1. CHE 106 CHAPTER NINE Molecular geometry and bonding theories

2. Molecular Geometry
Some helpful definitions: Bond Distance: the distance, usually given in Angstroms or pm, between two bonded atoms. Bond Angle: The angle formed between three bonded atoms.

3. Molecular Geometry
Lewis structures are used to show us the way atoms are arranged, but they leave much to be desired in describing how molecules appear in three dimensional space. The easiest types of molecules to study are those with a central atom, surrounded by varying number of peripheral atoms: An. The number of B atoms are large factor in determining the shape.

4. Molecular Geometry
In general: AB2: Linear or Bent with a bond angle of 180o. AB3: Trigonal Planar or Trigonal Pyramidal: less than 180o. Trigonal Planar: Bond angles of 120o and all elements are in the same plane. Trigonal Pyramidal: Angles of 109.5o and the central atom is set above the three peripheral. AB4: Tetrahedral, 109.5o. The main goal of all of the different shapes it to get pairs of electrons as far away from each other as possible.

5. Molecular Geometry
Valence Shell Electron Pair Repulsion Theory Electrons repel one another because they are the same charge. Our goal is to arrange electron pairs around atoms to maximize the distance between them and minimize repulsions. AXE Notation: A = Central Atom X = number of bond pairs of electrons E = number of lone pair of electrons

6. Molecular Geometry
Wherever electrons are found – bonding or non-bonding are sometimes referred to as electron domains. The electron domain geometry is a good place to start as you work towards molecular geometry. Electron domain considered all electron pairs while molecular geometry is only concerned with the bonding pair of electrons. Helpful tip: multiple bonds are still only considered one electron domain.

7. Molecular Geometry
2 electron pairs: AX2 E0

8. Molecular Geometry
3 electron pairs: AX3E0

9. Molecular Geometry
4 electron pairs: AX4E0

10. Molecular Geometry
5 electron pairs: AX5E0

11. Molecular Geometry
6 electron pairs: AX6E0

12. Molecular Geometry
-Determine Lewis Structure -Determine number of electron pairs around the central atom -Determine AXE notation -Assign structure based upon parent structure and minimizing repulsions -Determine any distortions in bond angles.

13. Molecular Geometry: 2 pairs
AXE: AX1E0: Linear AX2E0: Linear AX1E1: Linear

14. Molecular Geometry: 3 pairs
AX3E0: Trigonal Planar AX2E1: Bent AX1E2: Linear

15. Molecular Geometry: 4 pairs
Four electron domains around the central atom should give rise to a tetrahedral arrangement. However, when we look at molecules with 4 electron domains – but varying number of bonding / lone pair – the bond angles differ. H2O, NH3, CH4. Draw the Lewis dot structures for the 3 molecules. Compare their geometry.

16. Molecular Geometry: 4 pairs
Because of the presence of lone pair of electron in ammonia and water, the bonded atoms are forced to get closer and the bond is more compressed. The bond angles get a little smaller. Nonbonding electrons take up more space because they feel less nuclear attraction. This results in more repulsive forces and compressed bond angles.

17. Molecular Geometry: 4 pairs
AX4E0: Tetrahedron

18. Molecular Geometry: 4 pairs
AX3E1: Trigonal Pyramidal

19. Molecular Geometry: 4 pairs
AX2E2: Bent

20. Molecular Geometry: 5 pairs
When the central atom has 5 pairs, the electrons pairs can assume one of two positions: axial or equatorial. Axial: forms 90o angels with all equatorial domains Equatorial: forms 120o angles with other two equatorial domains, and 90o angles with axial. When determining where the lone pair of electrons will exist - they always will occupy an equatorial position because there is less repulsive force there.

21. Molecular Geometry

22. Molecular Geometry: 5 pairs
AX5E0: Trigonal bipyramidal: two triangle pyramids face to face. AX4E1: See Saw

23. Molecular Geometry: 5 pairs
AX3E2: T Shaped AX2E3: Linear

25. Molecular Geometry: 6 pairs
AX6E0: Octahedron

26. Molecular Geometry: 6 pairs
AX5E1: Square Pyramid

27. Molecular Geometry: 6 pairs
AX4E2: Square Planar AX3E3: T Shaped

28. Molecular Geometry
Example: BF4-2 vs. XeF4 BeF4-2: AX4E0: Tetrahedron XeF4: AX4E2: Square Planar

29. Molecular Geometry
Examples: I3 and SeF4 I3: AX2E3 : Linear SeF4: AX4E1: See Saw

30. Molecular Geometry
Some exceptions: Even though we count a double bond as 1 electron domain, a double or triple bond does influence the bond angles. Double and triple bonds take up more space, so the bond angles will be slightly smaller than expected. Example: COCl2

