account
  for the bonds and leave no unpaired electrons. If
  this is not the case, once the first three steps
  have been carried out, there are two strategies
  available
• Move electrons between the central atom and the
  terminal atoms as necessary. Make sure you keep
  track of the formal charges because you must be
  specific about their location. Enclosing a Lewis
  structure in brackets with the charge outside is
  not acceptable.
• f. If and only if the central atom comes from the
  second period or below (Na onwards, n3 and up),
  electrons can be placed into the nd subshell.
  (Whether the d orbitals play a significant role
  in bonding in main group compounds is debatable,
  but they do help to predict correct structure
  without invoking canonical structures with
  unreasonable charge separations.)

4
Typical Lewis structural types
Molecules that conform to the Octet Rule
saturated molecules
NH3
CH4
2s
2p
2s
2p
C
ground state
N
C
valence state
3 H
4 H
These are typical of the molecules of organic
chemistry.
5
Molecules that conform to the Octet Rule
unsaturated molecules.
NO3-
ClNO
2s
2p
2s
2p
N
N
N
O
Cl
O
2s
2p
3s
3p
2s
2p
O-
2s
2p
O-
2s
2p
6
Resonance
Resonance implies that there is more than one
possible way to distribute the valence electrons
in a Lewis structure. For an adequate
description, each canonical structure must be
drawn.
If different equivalent resonance structures are
possible, the molecule tends to be more stable
than one would otherwise expect. This is a
quantum mechanical effect that we will talk about
later.
I expect you to be able to Draw Lewis
structures (including resonance structures when
necessary), determine bond orders, determine and
place formal charges.
Less favourable canonical structure
7
Molecules that dont conform to the Octet Rule
Electron-deficient molecules
Expanded valence shell molecules
ClF3
BH3
3s
3p
Cl
2s
2p
3d
B
Cl
B
F
2s
2p
3 H
F
2s
2p
F
2s
2p
Hypervalent molecules
Lewis acids
8
Valence Shell Electron Pair Repulsion Theory
A basic geometry can be assigned to each
non-terminal atom based on the number of
objects attached to it. Objects include bonded
atoms (single, double, triple, partial bonds) and
lone pairs of electrons. VSEPR theory lets
us predict the shape of a molecule based on the
electron configurations of the constituent atoms.
It is based on maximizing the distance between
points on a spherical surface.
9
The geometry around an atom is described by the
general formula AXmEn Where X is a bonded
atom, E is a lone pair and (mn) is the number of
objects (sometimes called the steric number, SN)
around the central atom A.
10
Less common geometries
Xe-
F
F
F
F
F
Xe is described as AX5E2 and has a pentagonal
planar shape derived from the pentagonal
bipyramidal geometry.
XeF5-
NMe4
11
Refinement of VSEPR theory predicted geometries
The relative steric demand of objects is
different and amount of repulsion caused by the
object will alter the arrangement of the atoms
around the central atom.
CH4
Lone pair of electrons
109.5
Multiple bond polarized toward central atom
NH3
Increasing steric demand
106.6
Normal single bond
OH2
Long single bond polarized away from central atom
104.5
12
Valence Bond Theory
Valence bond theory (VBT) is a localized quantum
mechanical approach to describe the bonding in
molecules. VBT provides a mathematical
justification for the Lewis interpretation of
electron pairs making bonds between atoms. VBT
asserts that electron pairs occupy directed
orbitals localized on a particular atom. The
directionality of the orbitals is determined by
the geometry around the atom which is obtained
from the predictions of VSEPR theory.
In VBT, a bond will be formed if there is overlap
of appropriate orbitals on two atoms and these
orbitals are populated by a maximum of two
electrons.
? bonds have a node on the inter-nuclear axis
and the sign of the lobes changes across the axis.
? bonds symmetric about the internuclear axis
13
Valence Bond Theory
Detailed valence bond theory treatment of bonding
in H2.
VBT considers the interactions between separate
atoms as they are brought together to form
molecules.
