Molecular Geometry

1

• Molecular Geometry
• Molecular shape is determined by the number of
  atoms in a molecule, how the atoms are
  connected, the separation between atoms and the
  number of non-bonded electron pairs on those
  atoms.
• These factors determine the arrangement of the
  atoms in three space that make up molecules.
• Lewis dot structures do not generally indicate
  molecular geometry only how the atoms in a
  molecule are connected and indicates something
  about the nature of the chemical bonds between
  those connected atoms.
• VSEPR theory Valence Shell Electron Pair
  Repulsion theory
• The basis of this theory comes from the Pauli
  Exclusion Principle
• In simple terms electron pairs on an atom,
  whether they are bonding or non-bonding, will
  arrange themselves so as to minimize
  electrostatic repulsion.
• 2 electron pairs linear 5 electron pairs
  trigonal bipyramidal
• 3 electron pairs trigonal planar 6 electron
  pairs octaheral
• 4 electron pairs tetrahedral
• Fig. 9.2, p 297, Brown, LeMay Bursten, shows
  the arrangements for molecules with formula ABn

2

• Molecular Geometry
• Predicting Molecular Geometries
• CH4 NH3
• Both molecules have 4 electron pairs attached to
  the central atom
• The arrangement of these 4 regions of electron
  density is such that they point to the corners
  of a regular tetrahedron
• Table 9.1, p. 298, shows the arrangements of
  electron pairs attached to a central atom,
  including angles between them.
• 2 electron pairs - linear, 180o
• 3 electron pairs - trigonal planar, 120o
• 4 electron pairs - tetrahedral, 109.5o
• 5 electron pairs - trigonal bipyramidal, 90o and
  120o
• 6 electron pairs - octahedral, 90o
• The molecular geometry gives the arrangement of
  the atoms in three space but does not include
  non-bonded electron pairs.
• The non-bonded electron pairs are important in
  determining the molecular geometry.

3

• Molecular Geometry
• For CH4 and NH3, both will have a tetrahedral
  electron-pair geometry
• However, CH4 has a tetrahedral molecular geometry
  whereas NH3 has a trigonal pyramidal molecular
  geometry.

4

• Molecular Geometry
• Steps in using VSEPR theory to predict
  structures
• Draw the Lewis dot structure for the molecule
• Count the number of electron pairs - both bonding
  and non-bonding - attached to the central atom.
• Arrange the atoms and non-bonding electron pairs
  so as to minimize electron-pair repulsions.
• Describe the molecular geometry in terms of the
  arrangement of the atoms attached to the
  central atom. The non-bonded electron pairs are
  not counted in stating the molecular geometry,
  even though they are important in determining
  the molecular geometry.
• Multiple bonds have the same effect as that of an
  electron pair bond in determining the basic
  molecular geometry.
• HCN
• Its really the number of regions of electron
  density on the central atom that is important
  in VSEPR theory.

5
Molecular Geometry Electron pair geometries and
molecular shapes
e- e-Pair Bonding nonbonding
Molecular Pairs Geometry Pairs
Pairs Type Geometry
Example 2 2
0 AX2E0 linear

linear 3 trigonal
3 0 AX3E0 trigonal
planar
planar
2 1 AX2E bent
6
Molecular Geometry Electron pair geometries and
molecular shapes
e- e-Pair Bonding nonbonding
Molecular Pairs Geometry Pairs
Pairs Type Geometry Example
4 tetrahedral 4
0 AX4E0 tetrahedral

3 1
AX3E1 trigonal pryamidal
2
2 AX2E2 bent
7
Molecular Geometry Electron pair geometries and
molecular shapes
e- e-Pair Bonding nonbonding
Molecular Pairs Geometry Pairs
Pairs Type Geometry Example
5 trigonal 5
0 AX5E0 trigonal
bipyramidal bipyramidal

4
1 AX4E1 seesaw
3
2 AX3E2 T-shaped
2
3 AX2E3 linear
8
Molecular Geometry Electron pair geometries and
molecular shapes
e- e-Pair Bonding nonbonding
Molecular Pairs Geometry Pairs
Pairs Type Geometry Example
6 octahedral 6
0 AX6 octahedral
5
1 AX5E1 square
pyramidal
4 2 AX4E2
square planar
9

