1. Chapter 10 Chemical bonding: Molecular shapes, valence bond theory, and molecular orbital theory

2. Valence Shell Electron Pair Repulsion Theory
VSEPR theory:
Electron groups are atoms and lone pairs
Electrons repel each other
Electrons groups in a molecule arrange themselves so as to be as far apart as possible

3. Defining Molecular Shape
Electron pair geometry (EPG) - the geometrical arrangement of electron groups around a central atom
Atoms and lone pairs count as electron groups
Molecular Geometry (MG) - the geometrical arrangement of atoms around a central atom
Ignore lone pair electrons
Defining Molecular Shape

4. Make a table Create a table with 5 columns Electron groups Lone pairs
EPG MG
Example molecule

5. 2 electron groups
EPG: linear
MG: linear
Example: BeCl2, CO2

6. 3 electron groups 3 Atoms, 0 Lone Pairs 2 atoms, 1 Lone Pair
EPG: Trigonal Planar (Triangular planar)
MG: Trigonal Planar
BF3
2 atoms, 1 Lone Pair
EPG: Trigonal Planar (Triangular planar)
MG: Bent/angular
GeCl2

7. 4 electron groups 4 Atoms, 0 Lone Pairs 3 Atoms, 1 Lone Pair
EPG : Tetrahedral
MG: Tetrahedral
CH4
3 Atoms, 1 Lone Pair
EPG : Tetrahedral
MG: Trigonal pyramidal (triangular pyramidal)
NH3

8. 2 Atoms, 2 Lone Pairs
EPG: Tetrahedral
MG: Bent/Angular
H2O

10. Problems
Draw the Lewis dot structures of the following molecules and determine the EPG and MG for the central atom
CCl2Br2
PH3

11. Molecular Polarity

12. Determining molecular polarity
Draw Lewis dot structure taking into account 3-D molecular geometry
Indicate the dipole moment for each bond using EN values for each atom
Sum up the dipole moments as vectors and determine if there is a net dipole moment
Determining molecular polarity

14. Valence bond theory
Electrons are more appropriately represented in a quantum mechanical manner
Electrons exist in atomic orbitals that can interact with other atomic orbitals
Interactions between two atoms can be analyzed through their potential energy
So far we have talked about the Lewis model and VSEPR theory as ways to describe molecules and their bonding. Each model helps to get a better picture of the true nature of chemical bonds. Now we are going to keep going further. Making a bond starts by bringing two atoms together. For this process we can analyze the energy as an atom gets closer to another atom. Using coulombs law we can see that if the atoms are far away then potential energy is close to 0. As they come closer together the energy will decrease, resulting in a more favorable system and at this valley in the curve the energy is the lowerst. Also at this point, as you get closer the repulsion from the positvely charged nuclei start to become dominant and the energy increases. As far as a chemical bond is concerened, it wants to be at the lowest energy, the most stable distance, which is here at thebottom of the curve. This distance corresponds to the bond length of the molecule, the distance between the two atoms. This graph is for two hydrogen atoms, and for different molecules the graph will be slightly different, but the overall pattern should persist where the atoms get lower in energy as they get closer toegether, but once they get close enough, the nuclei start to repel each other enough to start increasing the energy of bringing the atoms closer together.

15. Valence bond theory summary
When bringing atoms close together, when orbitals with unpaired electrons interact this results in a lower (more negative) energy, promoting a chemical bond
Geometry and shape of orbitals interacting will affect the overall molecular geometry
So far we have talked about the Lewis model and VSEPR theory as ways to describe molecules and their bonding. Each model helps to get a better picture of the true nature of chemical bonds. Now we are going to keep going further. Making a bond starts by bringing two atoms together. For this process we can analyze the energy as an atom gets closer to another atom. Using coulombs law we can see that if the atoms are far away then potential energy is close to 0. As they come closer together the energy will decrease, resulting in a more favorable system and at this valley in the curve the energy is the lowerst. Also at this point, as you get closer the repulsion from the positvely charged nuclei start to become dominant and the energy increases. As far as a chemical bond is concerened, it wants to be at the lowest energy, the most stable distance, which is here at thebottom of the curve. This distance corresponds to the bond length of the molecule, the distance between the two atoms. This graph is for two hydrogen atoms, and for different molecules the graph will be slightly different, but the overall pattern should persist where the atoms get lower in energy as they get closer toegether, but once they get close enough, the nuclei start to repel each other enough to start increasing the energy of bringing the atoms closer together.