31. Molecular Geometry
Examples: OF2 ClO2-1 BF3 PBr3 TeCl4 BrO4-1 SnCl4 SF6 XeOF4

32. Molecular Geometry
It is slightly more difficult to determine bond angles for larger molecules, but we can still hone in on certain atoms to help us get an idea of the three dimensional molecule. Determine the bond angles around the three back bone elements in CH3COOH.

33. Molecular Geometry Vinyl Alcohol: CH2CHOH
Predict bond angles in Propyne

34. Molecular Polarity
Bond polarity is determined by electronegativity and is a measure of how the electrons in a bond are being shared. Expressed as dipole moments. Molecular polarity depends on the polarity of each bond as well as the molecular geometry. The overall dipole moment of the molecule is the sum of each dipole.

35. Molecular Polarity
Dipoles are vector quantities: both magnitude and charge. When we add them together, we have to consider both. Explains why CO2 is non polar and H2O is polar.

36. Molecular Polarity
BF3 vs. NH3

37. Molecular Polarity
Predict whether the following molecules are polar or non polar: BrCl, SO2, SF6

38. Orbital Overlap
In Lewis theory – covalent bonds are formed when two nuclei are simultaneously attracted a pair of electrons. The electron density is found between the two nuclei. Valence Bond Theory: a chemical bond is described as the overlap of atomic orbitals, with electrons of opposite spins sharing space in the orbital.

39. Orbital Overlap
Other examples that are easy to study: HCl, Cl2.

40. Orbital Overlap
As the atomic orbitals overlap, there is a relationship between the potential energy, stability and bond length of the molecule. As the atomic orbitals approach one another, there PE decreases, because they are becoming more stable. After a certain point, they get too close and the repulsive forces take over and cause a spike in energy. The bond length is the inter-nuclear distance that corresponds to the minimum energy on the PE curve.

41. Orbital Overlap

42. Hybrid Orbitals
If we consider the the molecule methane: CH4 Carbon orbital diagram: Hydrogen orbital diagram: If you look at carbons orbital diagram, it would suggest that carbon can only form 2 bonds. However, it often will surround itself with 4 bonds. How is that possible?

43. Hybrid Orbitals
One explanation would involve promoting one of the 2s electrons to the empty 2p orbital – giving us four lone electrons. Voila! If that were the case – the 1 of the hydrogen atoms would bond with the open 2s orbital, and the other 3 atoms would be found in each of the 2p orbitals. This would result in 3 bonds in p orbitals, and 1 bond in the s orbitals. If this were the case, we would expect the bond angles of methane to be different for the p bonds in comparison to the s bond. But we know - all the bond angles and lengths are identical.

44. Hybrid Orbitals
How can we explain the equivalent bond lengths and angles in CH4? The 2s and 2p orbitals actually hybridize to form 4 new sp3 orbitals that are equivalent. When we form hybrid orbitals – we still have the same number of available places to bond – they just have a different orbital geometry that allows equivalent bonds to be formed with the 1s electrons of hydrogen.

45. Hybrid Orbitals

46. Hybrid Orbitals

47. Hybrid Orbitals
If we look at other molecules, we see that the hybridization of s and p orbitals is rather common. Example: BeF2 Be: 1s22s2  0 unpaired electrons F: 1s22s22p5  1 unpaired electron in the 2p As is, there should be no driving force for Be to bond with Fluorine. However, it forms two bonds, which means two lone pairs or electrons are available for fluorine to overlap with.

48. Hybrid Orbitals
Again, we could arrange the 2s2 electrons differently: 2s1 and 2p1 – but this would give us non- equivalent bonds. And we know the molecule is linear.

49. Hybrid Orbitals
Instead, we hydridize one “s” orbital and one “p” orbital, which gives rise to 2 “sp” orbitals. Which are now equivalent.

