1. CHAPTER 7 Molecular Geometry, Intermolecular
Forces, and Bonding Theories

2. Shapes of Molecules and Ions
Molecules and ions have a three dimensional shape. This shape can be important in determining the chemical behavior of a substance.
We will discuss two types of geometries:
1) electron domain geometry - The arrangement of electron containing regions about a central atom. This is sometimes called electron cloud geometry.
2) molecular geometry - The arrangement of atoms about a central atom.
The number of electron containing regions about a central atom is equal to the number of lone pair regions + the number of covalent bonds. Note that in counting electron containing regions a single, double, or triple bond counts as one region.

3. Examples of Counting Electron Containing Regions
How many electron containing regions are there for central atoms in each of the mole-cules at left?

4. N 3 regions (two bonds, one lone pair)
C 3 regions (three bonds, no lone pairs)
C at left 4 regions (four covalent bonds)
C at right 3 regions (three covalent bonds)
Note the bond order does not matter in counting electron containing regions.

5. VSEPR Theory
We may predict both electron cloud geometry and molecular geometry using VSEPR (Valence Shell - Electron Pair Repulsion) theory. The idea behind this theory is that electron containing regions will arrange themselves about a central atom in such a way as to put those regions as far apart as possible. This is due to the repulsive force existing between particles of the same charge (in this case electrons).
The various common cases for electron and molecular geometry are given in Table 7.2.

6. Two Regions
If we have two electron containing regions around a central atom, then placing them opposite one another keeps them as far apart as possible.
In this case, both the electron geometry and the molecular geometry are linear.

7. Three Regions
For three regions about a central atom the electron geometry is trigonal planar (120 angle between the regions). There are two possible molecular geometries:
If all three regions are bonds - trigonal planar
If two of the three regions are bonds, and one is a lone pair of electrons - nonlinear (bent)

8. Four Regions
For four regions about a central atom the electron geometry is tetrahedral (109 angle between the regions). There are three possible molecular geometries:
4 bonds - tetrahedral 2 bonds - nonlinear (bent)
3 bonds - trigonal pyramid

9. Five Regions
For five regions about a central atom the electron geometry is trigonal bipyramid. In this case not all of the angles between electron containing regions are the same. Instead, we may divide the regions into equitorial regions and axial regions.

10. There are four possible molecular geometries:
Five Regions
There are four possible molecular geometries:
5 bonds - trigonal bipyramid 3 bonds - T-shape
4 bonds - “see-saw” 2 bonds - linear

11. Six Regions
For six regions about a central atom the electron geometry is octahedral. The bond angles between adjacent regions are all 90.

12. There are three common molecular geometries:
Six Regions
There are three common molecular geometries:
6 bonds - octahedral 5 bonds - square pyramid
4 bonds - square planar

13. Example: What are the electron geometries and molecular geometries around the central atom in BrF3, POCl3, and H2SO3?

14. Example: What are the electron geometries and molecular geometries around the central atom in BrF3, POCl3, and H2SO3?
BrF3 5 regions, so electron cloud geometry is trigonal bipyramid.
3 bonds, so molecular geometry is T-shape.
POCl3 4 regions, so electron cloud geometry is tetrahedral.
4 bonds, so molecular geometry is also tetrahedral.
H2SO3 4 regions, so electron cloud geometry is tetrahedral.
3 bonds, so molecular geometry is trigonal pyramid.

15. Summary electron cloud bonds electron molecular
regions geometry geometry
linear linear
trigonal planar trigonal planar
nonlinear (bent)
tetrahedral tetrahedral
trigonal pyramid
nonlinear (bent)

16. Summary electron cloud bonds electron molecular
regions geometry geometry
trig. bipyramid trig. bipyramid
see-saw
T-shape
linear
octahedral octahedral
square pyramid
square planar

17. Geometry in Large Molecules
For large molecules we can discuss the electron cloud and molecular geometry around each one of the interior atoms.
Example: Give the electron cloud and molecular geometry for each interior atom in the molecule glycine (NH2CH2COOH).