16. Valence bond theory: Hybridization
Orbitals in a molecule are not the same as in an atom
Orbitals can mix together to form hybrid orbitals
This occurs mostly with atoms that tend to make more bonds, like carbon
Hybrid orbitals will have altered energy and shape, depending on the orbitals that are mixing
Reasoning for hybridization….ENERGY!!
Results in overall lower potential energy for the molecule
Valence bond theory: Hybridization
Although for our previous example we easily combined the orbitals from their original electron configurations to give an explanation of the bonding, but in many cases this is not enough. In the molecule CH4, carbon makes 4 bonds, but looking at its electron configuration we can see only 2 unpaired electrons available for bonding. To explain this discrepency we must consider now that orbitals can mix together to form hybrid orbitals. The driving factor for hybridiation to occur is based on energy. If the overall energy of a system can decrease from hybridiing orbitals, to make more bonds, then this will be more likely to occur. Hybrid orbitals have a shape dependant on the orbitals that you are mixing together. So lets take a look at some examples of hybridied orbitals. One more note, for orbitals to potentially hybridize, they must also have relatively similar energies and good orbital overlap. We will getmore into that later.

17. sp3 hybridization
Mixing one s orbital and three p orbitals will give you four sp3 orbitals
Can explain geometries with four electron groups
If we take one s orbital and mix it with three p orbitals, we create four sp3 orbitals. Looking at the image you can see the original atomic orbitals for C. When it wants to make a molecule it becomes favorable to mix/hybridize those orbitals to create the sp3 orbitals. Keep in mind that the number of orbitals you start with is the number you end up with. You should also note that the energy is in between that of the original energies. In the hybridized form, this allows for an overall lower energy molecule. Now that we have 4 unpaired electrons, we can now bond to 4 other atoms, like hydrogen.

18. Shown here are the shapes of the orbitals before and after mixing
Shown here are the shapes of the orbitals before and after mixing. This the overall shapes produced are based on quantum mechanical calculations, but in some cases you can see how the original orbitals produce the hybrid orbitals. The shapes of each sp3 orbital is the same, but the 3D orientation is different. When you superimpose them on top of each other, it looks like this, which should look very similar to at tetrahedral geometry.

19. sp3 hybridization shape
If we now build our CH4 molecule we can see how the 1s orbital of each hydrogen interacts with one of the sp3 orbitals per hydrogen. And ust to reitterate, the tetrahedral geometry is apparent, and derived from the shape of the orbitals interacting in bonding.
We can apply a similar process for NH3, in which Nitrogen has one more electron than carbon. Due to this extra electron, one of those sp3 orbitals has to electrons in it, which is a lonepair. While the electron pair geometry is still tetrahedral, we can now see that the molecualr geometry is a trigonal pyrimid

20. Sigma (σ) and pi (π) bonds
To clarify this type of bonding interaction I must explain sigma and pi bonds. So far the bonds we have been coevering are sigma bonds. When there is a head on interaction between the lobe of one orbital with another. We can have an s orbital and a p orbital. Or a p orbital and another p orbital head on. This is a sigma interaction- and thus classified as a sigma bond. If instead of a head on interaction we have a side by side interaction where two lobes of one obrital match up with two orbitals of another, we get a pi interaction or pi bond. P orbital and d orbital can undergo this kind of an interaction, but an s orbital cant since it only has one “lobe”. So with this slide, this shows the difference between sigma and pi bonds. Also as a not, a sigma bond is stronger than a pi bond, and this is due to a more direct overlap, versus the side to side interaction in pi bonds

21. sp2 hybridization and double bonds
Mixing one s orbital and two p orbitals makes three sp2 orbitals
Explains 3 EPG geometries with double bonds
Moving onto another hybrid orbital type – sp2. In this case you are mixing one s orbital and two p orbitals two make three sp2 orbitals. Looking at the image you can see which orbitals are being mixed. After hybridization you can see the three hybrid orbitals and the unchanged p obritals. This type of hybridzation can be used to explain double bonds as you will see in the next slide. Any questions so far?.... Conitinuing on.

22. Upon mixing the s orbital with the two p orbitals, the px and py orbitals, you can see how the three sp2 orbitals are formed. These orbitals lie in the xy plane, because they come from those px and py orbitals. When overlapping the three orbitals, it looks like this which looks exactly like what kind of geometry??? Trigonal planar, that’s right. 3 EG = trigonal planar EPG. Once again shape and orientation will determine geometry

23. If we take a look at the formaldehyde molecule we now see the 3 sp2 orbitals and the p orbital of the C have unpaired electron that can bond with atoms. Two sp2 orbitals bond with hydrogen while one bonds to oxygen. In addition, we can see that a second interaction occurs between the p orbitals of the oxygen and thep orbital of the carbon. This makes another bond. In the overall lewis dot structure we have a double bond between carbon and oxygen. This is where it comes from.

24. Bond rotation
A sigma or pi bond also has other implications. If you have a sigma bond like in the molecule 1,1-dichloroethane, this carbon carbon single bond is a sigma bond. If you rotate the molecule the orbitals will still overlap and the bond will not break.
On theother hand if you had the molecule on the right, 1,2-dichloroethene, this double bond cannot rotate, because doing so would cause the p orbitals to no longer have the same overlap. Because of this double bonds which consistt of a sigma bond and a pi bond. Having that pi bond prevents rotation of the bond ( without breaking it that is).

