1. Molecular Geometry And Bonding Theories 熊同銘 tmhsiung@gmail.com
Chapter 9
Molecular Geometry
And Bonding Theories
熊同銘

2. 第二次會考 1051207 (ch5-8) 積極性補強教學： 週一、週二17：30-20：30 週三、週四17：30-21：30
海事大樓412教室

3. Contents
Molecular Shapes
The VSEPR Model
Molecular Shape and Molecular Polarity
Covalent Bonding and Orbital Overlap
Hybrid Orbitals
Multiple Bonds
Molecular Orbitals
Period 2 Diatomic Molecules

4. Molecular Shapes
Lewis structures is two-dimensional arrangement:
Molecular shapes three-dimensional arrangement:

5. *****
The VSEPR Model
Valence Shell Electron Pair Repulsion (VSEPR) theory: A theory that allows prediction of the shapes of molecules or polyatomic ion based on the idea that electron domain˗ either as lone pair (nonbonding pair) or as bonding pair ˗ repel one another.
Electron domain geometry: The geometrical arrangement of electron domain in a molecule.
Molecular geometry: The geometrical arrangement of atoms in a molecule.
Valence Shell Electron Pair Repulsion: 價殼[層]電子對互斥

6. VSEPR theory proceeding Write a best Lewis structure
*****
VSEPR theory proceeding
Write a best Lewis structure
Determine VSEPR notation:
ABnEm:
A: Central atoms
B: Terminal atoms
E: Lone pairs electrons
H2O for example:
AB2E2

7. Determine the electron geometry
*****
Determine the electron geometry
An electron group can be:
- either single bond or a multiple bond
- a (resonance) hybrid bond
- a lone pairs of electron
- a unpaired single-electron
Repulsion force in general:
LP vs. LP > LP vs. BP > BP vs. BP
* Lone Pairs (LP), Bonding Pairs (BP)
Angle for repulsion forces: 90° > 120° > 180°
For central (interior) atom belong to third-period or higher element with VSEPR notation such as AB5, AB4E, AB3E2, AB6, AB5E, AB4E2 require an expanded octet such as 3d orbital.
Multiple bond occupy more space than single bond

8. Determine the molecular geometry
*****
Determine the molecular geometry
Structures for the central atom without lone-pair electrons (ABn type), electron geometry and molecular geometry are identical.
Structures for the central atom with lone-pair electrons (ABnEm type) type), electron geometry and molecular geometry are different.

9. Determine the molecular geometry of NH3
*****
Determine the molecular geometry of NH3

10. *****
Bent: 彎曲
Linear: 直線
Octahedral: 八面體
Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體
* Count only electron groups around the central atom. Each of the following is considered one electron domain: a lone pair, a single bond, a double bond, a triple bond, or a single electron.

11. ***** Bent: 彎曲 Linear: 直線 Octahedral: 八面體 Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體

12. ***** Bent: 彎曲 Linear: 直線 Octahedral: 八面體 Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體

13. ***** Bent: 彎曲 Linear: 直線 Octahedral: 八面體 Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體

14. The Five Basic Shapes
(All electrons around the central atom are bonding group)
Two Electron Domain (AB2): Linear

15. Three Electron Domain (AB3): Trigonal Planar
* double bond contains more electron density than the single bond

16. Four Electron Domain (AB4): Tetrahedral
Five Electron Domain (AB5): Trigonal Bipyramidal

17. Six Electron Domain (AX6): Octahedral

18. Example Determine the molecular geometry of NO3−.
Solution
NO3− has 5 + 3(6) + 1 = 24 valence electrons. The Lewis structure has three resonance structures:
Use any one of the resonance structures to determine the number of electron groups around the central atom. The nitrogen atom has three electron domain.
The electron domain geometry is trigonal planar:
The molecular geometry is also trigonal planar.