• Molecular Geometry
• The effect of non-bonded electrons on the central
  atom is to distort the shape of a molecule from
  its ideal geometry.
• The distortion is caused because non-bonded
  electron pairs have a larger volume requirement
  than bonded electron pairs. Thus, non-bonded
  - single bond electron repulsions are greater
  than single bond - single bond repulsions
• Multiple bonds have more electrons than single
  bonds and so repulsions between multiple bonds
  and single bonds is greater than single bond -
  single bond repulsions

10

• Molecular Geometry
• Trigonal bypyramidal molecules with non-bonded
  electron pairs
• There are two kinds of sites in these molecules
  for bonded atoms and non- bonded electron pairs
• Groups in the trigonal plane have two 120o
  neighbors and two 90o neighbors.
• Groups in the axial positions have three 90o
  nearest neighbors
• Because non-bonded electron - bonded electron
  repusions are greater than bonded electron -
  bonded electron repusions, non-bonded electrons
  will find themselves in the equitorial trigonal
  plane of the trigonal bipyramid
• Molecules with more than one central atom are
  analyzed one atom at a time

11

• Molecular Geometry
• Electric Dipole moments whenever there is a
  charge separation in a molecule the molecule has
  an electric dipole moment. Molecules without any
  net charge separation within the molecule is
  nonpolar.
• All heteronuclear diatomic molecules are polar
  because of the electronegativity difference
  between the bonded atoms.

12

• Molecular Geometry
• Dipole moments for polyatomic molecules depend on
  the magnitude and direction of the individual
  bond dipole moments in a molecule.
• Dipole moments are vector quantities
• Both the magnitudes and directions of the
  individual moments must be summed.

CO2 is nonpolar because the two bond moments are
of equal magnitude but point in exactly the
opposite directions and cancel
Bond moment
H2O is polar because the two bond moments do not
cancel but co-add to give a net molecular dipole
moment
Bond moment
Total molecule moment
BF3 is nonpolar
NH3 is polar
CH4 is nonpolar
SF4 is polar
13

• Chemical Bonding Theory
• Valence bond theory is one of two methods of
  viewing how electrons are shared in covalent
  bonding.
• The quantum mechanical approach to valence bond
  theory is that the wave function associated with
  the shared electrons is made up from the atomic
  orbitals on the two bonded atoms so that their
  identity is retained.
• Electrons are localized in the region where the
  bond forms
• The atomic orbitals overlap so as to give a
  maximum in their overlap and put as much
  electron density as possible between the bonded
  atoms.
• H2 is a simple example each H atom has a 1s
  electron
• The two electrons are shared equally in each
  atoms 1s orbital
• For the heternuclear diatomic HF, the bond
  results from overlap of the 1s orbital on H and
  the half-filled p orbital on F

In terms of the valence bond theory, the bond is
formed by pairing the 1s electron from H with the
2p electron from F to form the electron pair bond.
14

• Chemical Bonding Theory
• Valence bond theory
• For H2O, one valence bond picture is that the 1s
  electrons on each H atom overlaps with two
  half-filled p orbitals on O to form two electron
  pair bonds.

For clarity, only the two 2p orbitals on O
involved in bonding are shown. There is also a 2s
and a third 2p valence orbital on O, each with a
pair of electrons. Note this picture predicts a
90o H-O-H bond angle in water. The actual bond
angle is 104.5o and the deviation could come from
the d charges on H due to the electronegativity
difference between H and O.

• For NH3 a similar picture gives three electron
  pair bonds from overlap of the three 1s
  electrons on each H atom and the three 2p
  orbitals on N each with one unpaired electron.

• N 1s22s22px12py12pz1
• This picture predicts
• The H-N-H bond angle of 90o giving a trigonal
  pramidal structure.
• The non-bonded valence electron pair is in a 2s
  orbital

15

• Chemical Bonding Theory
• Valence bond theory
• The bonding in carbon because the valence shell
  electron configuration is 2s22px12py1, we would
  expect the simplest compound between C and H
  would be CH2.
• This compound is known but is extremely reactive.
• CH4 is the compound between H and C with one atom
  of C per molecule.
• One way to explain this is to postulate that an
  excited electronic state of carbon forms

• Hybrid orbitals are formed by mixing the 2s
  orbital with the three 2p orbitals. These four
  new orbitals are degenerate

• The hybrid sp3 orbitals can form four CH bonds.
  These bonds point to the corners of a regular
  tetrahedron.

