1. Molecular Geometry and Chemical Bonding Theory
Chapter 10
Molecular Geometry and Chemical Bonding Theory

2. VSEPR
Molecular geometry refers to the general shape of a molecule. There is a simple model to follow that will allow you to predict the geometry from Lewis formulas—VSEPR—Valence Shell Electron Pair Repulsion model.

3. VSEPR
The VSEPR model predicts the shapes of molecules and ions by assuming the valence shell electron pairs are arranged around each atom to minimize electron pair repulsions.
This model helps us predict the correct general shape of the molecule—it DOESN’T explain bonding.

4. VSEPR
2 electron pairs move to opposite sides of the nucleus giving a linear arrangement.
Visualizing Linear

5. VSEPR
3 electron pairs move apart yielding a trigonal planar arrangement (equal sides of a triangle).
Visualizing Trigonal Planar

6. VSEPR
4 electron pairs move apart to give us a tetrahedral arrangement; depending on the number of bonds formed, we can have a variety of molecular geometries with 4 electron pairs.
Visualizing a Tetrahedron

7. VSEPR
5 electron pairs give us a trigonal bipyramidal shape. This shape “changes” a bit depending on what is attached to the central atom and how many free electon pairs there are.
Visualizing a trigonal bipyramidal shape

8. VSEPR 6 electron pairs yields an octahedral shape.
Visualizing a Octahedral Shape

9. VSEPR
When determining molecular geometry, you look at the positions of atoms, not electron pairs. When doing so, identify the central atom, its electron pairs, those involved in bonding, and those which are lone pairs.
The direction in space of the bonding pairs gives you the molecular geometry.
Consider 2 electron pairs—a linear arrangement.

10. VSEPR
First, identify the valence electrons around the central atom. Follow the rules from earlier (chapter 9) to give the correct Lewis diagram.
Place the other elements around the central atom.
Consider BeF2
VSEPR will predict a linear arrangement due to there being 2 electron pairs in the valence shell of Be.

11. VSEPR VSEPR can be used for multiple bonds as well. Consider CO2:
Each multiple bond is treated as though it were a single electron pair.
CO2 will be linear according to the VSEPR model.

12. VSEPR With 3 electron pairs, consider BF3:
We get a trigonal planar geometry.
SO2 gives an example of 3 electron groups about the central atom—1 group being a lone pair. When we write this molecule according to VSEPR, it is a bent or angular model.
This molecule allows us to see how VSEPR can be used involving resonance examples.

13. VSEPR
No matter how you look at it, the S atom has 3 groups of electrons around it. This molecule is described as bent (or angular).
Whenever a resonance description is given, any of the formulas can be used to describe the geometry using VSEPR.
SO2 shows us the importance of lone pairs of electrons in determining the molecular geometry.

14. VSEPR
The steps used in the prediction of molecular geometry using VSEPR are as follows:
1. Write the electron dot formula from the molecular formula.
2. Use the electron dot formula to predict the number of electron pairs around the central atom— both bonding and non bonding electrons. When resonance occurs, use one resonance formula to determine this number.

15. VSEPR
3. Determine the arrangement of the electron pairs about the central atom.
4. Obtain the molecular geometry from the directions of the bonding pairs for this arrangement.
Lone electron pairs occupy more space than do bonded atoms and electrons. Thus, the lone pair acts to push the bonded electrons apart, reducing the bond angle.

16. VSEPR
Multiple bonds require more space than single bonds because the greater number of electrons.
5 electron pairs tends to be trigonal bipyramidal. The electron pairs are directed toward the corners of the trigonal bipyramid.

17. Dipole Moments
A dipole moment is a quantitative way of showing the degree of charge separation in a molecule. We use d+ and d- to represent this.
HCl is a polar molecule so we represent the dipole as Hd+—Cld-
Sometimes the presence or absence of a dipole moment of a molecule can be used to determine the molecular geometry.

18. Dipole Moments Consider CO2: where the dipole is zero.
The bonds here are equal and opposite and we can use special arrows in our drawing to indicate this.
Not all molecules experience the same pull of electrons. Polar molecules contain elements that “hog” the electrons and change the shape of the molecule. Consider H2O: where the dipole is not zero.

19. Dipole Moments
A zero dipole moment does not automatically give us the molecular geometry. A trigonal planar molecule would be an example of this.

20. Quantum Mechanics
Quantum mechanics allows us to understand valence bond theory and molecular orbital theory.
Valence bond theory will allow us to quantitatively look at electron pair or covalent bonding using quantum mechanics—that is, see how the electron orbitals are involved in bonding.

21. Valence Bond Theory
A bond forms when the following conditions are met:
1. The orbitals of 2 different atoms come to overlap and occupy the same regions of space.
2. The total number of electrons in both orbitals is no more than 2—each with a different spin. The greater the overlap the stronger the bond.

