1. Chemistry: The Central Science
Fourteenth Edition
Chapter 9
Molecular Geometry and Bonding Theories
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2. Molecular Shapes
Lewis structures show bonding and lone pairs but do not denote shape.
However, we use Lewis structures to help us determine shapes.
Here we see some common shapes for molecules with two or three atoms connected to a central atom.

3. What Determines the Shape of a Molecule?
The bond angles and bond lengths determine the shape and size of molecules.
Electron pairs repel each other.
Electron pairs are as far apart as possible; this allows predicting the shape of the molecule.
This is the valence-shell electron-pair repulsion (V S E P R) model.

4. Electron Domains
We can refer to the directions to which electrons point as electron domains. This is true whether there is one or more electron pairs pointing in that direction. It is also true if it is a lone pair or a bond.
The central atom in this molecule, A, has four electron domains.

5. Valence-Shell Electron-Pair Repulsion (V S E P R) Model
“The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them.” (The balloon analogy in the figure to the left demonstrates the maximum distances that minimize repulsions.)

6. Electron-Domain Geometries (1 of 3)
The table shows the electron-domain geometries for two through six electron domains around a central atom.
To determine the electron-domain geometry, count the total number of lone pairs, single, double, and triple bonds on the central atom.

7. Electron-Domain Geometries (2 of 3)
Table 9.1 Electron-Domain Geometries as a Function of Number of Electron Domains
Number of
Electron Domains*
Arrangement of
Electron Domains
Electron Domain
Geometry
Predicted
Bond Angles 2
Two domains opposite each other, forming a straight line.
Linear
180º 3
Three domains forming the points of an equilateral triangle.
Trigonal planar
120º 4
Four domains forming the points of a pyramid.
Tetrahedral
109.5º

8. Electron-Domain Geometries (3 of 3)
[Table 9.1 Continued]
Number of
Electron Domains*
Arrangement of
Electron Domains
Electron Domain
Geometry
Predicted
Bond Angles 5
Three domains forming the points of an equilateral triangle. Two additional domains are found perpendicular, above and below, the triangle.
Trigonal
bipyramidal
120º
90º 6
Four domains forming the points of a square. Two additional domains are found perpendicular, above and below, the square
Octahedral
*The number of electron domains is sometimes called the coordination number of the atom.

9. Molecular Geometries Draw the best Lewis structure.
Determine the electron-domain geometry.
Use the arrangement of the bonded atoms to determine the molecular geometry.
Tables 9.2 and 9.3 show the potential molecular geometries.

10. Linear Electron Domain
In the linear domain, there is only one molecular geometry: linear.
Note: If there are only two atoms in the molecule, the molecule will be linear no matter what the electron domain is.
Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom
Number of
Electron Domains
Electron-Domain
Geometry
Bonding
Domains
Nonbonding
Molecular
Example 2
Two domains opposite each other, forming a straight line, linear.
Linear.
C O 2. A central C double bonded left and right to O; each O has two pairs of dots.

11. Trigonal Planar Electron Domain (1 of 3)
There are two molecular geometries:
Trigonal planar, if all electron domains are bonding electrons
Bent, if one of the domains is a lone pair
Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom
Number of
Electron Domains
Electron-Domain
Geometry
Bonding
Domains
Nonbonding
Molecular
Example 3
Three domains forming the points of an equilateral triangle, trigonal planar.
Trigonal planar.
B F 3. B is single left and right, angled down, and above to F; each F has three pairs of dots.
Blank 2 1
bent.
N O 2. N is double bonded left, angled down, to O, which has two pairs of dots, and single bonded right, angled down, to O, which has three pairs. The entire molecule has a negative charge

12. Trigonal Planar Electron Domain (2 of 3)
There are three molecular geometries:
Tetrahedral, if all are bonding pairs
Trigonal pyramidal, if one is a lone pair
Bent, if there are two lone pairs

13. Trigonal Planar Electron Domain (3 of 3)
Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom
Number of
Electron Domains
Electron-Domain
Geometry
Bonding
Domains
Nonbonding
Molecular
Example 4
Four domains forming the points of a pyramid, tetrahedral.
Tetrahedral.
C H 4. C is single bonded right, into the page, and out of the page, all angled down, to H, as well as single bonded above to H.
Blank 3 1
Trigonal pyramidal.
N H 3. N is single bonded right, into the page, and out of the page, all angled down, to H; N has a pair of dots above. 2
Bent
H 2 O. O is single bonded left and right, angled down, to H; O has two pairs of dots.

14. Nonbonding Pairs and Bond Angle
Nonbonding pairs are physically larger than bonding pairs.
Therefore, their repulsions are greater; this tends to compress bond angles.

15. Multiple Bonds and Bond Angles
Double and triple bonds have larger electron domains than single bonds.
They exert a greater repulsive force than single bonds, making their bond angles greater.

16. Expanding Beyond the Octet Rule
Remember that some elements can break the octet rule and make more than four bonds (or have more than four electron domains).
The result is two more possible electron domains: five = trigonal bipyramidal; six = octahedral (as was seen in the slide on electron-domain geometries).