50. sp Hybrid Orbitals
sp hybrid orbitals formed from the combination of one s and one p orbital (linear arrangement). + +
linear

51. Hybrid Orbitals
Each singly occupied “sp” orbital is now available to bond with the lone electron in the 2p orbital of fluorine. The two sp orbitals face away from one another, so this will imply a linear arrangement.

52. Hybrid Orbitals
SP2 hybridization: BF3 : Boron: 1s22s22p1

53. sp2 Hybrid Orbitals
sp2 hybrid orbitals formed from the combination of one s and one p orbital (linear arrangement). + + +
trigonal planar

54. sp3 Hybrid Orbitals
sp2 hybrid orbitals formed from the combination of one s and one p orbital (linear arrangement). + + + +
tetrahedral

55. Hybrid Orbitals
The three hybridizations we have discussed work well for smaller elements, which only involve the s and p valence electrons and obey the octet rule. For molecules that are hypervalent, we need more than just the four orbitals made available to use with sp, sp2 and sp3 hybridizations. One way of increasing the available hybrid orbitals is by incorporating the d orbitals as well.

56. Hybrid Orbitals
To accommodate five or more bonded atoms: the central atom can use its ns and np orbitals (n is the outer most shell) as well as the n-1 d orbitals. To accommodate 5: we use an “s”, three “p” and one “d” orbital to create equivalent: sp3d orbitals. To accommodate 6: sp3d2 orbitals

57. sp3 Hybrid Orbitals

58. Hybrid Orbitals

59. Hybrid Orbitals

60. Hybrid Orbitals Draw Lewis Structures
Determine VSEPR geometry using AXE notation
Determine the hybrid orbitals needed to fit the geometry:
sp = linear sp2 = trigonal planar
sp3 = tetrahedral sp3d = trig. Bipyramid
sp3d2 = octahedron.

61. Hybrid Orbitals
Examples: 1. Indicate the orbital hybridization around the central atom in NH Predict the electron domain geometry and hybridization of the central atom in SO3-2.

62. Multiple Bonds
When two nuclei come together to form a bond through orbital overlapping, the electron density can either be concentrated along the internuclear axis or above/ below the internuclear axis. Sigma Bond: Electron density along axis s Pi Bond: Electron density above and below p

63. Multiple Bonds
Whether the bond is considered a s or a p bond depends on what type of orbitals are overlapping. When s orbitals overlap in H2, the p orbitals overlap in HCl or the p and sp orbitals overlap – these all give rise to sigma bonds. All of these orbital overlaps lead to electron density located right in between the two nuclei.

64. Multiple Bonds
Pi bonds occur when the orbital overlap occurs perpendicular to the internuclear axis. The electron cloud density is located above and below the axis. These bonds tend to be weaker than sigma bonds. Pi bonds can only be formed after a sigma bond, because the sigma bond is what brings the p orbitals together in the first place. Some general helpful hints: Single bonds are sigma bonds Double bonds: 1 sigma, 1 pi Triple Bonds: 1 sigma and 2 pi.

65. Multiple Bonds
Ethylene: C2H4 There are three electron domains. Giving a trigonal planar structure around each carbon atom, indicating an sp2 hybridization. Recall carbon valence electrons:

66. Multiple Bonds
Each carbon has 3 sp2 orbitals prepared for bonding and 1 leftover p orbital. First a carbon – carbon sigma bond is formed by the overlap of each carbons sp2 orbital. Then the 4 hydrogens overlap and bond with the remaining sp2 orbitals. The leftover p orbitals on each carbon will also overlap, but they are oriented above and below the axis, hence forming a pi bond.

67. Multiple Bonds

68. Multiple Bonds
Sigma bonds are thought as end to end overlap between the nuclei, which allows them to spin and rotate without losing their overlap.
Because pi bonds are a side to side overlap, they are not able to rotate. By spinning, they would “come apart.” the The presence of pi bonds locks the carbon atoms in their place… which is why this molecule is a planar molecule.

69. Multiple Bonds
Acetylene: C2H2 – linear molecule containing a triple bond. Linear geometry indicates sp hybrization, leaving two p orbitals available for overlap.

70. Multiple Bonds
For the following molecules: Draw Lewis Structure Predict hybridization around central atom Using an orbital diagram, show this hybridization Identify the number of sigma and pi bonds in your Lewis dot structure and your orbital diagram. NH3, PF5, IF2-, CO3-2, HCN, TeF5-1, I3-, ClF3

71. Multiple Bonds
In all of these bonds, the electrons are localized; meaning they are still completely associated with the two atoms that came together to form the bond.
However, there are many cases where the electrons are considered delocalized – the electrons are far more fluid within the molecule.
This is the case when molecules have pi bonds and two or more resonance structures, like Benzene.