18. Example: Give the electron and molecular geometry for each interior atom in the molecule glycine (NH2CH2COOH).
Atom electron geometry molecular geometry
N atom tetrahedral trigonal pyramid
Left C atom tetrahedral tetrahedral
Right C atom trigonal planar trigonal planar
O atom tetrahedral nonlinear (bent)

19. Deviations From “Pure” Geometries
We have assumed that the angles observed in molecular geometries do not depend on how many bonds and lone pair regions there are. In fact, the number of regions containing lone pair electrons has a small effect on the observed bond angles.
In general we may say the repulsive forces between electron containing regions in a molecule or ion are stronger for lone pair electrons than for bonding electrons. So
lone pair - lone pair >
lone pair - bonding >
bonding - bonding
This is due to the fact that bonding electrons are more localized than lone pair electrons, as they must appear between bonded atoms.

20. In the molecules at left (all of which have four electron containing regions around a central atom) the bond angle decreases from  in CH4 (pure tetrahedral geometry) to  in NH3 to  in H2O.
In CH2O (below) all of the bond angles would be 120. ° in pure trigonal planar geometry.

21. Representing Three Dimensional Structure
Molecules have a three dimensional structure. We need a systematic method for representing these structures in two dimensions. We do this as follows
For convenience, we will sometimes used a dashed line to replace the hatched wedge for a bond going into the page.
Example: Give the three dimensional structures for CH3Cl and PF5.

22. Example: Give the three dimensional structures for CH3Cl and PF5.
CH3Cl PF5
tetrahedral trigonal bipyramid

23. Polar Molecule
A polar molecule is a molecule where the center of positive and negative charge do not coincide. Two things are required for a molecule to be polar
1) The molecule must have at least one polar bond.
2) The contributions from the polar bonds cannot cancel.

24. For a polar covalent bond the difference in electronegativity between the bonded atoms should be about 0.5 or greater. This means that carbon-carbon bonds are completely nonpolar, and carbon-hydrogen bonds are only slightly polar.
EN(C) = EN(H) = 2.1
The table of electronegativities and the molecular geometry for the molecule can be used to determine whether the molecule is polar or nonpolar.
The polarity of a molecule is expressed in terms of the dipole moment of the molecule. The symbol for dipole moment is . Dipole moments are measured in units of Debye (D).

25. Example
Consider the following molecules: H2O, CF4, NH3, and CH3COCH3. Which of these molecules is expected to have a permanent dipole moment?

26. H2O  = 1.85 D
CF4  = 0. D
NH3  = 1.47 D
CH3COCH3  = 2.88 D
EN Values: H = 2.1; C = 2.5; N = 3.0; O = 3.5; F = 4.0
1 Debye = x C.m

27. Intermolecular Forces
Intermolecular forces are the forces that exists between different molecules or particles. We are more concerned with long range attractive forces and will ignore short range repulsive forces.
Ion-ion - The attractive force acting between cations and anions. These are strong, and are found in substances where ionic bonding occurs..

28. Dipole-Dipole Forces
Dipole-dipole - The attractive force acting between polar molecules. The attraction is between the partial positive charge (+) on one molecule and the partial negative charge (-) on a different molecule. Generally speaking, the larger the partial positive and negative charges the stronger the dipole-dipole attraction.

29. Dipole-Dipole Forces and Boiling Point
When molecules have strong intermolecular attractive forces it takes more energy to overcome those attractive forces. One way of seeing this is in the boiling point for a substance. Generally speaking, the stronger the dipole-dipole attraction between molecules the higher
the boiling point, parti-cularly for substances with approximately the same molecular mass.

30. Hydrogen Bonding
Hydrogen bonding - A particularly strong form of dipole-dipole attractive force. It is the attractive force that exists between a hydrogen atom bonded to an N, O, or F atom and lone pair electrons on a different N, O, or F atom (often an atom in a different molecule).