19. The Effect of Lone Pairs
(Some electrons around the central atom are lone pairs)
Three Electron Domain with Lone Pairs
AB2E

20. Four Electron Domain with Lone Pairs
AB3E
AB2E2

21. * Effect of Lone Pairs on Molecular Geometry

22. Five Electron Domain with Lone Pairs
AB4E
AB3E2
AB2E3

23. Six Electron Domain with Lone Pairs
*****
AB5E
AB4E2

24. Sample Exercise 9.1 Use the VSEPR model to predict the molecular geometry of (a) O3, (b) SnCl3–.
Solution
(a)
(b)
electron domains geometry:
trigonal planar
molecular geometry:
bent
electron domains geometry:
tetrahedral
molecular geometry:
trigonal-pyramidal

25. Sample Exercise 9.2 Use the VSEPR model to predict the molecular geometry of (a) SF4, (b) IF5.
Solution
(a)
electron domains geometry:
trigonal bipyramid
molecular geometry:
seesaw-shaped

26. electron domains geometry: octahedral molecular geometry:
Continued
(b)
electron domains geometry:
octahedral
molecular geometry:
square pyramidal
Experimentally, the angle between the base atoms and the top F atom is 82゜, smaller than the ideal 90゜.

27. Representing Molecular Geometries on Paper
Examples:

28. Shapes of Larger Molecules
Example: acetic acid

29. *****
Sample Exercise 9.3 Eyedrops for dry eyes usually contain a water-soluble polymer called poly(vinyl alcohol), which is based on the unstable organic molecule vinyl alcohol:
Predict the approximate values for the H—O—C and O—C—C bond angles in vinyl alcohol.
Solution
H—O—C angle is slightly less than 109.5゜.
O—C—C angle is slightly greater than 120゜.

30. Without lone-pair electrons
*****
Memo for VSEPR
Without lone-pair electrons
VSEPR
Notation
Electron
Geometry
Molecular
AB2
Linear
AB3
Trigonal planar
AB4
Tetrahedral
AB5
Trigonal bipyramidal
AB6
Octahedral
Bent: 彎曲
Linear: 直線
Octahedral: 八面體
Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體

31. With lone-pair electrons
*****
With lone-pair electrons
VSEPR
Notation
Electron
Geometry
Molecular
AB2E
Trigonal planar
Bent
AB3E
Tetrahedral
Trigonal pyramidal
AB2E2
AB4E
Trigonal bipyramidal
Seesaw
AB3E2
T-shaped
AB2E3
Linear
AB5E
Octahedral
Square pyramidal
AB4E2
Square planar
Bent: 彎曲
Linear: 直線
Octahedral: 八面體
Seesaw: 蹺蹺板
Square planar: 平面正方形
Square pyramidal: 方錐體
Tetrahedral四面體:
Trigonal bipyramidal: 三角雙錐
Trigonal planar: 平面三角形
Trigonal pyramidal: 三角錐體

32. 3. Molecular Shape and Molecular Polarity
Bond dipole versus Molecular dipole
Bond dipole: A separation of positive and negative charge in an individual bond.
Molecular dipole:
For diatomic molecule: molecular dipole is identical to bond dipole.
For a molecule consisted by three or more atoms, molecular dipole is estimated by the vector sum of individual bond dipole moment (overall dipole moment).

33. Polar molecule versus Nonpolar molecule
Polar molecule: A molecule in which the molecular dipole is nonzero.
Nonpolar molecule: A molecule in which the molecular dipole is zero.
Molecular polarity prediction
Draw the Lewis structure for the molecule and determine its molecular geometry.
Determine if the molecule contains polar bonds by electronegativity values.
Determine if the polar bonds add together to form a overall dipole moment.