72. Multiple Bonds

73. Multiple Bonds

74. Multiple Bonds
Because the electrons are spread out amongst all 6 carbon atoms in the ring, they are considered delocalized. These pi bonds lock the surrounding carbon atoms into a particular rigid structure.
These delocalized electrons are responsible for many of the odors of organic compounds and the rigidity of pi bonds gives many organic compounds their properties.

75. Hybrid Orbitals Summary
Every bonded pair of atoms shares at least one electron pair - every bond has one sigma bond localizing the electrons between the atoms bonds. - there is a close relationship between molecular geometry and the hybrid orbitals that were formed. Sigma bonds contribute to the the bonding of two atoms Multiple bonding is only possible if pi bonds are introduced, which may result in delocalized electrons. Every pi bond involves two 2 overlaps (2 lobes in p orbital)

76. Molecular Orbitals
Although orbital hybridizations and VSEPR theory allow us to make sense of many of the observed properties of molecules, there are certain things that are not able to be explained with these theories. Molecular orbital theory relies on interpreting electrons as wave functions and are associated with the whole molecule rather than just the central atom (axe notation).

77. Molecular Orbital
Molecular orbitals are formed whenever atomic orbitals overlap. In a molecule of hydrogen, we have two 1s orbitals overlapping, which gives us two MO’s. Because molecular orbital theory uses the idea that electrons are waves, when we combine these two orbitals that overlap can either be constructive or destructive.

78. Molecular Orbital
If the addition of the wave functions of the 1s orbitals, this MO is a constructive combination. It’s energy is lower and more stable than the two 1s orbitals on their own. This is called a bonding MO. The other MO is formed when the two orbitals overlap and cancel each other out. This is called destructive combination and results in an antibonding orbital. This has higher energy than the atomic orbitals.

79. Molecular Orbital

80. Molecular Orbital
In this diagram, the bonding MO shows an electron density in between the two nuclei and the electrons are attracted to both nuclei. It is energetically favorable and more stable than the 1s orbitals by themselves. The antibonding MO shows electron density on opposite sides of the molecules and a node in the region between the two nuclei. Electrons are not present in the area where the bond should exist. They are repelled and have higher energy and are unstable.

81. Molecular Orbital
Because in both of these MO the electron density is located along the internuclear axis, they are referred to a sigma molecular orbitals. Bonding: s1s Antibonding: s*1s Molecular orbital diagrams or energy level diagrams are used to relate the energy of atomic and molecular orbitals.

82. Molecular Orbital
Energy level diagram for H2

83. Molecular Orbital
Energy level diagram for He2: why diatomic helium cannot exist

84. Molecular Orbital
Bond Order = ½ (# of bonding electrons – # of antibonding electrons). Bond Order of 1 = single bond, 2 = double bond, 3 = triple bond. Typically whole numbers, however can be a fraction: ½, 3/2, or 5/2. If a bond order is calculated to be zero, that bond does not exist. The higher the bond order, the greater the stability. Example: H2 has a bond order of 1, He2 has a bond order of 0.

85. Molecular Orbitals
Other new terminology: Diamagnetic: molecular orbitals contain no unpaired electrons. These molecules would be weakly repelled by a magnetic field. Paramagnetic: contains at least one unpaired electron. Strongly attracted into magnetic fields.

86. Molecular Orbital
Our study of molecular orbitals will focus on the diatomic molecules of Period 2 elements. The valence electrons are located in the 2s and 2p. Some things to consider:
The number of MO orbitals = atomic orbitals combined.
Atomic orbitals combine best with orbitals of similar energy.
As the overlap increases, the effectiveness increases and the bond energy decreases: making it more stable bonding MO and more unstable antibonding.
Each MO can hold 2 electrons with spins paired (Pauli exclusion)
When MO’s of same energy level are populated, one electron per orbitals before spin pairing (Hunds rule)

87. Molecular Orbitals for Li2
Li2 molecules exist in the vapor phase when lithium metal is heated to its boiling point. Electron configuration is 1s22s1. We can assume that because the 1s and 2s atomic orbitals are different energies, the 1s orbitals from each lithium will overlap and the 2s orbitals will overlap separately.