22. Valence Bond Theory
We can use valence bond theory to explain why H2 forms and why He does not bond to form He2.
H2 forms because both H atoms have the 1s1 configuration. Bringing them together brings electrons to occupy the same orbital, overlap and attraction binds the atoms together.
Helium stays separate because each 2s orbital has 2 electrons in it (1s2). Thus, trying to put 4 electrons in an orbital doesn’t work and the electrons strongly repel each other.

23. Valence Bond Theory
Bonding gives orbital overlap and atoms overlap to obtain a maximum attraction.
In HCl: H = 1s1; Cl = [Ne]3s23p5
In the valence shell, 3 orbitals are doubly occupied (one of the s-orbitals, and 2 of the p-orbitals) by electrons, one p orbital has an opening and the s orbital from H overlaps and hybridizes with it.

24. Valence Bond Theory To see how this occurs, consider the following:
Chlorine
Oxygen
Carbon
Chlorine and oxygen are easy to see, but what happens with carbon is a little different. A 2s electron gets “promoted” and 4 H atoms come to fill each of the empty orbitals.

25. Valence Bond Theory
When bonding like this occurs, the orbitals overlap forming hybrid-orbitals. They are obtained by taking the combinations of atomic orbitals of the isolated atoms.

26. Valence Bond Theory
Hybrid orbitals can be formed from various numbers of atomic orbitals. The number of hybrid orbitals always equals the number of atomic orbitals used.
eg., if an S and 2 P orbitals are used, sp2 hybrid orbitals are formed (3 of them).
See below for what the hybrid orbitals are and what they look like:

27. Valence Bond Theory

28. Valence Bond Theory
In the case of CH4, for example, 1s orbital and 3 2-p orbitals form the hybrid orbitals and hence they are called sp3 hybrid orbitals.
We can see that VSEPR predicts the tetrahedral shape of CH4. We can also show the hybridization as follows:

29. Valence Bond Theory VSEPR can be used:
There is a general scheme for describing bonding about any atom. The first task is to describe the geometric arangement about the central atom.
VSEPR can be used:
1. Write the Lewis dot formula of the molecule.
2. Use the VSEPR model to obtain the arrangement of electron pairs about this atom.
3. From the geometric arrangement of electron pairs, deduce the type of hybrid orbital on this atom required for the bonding description.

30. Valence Bond Theory
4. Assign valence electrons to the hybrid orbitals of this atom, one at a time, pairing them only when necessary.
5. Form bonds to this atom by overlapping singly occupied orbitals of other atoms with singly occupied hybrid orbitals of this atom.
Consider BF3:

31. Valence Bond Theory
Now we can describe bonding involving the overlap of more than one orbital from each bonding atom resulting in a multiple bond.
Consider C2H4
One hybrid orbital is needed for each bond (single or multiple bond) and for each lone pair.

32. Valence Bond Theory
Each C atom is bonded to 3 other atoms, there are no lone pairs and 3 hybrid orbitals are needed.
This suggests sp2.
During bonding, the 2s orbitals and two of the 2p orbitals of each carbon atom form three hybrid orbitals having a trigonal planar orientation.

33. Valence Bond Theory
The third 2p orbital remains unhybridized and is perpendicular to the plane of the three sp2 hybrids.

34. Valence Bond Theory
There are 2 types of bonds that help us explain multiple bonding: sigma (s) bonds and pi (p) bonds.
Sigma bonds are cylindrical about the bond as either the overlap of 2 s orbitals, 2 p orbitals along their axis, or 2 hybrids along their axis. H2 F2
C—C

35. Valence Bond Theory
A pi bond has electron distribution above and below the bond axis.
It’s formed from the sideways overlap of 2 parallel p orbitals. Pi bonds are weaker than sigma bonds and form after (if) 2 parallel orbitals are still available after sigma bonds have formed.

36. Valence Bond Theory
In the C2H4 molecule, the hybrid orbitals overlap first between the carbon hybrids and the hydrogens giving hybridized sp2 sigma bonds.

37. Valence Bond Theory
The 2 p orbitals that remain on the carbon atom extend above and below the bonding plane—they are parallel with each other and perpendicular to the CH2 plane. These come together to form a pi bond and “lock” the molecule in place.

38. Valence Bond Theory
The triple bond of C2H2 can be described the same way. We get sp hybridization.

39. Valence Bond Theory
This gives us a linear arangement. The hybrid orbitals overlap to give sigma bonds. The two 2p orbitals area not used (at first) and are perpendicular to the bond axis and to each other and form 2 pi bonds.
Thus, the C-C triple bond consists of one sigma bond and 2 pi bonds.

40. Molecular Orbital Theory
Valence bond theory doesn’t apply to all molecules because some atoms are paramagnetic. Some atoms with an even number of electrons have unpaired electrons; because of this, they are attracted to a magnet.
The best known example is liquid O2.

41. Molecular Orbital Theory
An alternative theory, Molecular Orbital Theory, can be used to explain this.
Molecular Orbital Theory is a theory of electronic structure of molecules in terms of molecular orbitals which may spread over several atoms or the entire molecule.