31. Evidence For Hydrogen Bonding
One effect of hydrogen bonding is to raise the boiling point of a liquid. This occurs because it requires more energy (and so a higher temperature) to break apart strong attractive forces between molecules than it does to break apart weak attractive forces between molecules.
substance boiling point hydrogen bonding?
H2O C yes
H2S C no
H2Se C no
H2Te C no

32. Boiling Points for Binary Hydrogen Compounds

33. London Dispersion Forces
London dispersion forces - The attractive force that is due to the formation of instantaneous dipoles in a molecule. These instantaneous dipoles arise from the random motion of the electrons in the molecule.

34. Strength of London Dispersion Forces
London dispersion forces are present in all molecules, but are the only intermolecular force present in nonpolar molecules. The strength of London dispersion forces is approximately proportional to the number of electrons, and so to the size of the molecule. Therefore, as a general rule, the larger the molecule the stronger the London dispersion forces.
substance boiling point
He C
Ne C
Ar C
Kr C
Xe C

35. Induced Dipole and Polarizability
London dispersion forces are closely related to a second property of molecules, called polarizability. The polarizability of a molecule refers to the extent to which the electron cloud distribution is distorted when a positive or negative charge is brought close to the molecule. In general, large molecules, and molecules containing atoms whose valence electrons are far away from the atomic nucleus are more polarizable than other molecules. The more polarizable a molecule the stronger the London dispersion forces it experiences.

36. Ion-Dipole Forces
Ion-dipole - The attractive force between an ion and a polar molecule. Responsible for the dissolution of some ionic substances in polar liquids such as water. In general, the smaller the ion and the larger the charge the stronger the ion-dipole attractive force.
Solvation - The close association of solvent molecules with solute molecules or ions.
Hydration - Solvation when the solvent is water.

37. Summary of the Types of Intermolecular Forces
Ion – ion. Forces between cations and anions.
Dipole – dipole. Forces between molecules with a permanent dipole moment. This category includes hydrogen bonding, a particularly strong type of dipole – dipole force.
London dispersion forces. Due to random movement of electrons. All particles have this type of force, but it is most important in molecules with no permanent dipole moment.
Mixed forces: Ion – dipole is the most important, but this also includes ion – induced dipole and dipole – induced dipole. It is responsible for the solubility of some ionic compounds in water. We will discuss these and related forces in detail when discussing solution formation.

38. Theories For Molecular Bonding
The Lewis dot structure method predates quantum mechanics. While it is a good qualitative description of covalent bonding it fails to work well in some cases (resonance structures are one example).
There are two general methods that use quantum mechanics to improve on the Lewis dot structure method:
Valence Bond theory - Discusses bond formation in terms of overlap of atomic orbitals (often hybrid orbitals).
Molecular Orbital theory - Uses quantum mechanics to solve the Schrodinger equation for a molecule or ion. This is a very mathematical approach.

39. Valence Bond Theory For H2
In valence bond theory bond formation is pictured as occurring due to the overlap of atomic orbitals of the atoms that are bonded together. Each of the orbitals contains one electron. When the orbitals overlap, the electron from each atomic orbital is shared by the two atoms. Notice the electrons need to be opposite spin.
The covalent bond forms from the overlap of the two 1s atomic orbitals of the hydrogen atoms that are bonded together. This places the electrons between the two hydrogen nuclei, which holds the molecule together.

40. Bond Formation and Energy
The formation of a covalent bond between two atoms occurs because it leads to a lower energy than exists for separate atoms. This can be seen in the bonding of two H atoms to form an H2 molecule.

41. Shortcoming of Simple Valence Bond Theory
The above picture breaks down when you need to form several different valence bonds for the same atom out of orbitals of different types.
Example: Be in BeH2
Be 1s2 2s H 1s1
We want the beryllium atom to contribute one electron to each bond between Be and an H atom, but the 2s orbital of beryllium is full, with no unpaired electron.
So what do we do?