88. Molecular Orbitals for Li2

89. Molecular Orbitals
One thing to notice about the molecular orbital diagram is the difference between the bonding and antibonding orbitals at the 1s level compared to the 2s level. The 2s MO bonding and antibonding orbitals have much greater difference in their energy. Because the 2s orbitals are larger than the 1s, they are able to overlap to a greater extent. This results in a much greater energy discrepancy between the bonding and antibonding orbitals.

90. Molecular Orbitals for Li2
The 6 electrons in a Li2 molecule are placed as follows:
2 electrons in s1s, 2 electrons in s*1s and 2 electrons in s2s.
This arrangement gives us a bond order of ½ (4-2) = 1. A bond order of 1 then can be interpreted to have a single bond which is consistent with what is observed experimentally.
This bond arises from the overlap of the 2s electrons because both the bonding and antibonding are filled at the 1s level.

91. Molecular Orbitals for Be2
Be has 4 valence electrons: 1s22s2. The Be2 molecule therefore requires Placing 8 electrons in MOs. With a bond order of Zero, can this Molecule exist?

92. Molecular Orbitals
What happens when we begin forming diatomic molecules with elements that have valence electrons in the p orbitals. We can overlap p orbitals and also describe them in terms of molecular orbitals. Because there are three p orbitals to overlap, we will form 6 MO’s. (3 from each of the elements in the diatomic molecule). These MOs can also be labeled as either sigma or pi.

93. Molecular Orbitals
The pz orbital overlap has been decided upon to be the overlap that concentrates the electron density along the internuclear axis. Considered end to end overlap. The 2pz overlap will give us a s2p and a s*2p

94. Molecular Orbitals
2px and 2py then are around rather than on the internuclear axis and will form p MO.

95. Molecular Orbitals
Using this information, we can construct molecular orbitals for diatomic molecules from B2 to Ne – which employ both 2s and 2p overlap.
Things to consider when looking at MO diagram:
2s atomic orbitals have less energy than the 2p atomic orbitals. The MO formed from 2s orbital are lower in energy than any MO formed from 2p overlap.
The overlap of the two 2pz orbitals is greater than the 2px and 2py, therefore more energy different between the bonding and antibonding 2pz MOs.
The p2p and p*2p MOs are “doubly degenerate”: there are two degenerate of each.

96. Molecular Orbitals

97. Molecular Orbitals
Finally, before we can construct a MO diagram of a diatomic molecules, we have to take into account one more behavior that has been noticed. The 2s orbital of one atom may interact with the 2p orbital of the neighboring atom. Due to 2s and 2p interaction in small molecules, the bonding s2pz and p2px,y will switch energies with the p2px,y having less energy (more stable) than the s2pz.

98. Molecular Orbitals O thru Ne Li thru N
*(2pz)
O thru Ne
 (2px,y) 2p 2p
 (2px,y)
 (2pz)
Bonding orbitals from the p’s switch energies for the smallest molecules due to 2s-2p interactions
*(2pz)
Li thru N
 (2px,y)
 (2pz) 2p 2p
 (2px,y)

99. Molecular Orbitals for B2

100. Molecular Orbitals for C2

101. Molecular Orbitals for N2
*(2pz)
 (2px,y)
 (2pz) 2p 2p
 (2px,y)
*(2s)
ENERGY
b.o. = 8-2 = 3 2
 (2s)
DIAMAGNETIC 2s 2s NA N2 NB

102. Molecular Orbitals for O2
*(2pz)
 (2px,y) 2p 2p
 (2px,y)
 (2pz)
*(2s)
ENERGY
b.o. = 8-4 = 2 2
 (2s) 2s 2s OA O2 OB

103. Molecular Orbitals for O2
*(2pz)
Unpaired Electrons PARAMAGNETIC
 (2px,y) 2p 2p
 (2px,y)
 (2pz)
*(2s)
 (2s) 2s 2s OA O2 OB

104. Molecular Orbitals for Period 2 p sublevel
B2 C N N2+1
*(2pz)
 (2px,y)
 (2pz)
 (2px,y)
*(2s)
 (2s)
bond order

105. Molecular Orbitals for Period 2 p sublevel
O2 F Ne F2+1
*(2pz)
 (2px,y)
 (2pz)
 (2px,y)
*(2s)
 (2s)
bond order