HA 1s1
HB 1s1
electron
?B (2)
?A (1)
Atomic wavefunction on atom B
?1 ?A(1) ?B(2)
Quantum mechanics demands that electrons can be
interchangeable so we must use a linear
combination of ?1 and ?2.
?2 ?A(2) ?B(1)
? N (?1 ?2) (bonding, H-H)
?3 ?A(1) ?A(2) (ionic H- H)
?- N (?1 - ?2) (anti-bonding)
?4 ?B(1) ?B(2) (ionic H H-)
?molecule N ?1 ?2 (C ?3
?4) ?molecule N ?covalent (C ?ionic)
N is a normalizing coefficient C is a coefficient
related to the amount of ionic character
14
Valence Bond Theory
Valence bond theory treatment of bonding in H2
and F2 the way it is generally used.
F
2s
2p
HA 1s1
HB 1s1
F
?A a
?B b
2s
2p
Z axis
2pz
2pz
This gives a 2p-2p ? bond between the two F atoms.
This gives a 1s-1s ? bond between the two H atoms.
For VBT treatment of bonding, people generally
ignore the anti-bonding combinations and the
ionic contributions.
15
Valence bond theory treatment of bonding in O2
Z axis
2pz
2pz
This gives a 2p-2p ? bond between the two O atoms.
Z axis
2py
(the choice of 2py is arbitrary)
2py
Double bond ? bond ? bond Triple bond ? bond
2 ? bond
This gives a 2p-2p ? bond between the two O
atoms. In VBT, ? bonds are predicted to be
weaker than ? bonds because there is less
overlap.
16
Directionality
The bonding in diatomic molecules is adequately
described by combinations of pure atomic
orbitals on each atom. The only direction that
exists in such molecules is the inter-nuclear
axis and the geometry of each atom is undefined
in terms of VSEPR theory (both atoms are
terminal). This is not the case with polyatomic
molecules and the orientation of orbitals is
important for an accurate description of the
bonding and the molecular geometry.
Examine the predicted bonding in ammonia using
pure atomic orbitals
2s
2p
N
The 2p orbitals on N are oriented along the X, Y,
and Z axes so we would predict that the angles
between the 2p-1s ? bonds in NH3 would be 90.
We know that this is not the case.
3 H
106.6
17
Hybridization
The problem of accounting for the true geometry
of molecules and the directionality of orbitals
is handled using the concept of hybrid orbitals.
Hybrid orbitals are mixtures of atomic orbitals
and are treated mathematically as linear
combinations of the appropriate s, p and d atomic
orbitals.
Linear sp hybrid orbitals
A 2s orbital superimposed on a 2px orbital
The two resultant sp hybrid orbitals that are
directed along the X-axis (in this case)
The 1/?2 are normalization coefficients.
18
Orthogonality and Normalization
Two properties of acceptable orbitals
(wavefunctions) that we have not yet considered
are that they must be orthogonal to every other
orbital and they must be normalized. These
conditions are related to the probability of
finding an electron in a given space.
Orthogonal means that the integral of the product
of an orbital with any other orbital is equal to
0, i.e.
where n ? m and dt means that the integral is
taken over all of space (everywhere).
Normal means that the integral of the product of
an orbital with itself is equal to 1, i.e.
This means that we must find normalization
coefficients that satisfy these conditions. Note
that the atomic orbitals (?) we use can be
considered to be both orthogonal and normal or
orthonormal.
19
Example of the orthogonality of ?1 and ?2
Thus our hybrid sp orbitals are orthogonal to
each other, as required.
20
Hybridization
Valence bond theory treatment of a linear
molecule the bonding in BeH2
BeH2
The promotion energy can be considered a part of
the energy required to form hybrid orbitals.
2s
2p
Be
Be
sp
2p
Be (sp)
2 H
The overlap of the hybrid orbitals on Be with the
1s orbitals on the H atoms gives two Be-H (sp)-1s
? bonds oriented 180 from each other. This
agrees with the VSEPR theory prediction.