34. Examples ***** CO2 Molecular geometry: linear
Overall dipole moment: m = 0 D
Nonpolar molecule
H2O
Molecular geometry: bent
Overall dipole moment: m = 1.85 D
Polar molecule

35. Quantum-Mechanical Approximation Technique
X. VB versus MO
Quantum-Mechanical Approximation Technique
Perturbation theory (used in valence bond theory): A complex system (such as a molecule) is viewed as a simpler system (such as two atoms) that is slightly altered or perturbed by some additional force or interaction (such as the interaction between the two atoms).
Variational method (used in molecular orbital theory): The energy of a trial function (educated function) within the Schrodinger equation is minimized.
Perturbation theory: 擾動理論
Variational method: 變分法

36. Schrodinger equation revisited H = E
H (Hamiltonian operator), a set of mathematical operations that represent the total energy (kinetic and potential) of the electron within the atom.
E is the actual energy of the electron.
 is the wave function , a mathematical function that describes the wavelike nature of the electron.
Perturbation theory: Approach by small changes to a known system in which Hamiltonian operator is modified.
Variational method: Approach by combining systems of comparable weighting in which wave function is modified.
Perturbation theory: 微擾法
Variational method: 變分法

37. Valence bond theory versus molecular orbital theory
Valence bond theory (VB): An advanced model of chemical bonding in which electrons reside in quantum-mechanical orbitals localized on individual atoms that are a hybridized blend of standard atomic orbitals; chemical bonds result from an overlap of these orbitals.
Molecular orbital theory (MO): An advanced model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule. In the simplest version, the molecular orbitals are simply linear combinations of atomic orbitals.
Reside: 駐在

38. 4. Covalent Bonding and Orbital Overlap
Valence bond theory describes that covalent bonds are formed when atomic orbitals on different atoms overlap.
Simple Atomic Orbitals (AO’s) Overlap
A covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms.
This overlap region has a high electron charge density.
The overall energy of the system is lowered.

39. Formation of the H2 molecule as atomic orbitals overlap.

40. Acceptable simple Atomic Orbitals (AO’s) Overlap
Bonding in H2S for example
Predicted H˗S˗H angle is 90o, actual H˗S˗H angle is 92o, therefore, the simple AO overlap is acceptable for H2S molecule.

41. Unacceptable simple Atomic Orbitals (AO’s) Overlap
Example: CH4
Ground-state electron configuration of C for example, it should form only 2 bonds
Actually, the central atom of H2S, H2O, NH3, and CH4, are sp3 hybridization

42. *****
5. Hybrid Orbitals
Hybridization: A mathematical procedure in which standard atomic orbitals are combined to form new, hybrid orbitals.
Hybridizing is mixing different types of orbitals in the valence shell to make a new set of degenerate orbitals such as sp, sp2, sp3, sp3d, sp3d2.
Hybrid orbitals minimize the energy of the molecule by maximizing the orbital overlap in a bond.
Those central atoms are available hybridized, however, those terminal atoms are supposed to be unhybridized.
Degenerate orbitals: 等能階軌域、退化軌域

43. General statements regarding hybridization
*****
General statements regarding hybridization
Hybridization is employed for central atom only, thus, the hybrid orbital describes the electron geometry for central atom.
Number of hybrid orbitals = Number of standard atomic orbitals combined = Number of σ bond + Number of lone pairs.
Number of hybridization obitals of a central atom = 2 → sp; = 3 → sp2; = 4 → sp3; = 5 → sp3d; = 6 → sp3d2.
Hybrid orbitals may overlap with standard atomic orbitals or with other hybrid orbitals to form σ bond.
Molecular geometry is described by the relative atomic position around central atom.

44. sp3 hybridization (C for example)
one s orbital with three p orbitals combine to form four sp3 hybrid orbitals (degenerate).