17. Trigonal Bipyramidal Electron Domain (1 of 3)
There are two distinct positions in this geometry:
Axial
Equatorial
Lone pairs occupy equatorial positions.

18. Trigonal Bipyramidal Electron Domain (2 of 3)
There are four distinct molecular geometries in this domain:
Trigonal bipyramidal
Seesaw
T-shaped
Linear

19. Trigonal Bipyramidal Electron Domain (3 of 3)
Table 9.3 Electron-Domain and Molecular Geometries for Five and Six Electron Domains around a Central Atom
Number of
Electron Domains
Electron-Domain
Geometry
Bonding
Domains
Nonbonding
Molecular
Example 5
Three domains forming the points of an equilateral triangle, and two more domains above and below, perpendicular to the plane of the triangle.
Trigonal bi-pyramidal.
P C l5
Blank 4 1
Seesaw.
S F4 3 2
T shaped.
C l F3
Linear.
X e F2

20. Octahedral Electron Domain (1 of 2)
All positions are equivalent in the octahedral domain.
There are three molecular geometries:
Octahedral
Square pyramidal
Square planar

21. Octahedral Electron Domain (2 of 2)
Table 9.3 Electron-Domain and Molecular Geometries for Five and Six Electron Domains around a Central Atom
Number of
Electron Domains
Electron-Domain
Geometry
Bonding
Domains
Nonbonding
Molecular
Example 6
Four domains forming the points of a square, and two more domains above and below, perpendicular to the plane of the square.
Octahedral.
S F6
Blank 5 X1
Square pyramidal.
B r F5 4 2
Square planar.
X e F4

22. Shapes of Larger Molecules
For larger molecules, look at the geometry about each atom rather than the molecule as a whole.

23. Polarity of Molecules Ask yourself: Covalent or ionic? If covalent:
Are the bonds polar? (Do they have a bond dipole?)
No: The molecule is nonpolar!
Yes: Continue—Do the average position of δ+ and δ– coincide? (Is the overall dipole moment equal to zero?)
Yes: The molecule is nonpolar.
No: The molecule is polar.
Note: Different atoms attached to the central atom have different polarity of bonds.

24. Comparison of the Polarity of Two Molecules
A nonpolar molecule
A polar molecule

25. Valence-Bond Theory (1 of 2)
In valence-bond theory, electrons of two atoms begin to occupy the same space.
This is called “overlap” of orbitals.
The sharing of space between two electrons of opposite spin results in a covalent bond.

26. Valence-Bond Theory (2 of 2)
Increased overlap brings the atoms together until a balance is reached between the like charge repulsions and the electron- nucleus attraction.
Atoms can’t get too close because the internuclear repulsions get too great.

27. V S E P R and Hybrid Orbitals
V S E P R predicts shapes of molecules very well.
How does that fit with orbitals?
Let’s use H2O as an example:
If we draw the best Lewis structure to assign V S E P R, it becomes bent.
If we look at oxygen, its electron configuration is
If it shares two electrons to fill its valence shell, they should be in 2p.
Wouldn’t that make the angle 90°?
Why is it 104.5°?

28. Hybrid Orbitals
Hybrid orbitals form by “mixing” of atomic orbitals to create new orbitals of equal energy, called degenerate orbitals.
This process is called hybridization.
When two orbitals “mix” they create two orbitals; when three orbitals mix, they create three orbitals; and so on.

29. B e—s p Hybridization
When we look at the orbital diagram for beryllium (B e), we see that there are only paired electrons in full sublevels.
B e makes electron-deficient compounds with two bonds for B e. Why? s p hybridization (mixing of one s orbital and one p orbital).

30. s p Orbitals
Mixing the s and p orbitals yields two degenerate orbitals that are hybrids of the two orbitals.
The s p hybrid orbitals each have two lobes like a p orbital.
One of the lobes is larger and more rounded, as is the s orbital.

31. Position of sp Orbitals
These two degenerate orbitals would align themselves 180° from each other.
This is consistent with the observed geometry of B e compounds (like B e F2) and V S E P R: linear.

32. Boron—Three Electron Domains Gives sp2 Hybridization
Using a similar model for boron leads to three degenerate

33. Carbon: sp3 Hybridization
With carbon, we get four degenerate

34. What Happens with Water?
We started this discussion with H2O and the angle question: Why is it degrees instead of 90 degrees?
Oxygen has two bonds and two lone pairs—four electron domains.
The result is
hybridization!

35. Hypervalent Molecules
The elements that have more than an octet
Valence-bond model would use d orbitals to make more than four bonds.
This view works for period 3 and below.
Theoretical studies suggest that the energy needed would be too great for this.
A more detailed bonding view is needed than we will use in this course.

36. Hybrid Orbital Summary (1 of 2)
Draw the Lewis structure.
Use V S E P R to determine the electron-domain geometry.
Specify the hybrid orbitals needed to accommodate these electron pairs.