21
Valence bond theory treatment of a trigonal
planar molecule the bonding in BH3
2s
2p
B
B
sp2
2p
B (sp2)
This gives three sp2 orbitals that are oriented
120 apart in the xy plane be careful the
choice of axes in this example determines the set
of coefficients.
22
Valence bond theory treatment of a trigonal
planar molecule the bonding in BH3
sp2
2p
B
3 H
The overlap of the sp2 hybrid orbitals on B with
the 1s orbitals on the H atoms gives three B-H
(sp2)-1s ? bonds oriented 120 from each other.
This agrees with the VSEPR theory prediction.
23
Valence bond theory treatment of a tetrahedral
molecule the bonding in CH4
2p
2s
C
C
sp3
C (sp3)
This gives four sp3 orbitals that are oriented in
a tetrahedral fashion.
24
Valence bond theory treatment of a tetrahedral
molecule the bonding in CH4
2p
2s
C
C
sp3
C (sp3)
4 H
The overlap of the sp3 hybrid orbitals on C with
the 1s orbitals on the H atoms gives four C-H
(sp3)-1s ? bonds oriented 109.47 from each
other. This provides the tetrahedral geometry
predicted by VSEPR theory.
25
Valence bond theory treatment of a trigonal
bipyramidal molecule the bonding in PF5
3s
3p
PF5 has an VSEPR theory AX5 geometry so we need
hybrid orbitals suitable for bonds to 5 atoms.
ns and np combinations can only provide four, so
we need to use nd orbitals (if they are
available).
P
3d
P
P (sp3d)
3d
3dz2
3pz
3py
3px
3s
sp3dz2
The appropriate mixture to form a trigonal
bipyramidal arrangement of hybrids involves all
the ns and np orbitals as well as the ndz2
orbital.
26
Valence bond theory treatment of a trigonal
bipyramidal molecule
The orbitals are treated in two different sets.
These coefficients are exactly the same as the
result for the trigonal planar molecules because
they are derived from the same orbitals (sp2)
These coefficients are similar to those for the
sp hybrids because they are formed from a
combination of two orbitals (pd).
Remember that d orbitals are more diffuse than s
or p orbitals so VBT predicts that the bonds
formed by hybrids involving d orbitals will be
longer than those formed by s and p hybrids.
27
Valence bond theory treatment of a trigonal
bipyramidal molecule the bonding in PF5
P (sp3d)
3d
F
2s
2p
F
F
2s
2p
2s
2p
F
2s
2p
F
2s
2p
The overlap of the sp3d hybrid orbitals on P with
the 2p orbitals on the F atoms gives five P-F
(sp3d)-2p ? bonds in two sets the two axial
bonds along the z-axis (180 from each other) and
three equatorial bonds in the xy plane (120 from
each other and 90 from each axial bond). This
means that the 5 bonds are not equivalent!
28
An alternative, and maybe more reasonable,
version of VBT treatment of a trigonal
bipyramidal molecule
The d orbitals are too high in energy to mix
effectively with the s and p orbitals, so the
trigonal bipyramidal molecule is actually
composed of an equatorial set of trigonal (sp2)
hybrids and the axial bonds come from an MO
interaction between the two ligand orbitals and
the pz orbital on the central atom.
29
The square pyramidal AX5 geometry requires mixing
with a different d orbital than in the trigonal
bipyramidal case.
Sb(C6H5)5
d orbitals
You should consider what orbital(s) would be
useful for such a geometry and we will see a way
to figure it out unambiguously when we examine
the symmetry of molecules.
30
Valence bond theory treatment of an octahedral
molecule the bonding in SF6
3s
3p
S
3d
S
S (sp3d2)
3d
F
F
F
F
F
F
3dz2
3pz
3py
3px
3s
sp3d2
3dx2-y2
The overlap of the sp3d2 hybrid orbitals on S
with the 2p orbitals on the F atoms gives six S-F
(sp3d2)-2p ? bonds 90 from each other that are
equivalent. You can figure out the normalization
coefficients. As in the case of the TBP, there
is also an MO approach that does not require d
orbitals.