46. Examples of sp3 hybridization (for central atom)
*****
Examples of sp3 hybridization (for central atom)
Central
atom
Mole-
cule
Standard
orbitals
Hybrid
Orbital
Geometry σ σ σ σ C 2s 2p
sp3
lone σ σ σ N 2s 2p
sp3
CH4: four σ bonds / C(sp3)-H(s)
NH3: three σ bonds / N(sp3)-H(s), one lone pairs / N(sp3)
H2O: two σ bonds / O(sp3)-H(s), two lone pairs / O(sp3)
lone
lone σ σ O 2s 2p
sp3

47. sp2 hybridization (B for example)
one s orbital with two p orbitals combine to form three sp2 hybrid orbitals

48. Examples of sp2 hybridization (for central atom)
*****
Examples of sp2 hybridization (for central atom)
Central
atom
Mole-
cule
Standard
orbitals
Hybrid
Orbital
Unhybridized
Orbital σ σ σ B 2s 2p 2p
sp2 σ σ σ π C 2s 2p 2p
sp2
lone σ σ π
BF3: three σ bonds / B(sp2)-F(p)
H2C=CH2: each carbon, three σ bonds / two C(sp2)-H(s) and one C(sp2)- C(sp2), one π bond / C(p)- C(p)
HN=NH: each nitrogen, two σ bonds / one N(sp2)-H(s) and one N(sp2)- N(sp2), , one lone pairs / N(sp2), one π bond / N(p)- N(p) N 2s 2p 2p
sp2

49. sp hybridization (Be for example)
one s orbital with one p orbitals combine to form two sp hybrid orbitals

50. Examples of sp hybridization (for central atom)
*****
Examples of sp hybridization (for central atom)
Central
atom
Mole-
cule
Standard
orbitals
Hybrid
Orbital
Unhybridized
Orbital σ σ Be 2s 2p 2p sp π π σ σ C 2s 2p 2p sp
BeCl2: two σ bonds
HCCH: each carbon, two σ bonds, two π bonds

51. Hypervalent Molecules
(elements of period 3 and beyond may have more than octet electrons around central atom)
sp3d hybridization, AsF5 for example

52. Continued

53. sp3d2 hybridization, SF6 for example

54. Continued

55. Procedure for Hybridization and Bonding Scheme
*****
Procedure for Hybridization and Bonding Scheme
Write the Lewis structure for the molecule.
Use VSEPR theory to predict the electron geometry about the central atom.
Select the correct hybridization for the central atom based on the electron geometry.
Sketch the molecule, beginning with the central atom and its orbitals. Show overlap with the appropriate orbitals on the terminal atoms.
Label all bonds using the σ or π notation followed by the type of overlapping orbitals.

56. *****
Example for hybridization/electron geometry types versus molecular geometry
Number of
σ + lone
Hybridi-zation
VSEPR
notation
Electron
geometry
Molecular
Example 2 sp
AX2
Linear
linear
Cl-Be-Cl 3
sp2
AX3
AX2E
Trigonal planar
Angular
BCl3
SO2 4
sp3
AX4
AX3E
AX2E2
Tetrahedral
Trigonal pyramidal
CH4
NH3
H2O 5
sp3d
AX5
AX4E
AX3E2
AX2E3
Trigonal bipyramidal
Seesaw
T-shaped
PBr5
SF4
ClF3
XeF2 6
sp3d2
AX6
AX5E
AX4E2
Octahedral
Square pyramidal
Square planar
SF6
BrF5
XeF4

57. s + s, s + p, p + p (end-to-end), s + hybrid orbital
*****
6. Multiple Bonds
σ (sigma) bond: The first covalent bond formed by end-to-end overlap of standard or hybridized orbitals between the bonded atoms:
s + s, s + p, p + p (end-to-end), s + hybrid orbital
p + hybrid orbital, hybrid orbital + hybrid orbital
π (Pi) bond: The second (and third, if present) bond in a multiple bond, results from side-by-side overlap of unhybridized p orbitals:
p + p (side-by-side)

58. σ bonding and π bonding
* The electron density on internuclear axis, π bond less than σ bond. Therefore, π bond makes weaker overlap than σ bond.