42. Hybrid Orbitals
In this case, before we form the valence bonds we first construct a new set of equivalent orbitals, called hybrid orbitals (in this case sp hybrid orbitals).
We can envision the process taking place as indicated below.
While the process of forming hybrid orbitals raises the energy of the electrons in Be, this is more than made up for when the two Be - H bonds are formed.

43. Formation of sp Hybrid Orbitals
The sp hybrid orbitals are formed from combinations of the s and px atomic orbitals. Since we begin with two atomic orbitals, we end up with two hybrid orbitals.

44. Use of sp Hybrid Orbitals For Bonding (BeH2)
The two sp hybrid orbitals formed in Be can now be used to form the two Be - H valence bonds.

45. sp3 Hybrid Orbitals
In methane (CH4) we need the central carbon atom to have four equivalent hybrid orbitals to form the four C - H bonds. This is done using sp3 hybridization.
CH4. C: 1s2 2s2 2p2
As before, we start by “unpairing” the electrons in the carbon atom by promoting one electron from a 2s to a 2p orbital
__ __ __ __ promote __ __ __ __
2s p s p

46. sp3 Hybrid Orbitals (Continued)
Now that we have one electron in our 2s atomic orbital, and in each of the three 2p atomic orbitals, we combine the four orbitals to form our set of four sp3 hybrid orbitals.
Since we began with four atomic orbitals, we end up with four hybrid orbitals.

47. These sp3 hybrid orbitals can now be used to form valence bonds or to hold lone pairs of electrons.

48. Naming and Use of Hybrid Orbitals
We name hybrid orbitals by listing the type of atomic orbitals used to construct the hybrid orbitals (s, p, or d). If we use more than one of a particular type of orbital, we indicate the number of orbitals used by a superscript to the right of the symbol for the orbital.
There is a simple relationship between the number of electron containing regions around a central atom and the type of hybrid orbitals that are required.
Number of regions Hybrid orbitals Electron geometry sp linear
sp2 trigonal planar
sp3 tetrahedral
5* sp3d trigonal bipyramid
6* sp3d2 octahedral
* Not possible for atoms from 2nd row of periodic table

49. Why PF5 Exists and NF5 Does Not
We can now return to an observation we made in the last chapter, that in looking at molecules made from a group 5 nonmetal and fluorine the molecule PF5 exists, but NF5 does not. We can see why this is the case by looking at the hybridization required for the central atom in these two molecules.
N [He] 2s2 2p3
P [Ne] 3s2 3p3 3d0 __ __ __ __ __ __ __ __ __
promote __ __ __ __ __ __ __ __ __
3s p d
Hybridize to get 5 sp3d hybrid orbitals. This is not possible for nitrogen because there are no 2d orbitals, and so hybrid orbitals requiring use of one or more d orbitals cannot be formed.

50. Appearance of Hybrid Orbitals
Each particular type of hybrid orbital has its own geometry, which in all cases corresponds to the geometries predicted using VSEPR theory.
Also notice that in all cases the number of atomic orbitals we begin with is equal to the number of hybrid orbitals we end up with.

51. Sigma () and Pi () Bonds
The above description works well for single bonds between atoms. However, when we have a multiple bond (double or triple bond), the bonds can be divided into two types:
sigma bond - Formed from the overlap of atomic or hybrid orbitals; places electrons directly between the bonded atoms.
pi bond - Formed from the overlap of p type atomic orbitals; places electrons above and below the region between the bonded atoms.
In general, a single bond will always be a sigma bond. For a multiple bond, one of the bonds will be a sigma bond and the other bonds will be pi bonds.

52. Example: C2H4 (ethene) (C atoms are sp2 hybridization)

53. Summary Total number Number of Number of bonds sigma bonds pi bonds
So the first bond is always a sigma bond, while any additional bonds are pi bonds.