31
Valence bond theory treatment of p-bonding the
bonding in ClNO
2s
2p
N
sp2
2p
There are three objects around N so the
geometry is trigonal planar. The shape is given
by AX2E (angular or bent).
N(sp2)
?
?
?
Cl
O
3s
3p
2s
2p
A drawing of the VBT p bond in ClNO.
The overlap of the sp2 hybrid orbitals on N with
the 3p orbital on Cl and the 2p orbital on O give
the two ? bonds and it is the overlap of the
left over p orbital on N with the appropriate
orbital on O that forms the (2p-2p) p bond
between the two atoms.
32
Valence bond theory treatment of p-bonding the
bonding in the nitrate anion
2s
2p
N
N
sp2
2p
There are three objects around N so the
geometry is trigonal planar. The shape is given
by AX3 (trigonal planar).
N(sp2)
?
O-
?
?
?
2s
2p
O-
2s
2p
O
VBT gives only one of the canonical structures at
a time.
2s
2p
The overlap of the sp2 hybrid orbitals on N with
the the 2p orbitals on the O give the three
(sp2-2p) ? bonds and it is the overlap of the
left over p orbital on N with the appropriate
orbital on the uncharged O atom that forms the
(2p-2p) p bond.
33
Valence bond theory treatment of p-bonding the
bonding in ethene
2s
2p
Each C
Each C
There are three objects around each C so the
geometry is trigonal planar at each carbon. The
shape is given by AX3 for each carbon.
sp2
2p
C(sp2)
?
2p
sp2
?
?
?
?
C(sp2)
?
4 H
The overlap of the sp2 hybrid orbitals on C with
the the 1s orbitals on each H give the four
terminal (sp2-1s) ? bonds. The double bond
between the C atoms is formed by a (sp2- sp2) ?
bond and the (2p-2p) p bond.
34
Valence bond theory treatment of p-bonding the
bonding in SOCl2
3s
3p
S
3d
S
There are four objects around S so the geometry
is tetrahedral and the shape is given by AX3E
(pyramidal).
sp3
3d
S(sp3)
?
?
?
?
O
Cl
Cl
2s
2p
The overlap of the sp3 hybrid orbitals on S with
the 3p orbitals on Cl and the 2p orbital on O
give the three ? bonds and, because the lone pair
is located in the final sp3 hybrid, it is the
overlap of the left over d orbital on S with an
appropriate p orbital on O that forms the (3d-2p)
p bond in the molecule.
35
Valence bond theory treatment of bonding a
hypervalent molecule, ClF3
3s
3p
Cl
3d
Cl
There are five objects around Cl so the
geometry is trigonal bipyramidal and the shape is
given by AX3E2 (T-shaped). Consider this Why
are such molecules T-shaped instead of pyramidal?
Cl (sp3d)
3d
F
F
F
The overlap of the sp3d hybrid orbitals on Cl
with the 2p orbitals on the F atoms gives three
P-F (sp3d)-2p ? bonds in two sets the two axial
bonds along the z-axis (less than 180 from each
other because of the repulsion from the lone
pairs) and the one equatorial bond halfway
between the other Cl bonds. Again, the bond
lengths will not be the same because there is
more d contribution to the axial hybrid orbitals.
36
Summary of Valence Bond Theory

• Write an acceptable Lewis structure for the
  molecule.
• Determine the number of VSEPR objects around all
  central atoms and determine the geometry around
  the atom.
• Construct hybrid orbitals suitable for the
  predicted bonding.
• Link orbitals together to make bonds.
• Describe the bonding. Include the names of the
  orbitals involved in each bond. Draw pictures of
  the bonds formed by the overlap of these orbitals.

Two objects around Be, so AX2 (linear)
Two orbitals pointing 180 from each other
needed, so use two sp hybrids
1s
sp
Two (sp-1s) Be-H ? bonds.