59. Single Bond and Multiple Bonds
Single bonds: one σ bond
Double bond: one σ bond and one π bond
Triple bond: one σ bond and two π bonds

60. VB theory of bonding in ethylene (H2C=CH2)
example of sp2 hybridization and a double bond
Lewis structure
A π-bond has two lobes (above and below plane), but is one bond, side-by-side overlap of 2p–2p

61. Continued
All six atoms in C2H4 lie in the same plane

62. VB theory of bonding in Acetylene (HCCH)
example of sp hybridization and a triple bond
Lewis structure
Two π-bonds from 2p–2p overlap forming a cylinder of π-electron density around the two carbon atoms

63. Continued
Scheme: 圖解

64. VB theory of bonding in Formaldehyde (H2C=O)
example of sp2 hybridization and a double bond
Lewis structure

65. Continued
lone
lone σ π σ σ σ π
Valence bond model

66. Resonance Structures, Delocalization, and π Bonding
Localized or Delocalized Electrons
Localized electrons: Bonding electrons (σ or π) that are specifically shared between two atoms.
Delocalized electrons: Electrons that are spread over a number of atoms in a molecule or a crystal rather than localized on a single atom or a pair of atoms.

67. Delocalized π bonds in benzene
Benzene, total of 30 valence electrons, 24 valence form the σ bonds, 6 C(sp2)-C(sp2) and 6 C(sp2)-H(1s)
The remaining six valence electrons occupy these six pπ orbitals

68. Continued
benzene has a six-electron π system delocalized among the six carbon atoms.

69. Delocalized π bonds in NO3-
NO3-, total of 24 valence electrons, 12 as nonbonding pairs and 6 σ bonds (3 C(sp2)-N(sp2) bonds)

70. Continued
Delocalized the six-electron π system in NO3-.

71. 8. Molecular Orbital Theory: Electron Delocalization Chemical Bond
Molecular Orbital (MO): A model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule.
The molecular orbitals are linear combinations of atomic orbitals (LCAO).
Because the orbitals are wave functions, the waves can combine either constructively or destructively.
Reside: 駐在

72. MOs formed by combining two 1s AOs

73. *****
LCAO–MO Theory:
The total number of MOs formed from a particular set of AOs always equals the number of AOs in the set.
When two AOs combine to form two MOs, one MO is lower in energy (the bonding MO) and the other is higher in energy (the antibonding MO).
When assigning the electrons of a molecule to MOs, fill the lowest energy MOs first with a maximum of two spin-paired electrons per orbital.
When assigning electrons to two MOs of the same energy, follow Hund’s rule—fill the orbitals singly first, with parallel spins, before pairing.

74. Estimate the bond order: Bond Order (BO) =
*****
Applications of MOs
Estimate the bond order:
Bond Order (BO) =
(Σ bonding e– － Σ antibonding e–)/2
Predict the existence of molecule
Estimating bond length and bond energy
Predicting magnetic properties

75. 1st Period Homonuclear Diatomic MOs H2 and He2 for example:
*****
1st Period Homonuclear Diatomic MOs
H2 and He2 for example:
σ1s*
σ1s*
σ1s
σ1s
AOs of H
(two 1s AOs)
AOs of He
(two 1s AOs)
MOs of H2
MOs of He2
BO = (2−0)/2 = 1
H2 molecule does exist
Diamagnetic
BO = (2−2)/2 = 0
He2 molecule does not exist

76. 8. Period 2 Diatomic Molecules
MOs formed by combining two set 2p AOs
σ2p and σ2p*:
end-to-end overlap of AOs
π2p and π2p*: side-by-side overlap of AOs

77. 2nd Period Homonuclear Diatomic MOs
* Effects of 2s–2p Mixing: Increasing energy difference, decreasing the degree of mixing.

78. *****
Continued

79. Predicting magnetic properties by MOs
Lewis structure
For O2:
Experiment showed O2 is paramagnetic
MO prove O2 have unpaired electrons

80. 2nd Period Heteronuclear Diatomic MOs NO for example
Oxygen is more electronegative than nitrogen, so its atomic orbitals are lower in energy than nitrogen’s atomic orbitals.
The lower energy atomic orbital makes a greater contribution to the bonding molecular orbital and the higher energy atomic orbital makes a greater contribution to the antibonding molecular orbital.

81. End of Chapter 09