42. Molecular Orbital Theory
According to this theory, the electronic structure of molecules is much like the electronic structure of atoms. Each orbital has a definite energy, and to obtain the ground state of a molecule electrons are put into orbitals of the lowest energy (consistent with the Pauli exclusion principle) just like atoms.

43. Molecular Orbital Theory
Bonding orbitals are regions where electrons are concentrated between nuclei. In H2, we would say it is a s1s; s meaning it is cylindrical shaped along the bond axis, 1s means that the molecular orbital is obtained from the 1s atomic orbital.

44. Molecular Orbital Theory
The other type of molecular orbital is called the antibonding orbital. These are regions with zero values between nuclei (electrons spending little time here). We denote this as s* (sigma-star) which tells us the molecular orbital is antibonding.

45. Molecular Orbital Theory
The bond order is the number of bonds that exist between 2 atoms.
According to molecular orbital theory, bond order of diatomics is ½ the difference between the number of electrons in bonding orbitals, nb and the number of electrons in antibonding orbitals, na.
Bond order = ½ (nb –na)
H2—2 bonding electrons. Bond order = ½ (2-0) = 1
For He2—2 bonding, 2 antibonding, bond order = (2-2) = 0— which is why He2 doesn’t exist.
Bond orders don’t need to be whole numbers.

46. Molecular Orbital Theory
How do we know which orbitals overlap? Take Li for instance.
The strength of interaction is determined by:
1. The energy difference of the interacting orbitals.
2. The magnitude of the overlap.
Strong interaction occurs when the energies of the 2 orbitals are approximately equal and there is a large overlap.

47. Molecular Orbital Theory
In Li2, the 2s orbitals have the same energy and don’t interact much with the 1s orbitals of the other atom.
The 2s orbitals overlap and interact strongly when the atoms approach one another.
The bonding electron configuration of Li2 would be given as:
(s1s)2(s*1s)2(s2s)2
(s1s)2(s*1s)2 = KK = 0, signifying these inner shells aren’t much involved in bonding.
Thus, Li2 = KK(s2s)2

48. Molecular Orbital Theory
When calculating bond order, KK can be ignored because KK = 0, ½ (2-2) = 0, so the bond order for Li2 is simply 1, ½ (2-0) = 1
Be2 = KK(s2s)2(s*2s)2 = ½ (2-2) = 0
The bond order of Be2 = 0, so Be is unstable and no bond is formed.
Above were examples of homonuclear diatomic molecules.

49. Molecular Orbital Theory
Heteronuclear diatomic molecules are molecules composed of 2 different nuclei—CO and NO, for example.
To find the electron configurations, we need to have additional molecular orbitals.
We just looked at overlapping s orbitals.
Now, we can look at overlapping p orbitals.

50. Molecular Orbital Theory
There are two different ways in which the p orbitals can interact here:
One set of 2p orbitals can overalap along their axis to give the bonding and antibonding s orbitals.
The other two sets of 2p orbitals can overlap sideways to give two bonding and two antibonding p orbitals, p2p and p*2p).

51. Molecular Orbital Theory

52. Molecular Orbital Theory
When 2 atoms in a heteronuclear diatomic molecule differ appreciably, the homonuclear scheme no longer applies.
HF, for example:
The 1s on H and the 2 p on F, s bond and antibond along the bond axis.
The 2s and other 2p orbitals on fluorine remain as nonbonding orbitals.

53. Molecular Orbital Theory
The bonding orbital is this molecule (HF) is made up of a greater percentage of the fluorine 2p orbital than the 1 s of hydrogen—because of the electronegativity of fluorine.

54. Molecular Orbital Theory
One advantage of this over Valence Bond Theory is that resonance structures don’t need to be accounted for.
Molecular orbital theory describes resonance bonding in terms of a single electron configuration.
Consider O3.
The electrons are spread over all three O atoms. Because of this, each O atom is said to have 3 localized electron pairs around it.
This suggests each O atom uses sp2 hybrid orbitals.

55. Molecular Orbital Theory
The overlap of one hybrid orbital on the center O atom with a hybrid orbital on the end O atom at the left forms the left O-O bond.
The overlap of another hybrid orbital on the center O atom with a hybrid orbital on the end O atom at the right forms the other O-O bond.

56. Molecular Orbital Theory
This leaves one hybrid orbital on the center O atom and 2 on each of the end O atoms as lone pairs.

57. Molecular Orbital Theory
After the hybrids are formed, one hybridized p orbital remains on each O atom. These 3 (total) p’s are now perpendicular to the plane of the molecule and parallel with one another. They can overlap sideways to give 2 pi molecular orbitals.
Of these 3, one is bonding, one is non-bonding, and one is antibonding.
The bonding and non-bonding pi prbitals are doubly occupied which agrees with the resonance description in which one delocalized pair is bonding and the other is a lone (non-bonding) pair on the end O atoms.