25. sp hybridization
Mixing one s orbital and one p orbital makes 2 sp orbitals
Explains triple bonds
Continuing on with other hybrid orbitals, sp orbitals come from mixing one s and one p orbital to produce 2 sp orbitals. If we look at the image we can now see the original orbital being hybridized, while two p orbitals remain unchanged. This will allow us to explain triple bonds.

26. Mixing the s orbital with a px orbital produxes two sp orbitals which are aligned along the x axis. Shown overlapping we have the two sp hybrid orbitals, which easily looks like a linear electron pair geometry.

27. Looking at an acetylene molecule we see the orbitals of the carbons and hydrogens. The Hydrogen s orbital interacts with one sp orbital,while the other sp orbital interacts with the sp orbital of the oether carbon. We still have two p orbitals on each carbon left over,with unpaired electrons in each one. These can interacct with the other carbons p orbitals to produce two pi bonds. The py orbitals have pi interactions, and the pz orbitals have pi interactions. If we count up the bonds, one sigma, and two pi bonds, how many bonds total?????? 3!!!! This is how you make a triple bond. Imploying these hybrid orbitals to make anoverall lower energy molecule.

28. sp3d hybridization
Mixing one s, three p, and one d orbital produce five sp3d orbitals
This can explain 5 EPG geometries
With more orbitals you can get more types of hybrids. Sp3d orbitals can be derived yatta yt=atta…. This can help to explain the geometry of molecules with five electron groups.Show on the right is the overall shape of the overlapping sp3d orbitals.

29. Looking at the molecule here astatine pentafluoride, we can see it has a trigonal bipyrimad geometry as the sp3d orbitals overlap with the p orbitals of the fluorines ( remember in fluorines case, the p orbital is the one with an unpaired electron, vs hydrogen and a 1s orbital. Based on the shape of the orbitals you see the geometry that is produced in the molecule.

30. sp3d2 hybridization
Mixing one s, three p, and two d orbitals produce five sp3d2 orbitals
This can explain 6 EPG geometries
Not done yet, sp3d2 hybrid orbitals arecomposed from the corresponding components. In this case we can now explain octahedral geometries of molecules that have 6 electron groups about a central atom.

31. Shown here is sulfur hexafluoride
Shown here is sulfur hexafluoride. Sulfur usually likes to act like oxygen and make 2 bonds. But now we can see that through hybrdiation it can bond to up to 6 atoms. This is the powerof hybridization, letting us further explain properties of more and more atoms.

32. This is just an overview of the electron geometries and the corresponding hybrid orbitals that can explain those geometryies

33. Molecular orbital (MO) theory!!!
Solving the Schrodinger equation allowed for the calculation of the atomic orbitals (1s, 2p, 3d, etc.)
A similar calculation can be applied for molecular orbitals, this results in a process similar to hybridization
Linear combination of atomic orbitals (LCAOs) – a weighted linear sum of the valence atomic orbitals
a mixing of the atomic orbitals to produce molecular orbitals
Molecular orbital (MO) theory!!!

34. Making molecular orbitals from atomic orbitals

35. Molecular orbital energy diagram
Similar to orbital diagrams for atoms, but now for molecules
Molecular orbitals are labeled based on
the interaction between the orbitals (σ in the case below)
The type of bonding orbital (bonding or antibonding)
The orbitals involved (1s orbitals)
Molecular orbital energy diagram

36. Bond order
Bond order – relates to the strength of a bond and is dependent on the number of electrons in bonding and antibonding orbitals

37. Summary of LCAO-MO Theory
We can represent molecular orbitals (MOs) as a linear combination of atomic orbitals (AOs), where the total number of atomic orbitals will equal the total number of produced MOs
When two AOs mix, a lower energy bonding MO is produced, and a higher energy antibonding MO is produced
Filling in the molecular orbital energy diagram with the total number of electrons from the atoms, following general electron configuration rules
Bond order can be determined from the bond order formula
Summary of LCAO-MO Theory

38. Period two homonuclear diatomic molecules
With period two diatomic molecules 2s and 2p orbitals must be considered (the valence orbitals in these atoms)
Period two homonuclear diatomic molecules

39. For B2, C2, and so on, we need more orbitals to store electrons
Mixing of the positive and the negative to produce the bonding and antibonding MOs
p orbital based MOs

42. Explanation of change in orbital ordering
Orbitals with similar phases and similar energies can mix
The more 2s and 2px mixing lowers the σ2s energy and raises the σ2p energy

43. Summary

44. Power of the MO theory
Lewis dot structure shows oxygen with no unpaired electrons
From the MO diagram you can see that it does have 2 unpaired electrons
Real life liquid O2 displays paramagnetism, as expected from a compound with unpaired electrons

45. Second period heteronuclear diatomic molecules
Different atoms have different energies for their atomic orbitals
Mixing is not as strong in heteronuclear diatomic molecules

46. Polyatomic molecules

47. No MO Chapter 10