54. Example
How many sigma bonds and how many pi bonds are present in the molecule shown below?

55. How many sigma bonds and how many pi bonds are present in the molecule shown below?
There are seven sigma bonds.
There are two pi bonds.

56. Pi Bonds and Free Rotation
Because pi bonds are formed from the overlap of p orbitals, molecules that contain pi bonds (molecules with double or triple bonds) cannot rotate freely around those bonds, since to do so would mean breaking one or more pi bond.
In ethane (C2H6) rotation around the C - C bond does not affect the bond and so is allowed. In ethene (C2H4) rotation around the C = C bond breaks the pi bond, and so will not occur (except at high energy).

57. Molecular Orbital Theory
In molecular orbital theory we solve the Schrodinger equation to find information about molecules (energies, geometries, electron distribution, and so forth). Just as we find atomic orbitals for atoms, we find molecular orbitals for molecules or ions. This is a very mathematical theory, and so we will only discuss simple cases in a nonmathematical way.
The usual way people do MO theory is called the LCAO-MO method. In this method, linear combinations of atomic orbitals are used to construct molecular orbitals. We also focus on the valence electrons, and generally ignore core electrons.

58. Molecular Orbital Theory for H2
For H2, we begin with the two 1s atomic orbitals on the two H atoms. There are two ways in which these can be combined, cor-responding to two molecular orbitals. One molecular orbital lowers the energy and therefore corresponds to a  bonding orbital, while the other molecular orbital raises the energy and therefore corresponds to a * antibonding orbital (note we use a * to indicate an antibonding orbital). We often also indicate the starting atomic orbitals.
1s atomic orbitals 1s MO *1s MO

59. MO Diagram
In a molecular orbital diagram we indicate the starting atomic orbitals and the molecular orbitals made from them with the correct relative energies.
The above diagram represents the MO picture for the H2 molecule. As is the case for atoms, we can give an electron configuration for molecules as well. For the above we have H2: (1s)2

60. Rules for Adding Electrons
The rules for filling molecular orbitals are the same as filling atomic orbitals. They are:
Pauli principle.
Aufbau principle
Hund’s rule
Just as for atoms, we can write electron configurations for molecules by listing the occupied orbitals in order of energy, and indicating the number of electrons in an orbital by a superscript to the right of the orbital name. We usually place each orbital in parentheses.

61. Example H2 molecule H2- ion He2 “molecule” So H2 (1s)2
H2- (1s)2 (1s*)1
He2 (1s)2 (1s*)2 61

62. Bond Order We may define the bond order (BO) as follows
BO = (# bonding e-) - (# antibonding e-) 2
The higher the bond order the stronger the bond. Note that fractional bond orders are possible.
H2 (1s)2 BO = 1
H2- (1s)2 (1s*)1 BO = 1/2
He2 (1s)2 (1s*)2 BO = 0
If the bond order is zero, then we don’t expect the molecule or ion to be stable.

63. Period 2 Homonuclear Diatomics
We may apply the above procedure to the period 2 homonuclear diatomic molecules and ions. Note that we only look at he molecular orbitals involving atomic orbitals in the valence shell.
The 2s atomic orbitals present in the valence shell of second row atoms can be used to form a bonding and an antibonding sigma orbital, as was the case with the 1s atomic orbitals.
*2s
2s s
2s
AO MO AO

64. Molecular Orbitals From 2p
Atomic Orbitals
The 2p atomic orbitals present in second row atoms can be used to form two types of molecular orbitals - sigma orbitals (bonding and antibonding) and pi orbitals (bonding and antibonding).
*2p
*2p
2p p
2p
2p
AO MO AO

65. Formation of  Molecular Orbitals From px Atomic Orbitals

66. Formation of  Molecular Orbitals From py and pz Atomic Orbitals

67. Period 2 Homonuclear Diatomics
The molecular orbitals formed from the 2s and 2p atomic orbitals of second period atoms are shown below. The order of these orbitals in terms of energy depends on the particular type of homonuclear diatomic species being discussed.
Order for Li2 to N Order for O2, F2