16

• Chemical Bonding Theory
• Valence bond theory
• The bonding in carbon
• One advantage of this scheme is that four bonds
  are formed between C and H instead of two bonds.
  Bond formation is exothermic and produces a more
  stable state for carbon and hydrogen. This
  process more than compensates for the energy
  required to form the hybrid orbitals.
• The four new sp3 orbitals are one fourth s and
  three-fourths p in character and are fatter
  than a p orbital.
• Each sp3 orbital has a nodal plane containing the
  nucleus. The lobes are not symmetrical in
  size like a p orbital.

17

• Chemical Bonding Theory
• Valence bond theory
• H2O revisited if the O is hybridized sp3,
• There are 2 electron pairs in two sp3 orbitals
  and two unpaired electrons in the other two sp3
  orbitals
• This allows for the formation of two bonds
  between H and O
• The H-O-H bond angle is predicted to be 109.5o,
  but its found to be 104.5o
• The decrease of 5.0o is due to non-bonded
  electron pair - bonded electron pair repulsions
  from the two pair of non-bonded electrons.
• This is easier to explain than the 14.5o increase
  from the earlier model not involving orbital
  hybridization.
• NH3 revisited if the N is hybridized sp3,,
• There is one electron pair in one of the sp3
  orbitals and three unpaired electrons in the
  other three sp3 orbitals.
• This allows for the formation of three bond
  between H and N
• The H-N-H bond angle is predicted to be 109.5o,
  but its found to be 107o
• The decrease is only 2.5o caused by repulsion
  between the non-bonded electron pair and the
  bonding pairs of electrons.

18

• Chemical Bonding Theory
• Valence bond theory
• BF3 Only three electron pair bonds are formed.
• The orbital hybridization scheme produces three
  electrons in three equivalent sp2 orbitals.
• Overlap between each sp2 orbital and a p orbital
  in F with one unpaired electron produces three
  electron pair bonds.
• The three sp2 orbitals point to the corners of a
  planar triangle.

For clarity, the non-bonding electrons on F are
not shown Note, there is a left over,
unhybridized p orbital on B. When BF3 reacts
with NH3, the NH3 provides the electrons for a
coordinate- covalent bond. In this case, B will
rehybidize to four sp3 orbitals
19

• Chemical Bonding Theory
• Valence bond theory
• BeCl2 Only two electron pair bonds are formed.
• The orbital hybridization scheme produces three
  electrons in two equivalent sp orbitals.
• Overlap between each sp orbital and a p orbital
  in Cl with one unpaired electron produces three
  electron pair bonds.
• The three sp orbitals point in a strait line.

• PCl5 sp3d

• SF6 sp3d2

20

• Chemical Bonding Theory
• Single bonds in the valence bond theory, single
  bonds are made up of atomic orbitals that are
  cylindrically symmetric about the line joining
  the bonded atoms.
• Such bonds are called sigma - s - bonds.
• Overlap of 2 s orbitals in H2
• Overlap of an s and a p orbital in HF
• Overlap of 2 p orbitals in F2
• Overlap of an s or p orbital with an spy hybrid
  orbital - BeCl2, CH4, PCl5, etc.
• Multiple bonds the second bond involves overlap
  of two p orbitals on different atoms that are
  perpendicular to the internuclear axis

The internuclear axis contains a nodal
plane Electron density is above and below the
nodal plane These bonds are called pi - p - bonds
Single bonds in valence bond theory are s
bonds. Double bonds in valence bond theory are
one s bond and one p bond. Triple bonds in
valence bond theory are one s bond and two p
bonds.
21

• Chemical Bonding Theory
• Multiple bond examples
• Ethylene

The 2 s bond from each C to H involve overlap of
C sp2 and H s orbitals The single s bond between
each C involves overlap of C sp2 orbitals The
single p bond between each C involve p overlap of
C unhybridized p orbitals
2 lobes of p bond
The p bond locks this molecule into a planar
structure all 6 atoms are in the same plane.
22

• Chemical Bonding Theory
• Multiple bonds example acetylene

The s bonds between C and H involve overlap of C
sp and H s orbitals The s bond between C and C
involve overlap of C sp orbitals The p bonds
between each C involve overlap of two pairs of
unhybridized p orbitals.
23

• Chemical Bonding Theory
• Delocalized p bonds When two or more resonance
  structures can be written involving p bonds, the
  p bonds can be represented as being spread out
  over the molecule where the p bonds occur.
• The electrons and the bonds containing them are
  delocalized.
• Example Benzene