37. Hybrid Orbital Summary (2 of 2)
Table 9.4 Geometric Arrangements Characteristic of Hybrid Orbital Sets
Atomic Orbital Set
Hybrid Orbital Set
Geometry
Examples
s,p
Two s p
Linear, 180 degrees.
B e F2, H g C l2
s,p,p
Three, s p 2
Trigonal planar, 120 degrees
B F3, S O3
s,p,p,p
Four, s p 2
Tetrahedral, degrees
C H 4. N H 3. H 2 O. N H 4, plus.

38. Types of Bonds How does a double or triple bond form?
It can’t, if we use only hybridized orbitals.
However, if we use the orbitals that are not hybridized, we can have a “sideways” overlap.
Two types of bonds:
Sigma (σ) bond
Pi (π) bond

39. Sigma () and Pi () Bonds
Sigma bonds are characterized by
head-to-head overlap.
cylindrical symmetry of electron density about the internuclear axis.
Pi bonds are characterized by
sideways overlap.
electron density above and below the internuclear axis.

40. Bonding in Molecules Single bonds are always Multiple bonds have one
all other bonds are

41. Localized or Delocalized Electrons
that are specifically shared between two atoms are called localized electrons.
In many molecules, we can’t describe all electrons that way (resonance); the other electrons (shared by multiple atoms) are called delocalized electrons.
Bonding electrons

42. Benzene The organic molecule benzene has and a p
orbital on each C atom, which form delocalized bonds using one electron from each p orbital.

43. Molecular Orbital (M O) Theory (1 of 2)
Wave properties are used to describe the energy of the electrons in a molecule.
Molecular orbitals have many characteristics like atomic orbitals:
Maximum of two electrons per orbital
Electrons in the same orbital have opposite spin
Definite energy of orbital
Can visualize electron density by a contour diagram

44. More on M O Theory
They differ from atomic orbitals because they represent the entire molecule, not a single atom.
Whenever two atomic orbitals overlap, two molecular orbitals are formed: one bonding, one antibonding.
Bonding orbitals are constructive combinations of atomic orbitals.
Antibonding orbitals are destructive combinations of atomic orbitals. They have a new feature unseen before: A nodal plane occurs where electron density equals zero.

45. Molecular Orbital (M O) Theory (2 of 2)
Whenever there is direct overlap of orbitals, forming a bonding and an antibonding orbital, they are called sigma (σ) molecular orbitals. The antibonding orbital is distinguished with an asterisk as
Here is an example for the formation of a hydrogen molecule from two atoms.

46. M O Diagram
An energy-level diagram, or M O diagram, shows how orbitals from atoms combine to form molecular orbitals. In
the two electrons go into the bonding molecular orbital (lower in energy).

47. Can H e2 Form? Use M O Diagram and Bond Order to Decide!
Therefore,
does not exist.

48. Guiding Principles for the Formation of Molecular Orbitals
The number of M O s formed equals the number of A O s combined.
A O s combine with A O s of similar energy.
The effectiveness with which two A O s combine is proportional to their overlap.
Each M O can accommodate at most two electrons with opposite spin. (They follow the Pauli exclusion principle.)
When M O s of the same energy are populated, one electron enters each orbital (same spin) before pairing. (They follow Hund’s rules.)

49. M O s, Bonding, and Core Electrons
occurs at high temperatures.
Lewis structure:
The M O diagram is on the right.
Notice that core electrons don’t play a major part in bonding, so we usually don’t include them in the M O diagram.

50. M O s from p-Orbitals p-orbitals also undergo overlap.
They result in either direct or sideways overlap.

51. M O Diagrams for the Second Period p-Block Elements
There are σ and
orbitals from s and p atomic orbitals.
There are π and
orbitals from p atomic orbitals.
Since direct overlap is stronger, the effect of raising and lowering energy is greater for σ and

52. s and p Orbital Interactions
In some cases, s orbitals can interact with the pz orbitals more than the px and py orbitals.
It raises the energy of the pz orbital and lowers the energy of the s orbital.
The px and py orbitals are degenerate orbitals.

53. M O Diagrams for Diatomic Molecules of Second Period Elements

54. M O Diagrams and Magnetism
Diamagnetism is the result of all electrons in every orbital being spin-paired. These substances are weakly repelled by a magnetic field.
Paramagnetism is the result of the presence of one or more unpaired electrons in an orbital.
Is oxygen
paramagnetic or diamagnetic? Look back at the M O diagram! It is paramagnetic.

55. Paramagnetism of Oxygen
Lewis structures would not predict that
is paramagnetic.
The M O diagram clearly shows that
is paramagnetic.
Both show a double bond (bond order = 2).

56. Heteronuclear Diatomic Molecules
Diatomic molecules can consist of atoms from different elements.
How does a M O diagram reflect differences?
The atomic orbitals have different energy, so the interactions change slightly.
The more electronegative atom has orbitals lower in energy, so the bonding orbitals will more resemble them in energy.

57. Copyright