68. Example: Give the electron configuration and bond order for C2, C2+, and C2-.

69. Example: Give the electron configuration and bond order for C2, C2+, and C2-.
C2 (8 e-) (2s)2 (2s*)2 (2p)4 BO = (6-2)/2 = 2
C2+ (7 e-) (2s)2 (2s*)2 (2p)3 BO = (5-2)/2 = 1 1/2
C2- (9 e-) (2s)2 (2s*)2 (2p)4 (2p)1 BO = (7-2)/2 = 2 1/2

70. MOs For Period 2 Homonuclear Diatomics

71. Summary of Bonding Theories
Lewis theory - Simple to use, useful in making qualitative predictions about bond lengths and bond strengths. Not directly useful for three dimensional structure of molecules, sometimes makes incorrect predictions concerning bond order, unpaired electron spins. Difficulties in use for some molecules (requiring resonance structures).
VSEPR- Based on Lewis theory, and allows predictions of molecular geometries. However, some of the same weaknesses of Lewis theory.
Valence Bond theory (with hybridization) - Explains the formation of covalent bonds in more detail than Lewis theory, and also why atoms in the third row and below can violate the octet rule. Fails in the prediction of some properties of molecules, such as paramagnetism in O2.
Molecular Orbital theory - Most rigorous theory for molecules, but also the most complicated and mathematical theory. Difficult to apply in a simple way for large molecules.

72. Multicenter Pi Bonding
We may combine valence bond theory and MO theory to account for resonance structures in terms of multicenter pi bonds, that is, pi bonds among more than two atoms.
NO valence electrons (and so 4 covalent bonds)
When there are resonance structures that is usually evidence that the bonding needs to be described in terms of multicentered pi bonds. A correct description of bonding in this case requires use of both valence bond theory and molecular orbital theory.

73. Formation of Sigma Bonds
The N atom and three O atoms can each form sp2 hybrid orbitals. These form the N - O sigma bonds, and also contain two sets of lone pair electrons for each oxygen atom.

74. Formation of Multicenter Pi Bonds
The remaining p orbitals on each atom that are perpendicular to the plane of the molecule can be used to form a final, multicentered pi bond, along with two other multicentered molecular orbitals (not shown) for the additional two sets of lone pair electrons.
4 pz
antibonding MO
lone pair MOs
bonding MOs (multicentered pi bond)

75. Benzene
Benzene (C6H6) is an important example of a molecule that gains stability due to the presence of multicentered pi bonds.

76. Sigma Bonds in Benzene
Each carbon aton in benzene has sp2 hybridization. Overlap between hybrid orbitals between adjacent carbon atoms form the C - C and C - H sigma bonds. This leaves six pz orbitals perpendicular to the plane of the molecule for formation of multicentered pi bonds, one of which is shown below.

77. Multicenter Pi Bonds in Benzene
The multicentered pi bonds in benzene are generated from the six pz atomic orbitals on the six carbon atoms. Note that not all of the pi bonds have the same energy. There are a total of three pi bonds, as expected, since there are six electrons not accounted for in the sigma bonding.
6 pz
antibonding MOs
bonding MOs (these hold the six electrons from the six pz orbitals of carbon)

78. End of Chapter 7
“Physicists are notoriously scornful of scientists from other fields. When the wife of the great Austrian physicist Wolfgang Pauli left him for a chemist, he was staggered with disbelief. ‘Had she taken a bullfighter I would have understood,’ he remarked in wonder to a friend. ‘But a chemist…’” Bill Bryson, A Short History of Nearly Everything
“The physicist's greatest tool is his wastebasket.”
- Albert Einstein
“Hofstadter's law: It always takes longer than you expect, even when you take into account Hofstadter's law.” - Douglas Hofstadter
“Love hides in molecular structures.” - Jim Morrison