Delocalized p bonds
24

• Chemical Bonding Theory
• Summary of Valence Bond Results
• Bonded atoms share one or more pairs of electrons
• At least one s bond exists between each pair of
  bonded electrons.
• s bonds are cylindrically symmetric along the
  internuclear axis and electrons are concentrated
  - localized - between the bonded atoms.
• An appropriate set of hybrid atomic orbitals is
  formed to form s bonds.
• The set of hybrid orbitals depends on the number
  of s bonds to be formed, the number of
  nonbonded electron pairs and the geometry of the
  molecule.
• AX2 type sp hybridization linear molecular
  geometry
• AX3 or AX2E type sp2 hybridization trigonal
  planar or bent geometry
• AX4, AX3E or AX2E2 type sp3 hybridization
  tetrahedral, trigonal pyramidal, bent molecular
  geometry.
• AX5, AX4E, AX3E2, AX2E3 type sp3d hybridization
  trigonal bipyramid, see saw, T shape or linear
  molecular geometry.
• AX6, AX5E, AX4E2 type sp3d2 hybridization
  octahedral, square pyramid, square planar
  molecular geometry.

25

• Chemical Bonding Theory
• Summary of Valence Bond Results
• Atoms sharing more than one pair of electrons
  form p bonds by sideways overlap of p atomic
  orbitals.
• p bonds have a nodal plane containing the
  internuclear axis
• In p bonds, electron density is concentrated
  above and below the nodal plane.
• Molecules with two or more resonance structure
  can have p bonds delocalized over more than two
  atoms.
• Molecular Orbital Theory (MO theory)
• This method deals with interactions of shared
  electrons in a different way.
• Molecular orbitals are formed in such a way that
  they cover the entire molecule.
• The method used is to form Linear Combinations of
  Atomic Orbitals - LCAOs
• There are 2 such combinations from any two
  orbitals
• yMO a1yAO 1 a2yAO 2
• yMO a1yAO 1 - a2yAO 2
• The as indicate how much of each AO is involved
  in yMO. In our case, the as are 1.

26

• Chemical Bonding Theory
• MO Theory
• Two results obtain from MO theory
• The shapes of the molecular orbitals can be
  determined.
• The energies of the molecular orbitals can be
  determined.
• Example H2 molecule

yMO y1s H1 y1s H2 s1s yMO y1s H1 - y1s
H2 s1s
s1s2s1s 0
s1s orbital is a bonding orbital - there is
electron density between atoms s1s orbital is an
antibonding MO - there is a nodal plane
perpendicular to the internuclear axis between
the nuclei
27

• Chemical Bonding Theory
• MO Theory
• Energy Level Diagram for H2
• Bond order 1( bonding electrons - antibonding
  electrons)
• Energy Level Diagram for He2 Energy
  Level Diagram for He2
• s1s2 s1s1 B. O. 1
  s1s2 s1s2
  B. O. 0
• paramagnetic

28

• Chemical Bonding Theory
• MO Theory
• 2nd Period Homonuclear Diatomic Molecules
• Li2 Be2

s1s2 s1s2 s2s2 B. O. 1 s1s2 s1s2
s2s2 s2s2 B. O. 0
diamagnetic
29

• Chemical Bonding Theory
• MO Theory
• 2nd Period Homonuclear Diatomic Molecules
• LCAOs for 2p orbitals
• Head-to-head LCAOs
• Sideways overlap

There is a 2nd set of p orbitals perpendicular
to to those shown.
30

• Chemical Bonding Theory
• MO Theory
• 2nd Period Homonuclear Diatomic Molecules
• B2 C2

s1s2 s1s2 s2s2s2s2p2p2 B. O. 1 s1s2
s1s2s2s2s2s2p2p4 B. O. 0
paramagnetic
31

• Chemical Bonding Theory
• MO Theory
• 2nd Period Homonuclear Diatomic Molecules
• N2 O2

s1s2 s1s2 s2s2s2s2p2p4s2p2 B. O. 3 s1s2
s1s2 s2s2s2s2s2p2p2p4p2p2 B. O. 2
diamagnetic paramagnetic
32

• Chemical Bonding Theory
• MO Theory
• 2nd Period Homonuclear Diatomic Molecules
• F2 Ne2

s1s2 s1s2 s2s2s2s2s2p2p2p4p2p4 B. O. 1 s1s2
s1s2 s2s2s2s2s2p2p2p4p2p4s2p2 B. O.0
diamagnetic