1. Bonding Theories: Valence Bond Theory Molecular Orbital Theory

2. Lewis Theory: Electron Groups and Molecular Shapes
There are Regions of electrons in an atom:
Some from placing shared pairs of valence electrons between bonding nuclei;
Other from placing lone pairs valence electrons on a single nuclei
Regions of electron groups should repel each other (VSEPR) and determines the molecular shape and molecular polarity
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4. Problems with Lewis Theory
Useful predicting trends, but not quantitative e.g. bond angles, bond strength, bond length
Can not give one correct structure for many molecules where resonance is important
Often does not predict the correct magnetic behavior of molecules
e.g. O2 is paramagnetic, though the Lewis structure predicts it is diamagnetic
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5. Valence Bond Theory. I Linus Pauling et al:
Chemical bonds form when the orbitals (wave functions of electrons in the atoms) on those atoms interact (overlap)
The kind of interaction depends on whether the orbitals align along the axis between the nuclei, or outside the axis
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6. Orbital Interaction
As two atoms approach, the half-filled valence atomic orbitals on each atom would interact and become more stable: covalent bonds
Covalent bonds are regions of high probability of finding the shared electrons in the molecule
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7. Orbital interaction Stabilizes the molecule
Forming covalent bond would stabilize the molecule because they would contain paired electrons shared by both atoms
Attraction between the shared electrons and the nuclei > Repulsion between the nuclei
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8. Atomic Orbital in the Bonding of H2S↑ H 1s ↑↓
H─S bond + S ↑ ↑↓ 3s 3p ↑ H 1s ↑↓
H─S bond
Predicts bond angle = 90°
Actual bond angle = 92°
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9. Valence Bond Theory I – Problem
Many molecules such as methane (tetrahedral, bond angle = 109.5°) can not be explained by half-filled atomic orbitals
C = 2s22px12py12pz0 would predict two or three bonds that are 90° apart
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10. Valence Bond Theory II: Orbital Hybridization
When forming covalent bonds, each valence electron can reside in either standard s, p, d, and f orbitals, or in hybridized orbitals of these atomic orbitals.
Covalent bond forms via half-filled atomic orbitals interacting, ONE pair of electrons (↑↓) in the new bonding orbital
Shape of the molecule determined by the geometry of the interacting orbitals
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11. Hybridization =
Some atoms hybridize their orbitals to maximize bonding
Hybridization: mixing different types of orbitals in the valence shell to make a new set of degenerate (equal energy) orbitals
1 x s orbital + 2 x p orbital = 3 x sp2 hybrid orbital
Same type of atom can have different types of hybridization
C = sp, sp2, sp3
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12. Hybrid Orbitals
The number of standard atomic orbitals combined = the number of hybrid orbitals formed
combining a 2s with a 2p gives 2 x sp hybrid orbitals
H cannot hybridize!!
its valence shell only has one orbital
The number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals

13. Orbital Diagram of sp3 Hybridization in C

14. Orientation of sp3 Hybridized Orbitals
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15. Methane: Hydrogen bonded with sp3-hybridized Carbon
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16. Various Carbon Hybridizations
Unhybridized    2s 2p
sp hybridized    
2sp 2p
sp2 hybridized    
2sp2 2p
sp3 hybridized    
2sp3
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17. sp3 Hybridization Atom with _____ electron groups around it
tetrahedral geometry
109.5° angles between hybrid orbitals
Atom uses hybrid orbitals for all bonds and lone pairs
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18. sp3 Hybridized Atoms Orbital Diagrams
Place electrons into hybrid and unhybridized valence orbitals as if all the orbitals have equal energy
Lone pairs generally occupy hybrid orbitals
Unhybridized atom
sp3 hybridized atom C        2s 2p
2sp3 N         2s 2p
2sp3
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19. Bonding with Valence Bond Theory
According to valence bond theory, bonding takes place between atoms when their atomic or hybrid orbitals interact (“overlap”). To interact,
The orbitals must either be aligned along the axis between the atoms. or
The orbitals must be parallel to each other and perpendicular to the interatomic axis
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20. Ammonia Formation with sp3 N
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21. Sigma (s) bond
The interacting atomic orbitals point along the axis connecting the two bonding nuclei
either standard atomic orbitals or hybrids
s–to–s, p–to–p, hybrid–to–hybrid, s–to–hybrid, etc.
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22. pi (p) bond
Definition: The bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei
between unhybridized parallel p orbitals
Double bond = one s bond + one p bond
Triple bond = one s bond + two p bonds
Strength of orbital overlap: s bonds > p bonds
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23. sp2 Atom with _____ electron groups around it
trigonal planar system
C = trigonal planar
N = trigonal bent
O = “linear”
120° bond angles
flat
Atom uses hybrid orbitals for s bonds and lone pairs, uses nonhybridized p orbital for p bond
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24. sp2 Hybridized Atoms Orbital Diagrams
Unhybridized atom
sp2 hybridized atom C
3 s
1 p        2s 2p
2sp2 2p N
2 s
1 p         2s 2p
2sp2 2p
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26. Formaldehyde, CH2O Orbital Diagramp  
p C
p O s
sp2 C      
sp2 O s s  
1s H
1s H
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27. Hybrid orbitals overlap to form a s bond.
Unhybridized p orbitals overlap to form a p bond.
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28. CH2NH Orbital Diagram ･ p   p C p N s sp2 C       sp2 N s s s
1s H
1s H
1s H
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29. Does Bond Rotation Affect Bonding?
s bond forms along the internuclear axis, rotation around that bond does not affect the interaction between the orbitals.
p bond interacts above and below the internuclear axis, so rotation around the axis requires the breaking of the interaction between the orbitals
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30. Bond Rotation: s bond vs. p bond
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31. Rigidity of double bonds leads to TWO different compounds
Different Polarity (dipole moment), Density, melting points, boilding points:
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32. sp hybridization Atom with _____ electron groups
linear shape
180° bond angle
Atom uses hybrid orbitals for s bonds or lone pairs, uses nonhybridized p orbitals for p bonds p s
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35. HCN Orbital Diagram 2p     p C p N s sp C     sp N s  1s H
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36. sp Hybridized Atoms Orbital Diagrams
Unhybridized atom
sp hybridized atom C 2s 2p        2s 2p
2sp 2p N 1s 2p         2s 2p
2sp 2p
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37. sp3d Atom with five electron groups
trigonal bipyramid electron geometry
Seesaw, T–Shape, Linear
120° & 90° bond angles
Use empty d orbitals from valence shell
d orbitals can be used to make p bonds
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39. sp3d Hybridized Atoms Orbital Diagrams
Unhybridized atom
sp3d hybridized atom     P      3s 3p
3sp3d 3d     S      3s 3p 3d
3sp3d
(non-hybridizing d orbitals not shown)
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40. SOF4 Orbital Diagram p   d S p O s sp3d S         sp2 O s
2p F
2p F
2p F
2p F
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41. sp3d2 Atom with six electron groups around it
octahedral electron geometry
Square Pyramid, Square Planar
90° bond angles
Use empty d orbitals from valence shell to form hybrid
d orbitals can be used to make p bonds
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43. sp3d2 Hybridized Atoms Orbital Diagrams
Unhybridized atom
sp3d2 hybridized atom ↑↓ ↑↓ ↑ ↑ S ↑ ↑ ↑ ↑ ↑ ↑ 3s 3p 3d
3sp3d2 5s 5p ↑↓ 5d ↑ I ↑↓ ↑ ↑ ↑ ↑ ↑
5sp3d2
(non-hybridizing d orbitals not shown)
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45. Predicting Hybridization and Bonding Scheme
1. Start by drawing the Lewis structure 2. Use VSEPR Theory to predict the electron group geometry around each central atom 3. Select the hybridization scheme based on the electron group geometry 4. Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals 5. Label the bonds as s or p
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46. Example: Predict the hybridization and bonding scheme for CH3CHO
Draw the Lewis structure
Predict the electron group geometry around inside atoms
C1 = 4 electron areas
 C1= tetrahedral
C2 = 3 electron areas
 C2 = trigonal planar
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47. Predict the hybridization and bonding scheme for CH3CHO
Determine the hybridization of the interior atoms
C1 = tetrahedral
 C1 = sp3
C2 = trigonal planar
 C2 = sp2
Sketch the molecule and orbitals
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48. Predict the hybridization and bonding scheme for CH3CHO
Label the bonds
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49. Practice – Predict the hybridization of all the atoms in H3BO3
H = can’t hybridize
B = 3 electron groups = sp2
O = 4 electron groups = sp3
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50. Practice – Predict the hybridization and bonding scheme of all the atoms in NClO• • • • • • • O N C l • • • •
s:Osp2─Nsp2 ↑↓ ↑↓ ↑↓
N = 3 electron groups = sp2
O = 3 electron groups = sp2
Cl = 4 electron groups = sp3 ↑↓
s:Nsp2─Clp ↑↓ ↑↓
p:Op─Np
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51. Problems with Valence Bond Theory
VB theory predicts many properties better than Lewis theory
bonding schemes, bond strengths, bond lengths, bond rigidity
However, VB theory doesn’t predict many other properties
magnetic behavior of O2
In addition, VB theory treats the electrons as localized in orbitals on the atoms in the molecule
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52. Molecular Orbital Theory
In MO theory, solving Schrödinger’s wave equation to calculate a set of molecular orbitals
In this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole molecule
delocalization
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53. LCAO
The simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals – this is called the Linear Combination of Atomic Orbitals method
weighted sum
Because the orbitals are wave functions, the waves can combine either constructively or destructively
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54. Molecular Orbitals
Wave functions combine constructively forms molecular orbital _____ energy than the original atomic orbitals  Bonding Molecular Orbital
s, p
most of the electron density between the nuclei
Wave functions combine destructively forms molecular orbital ______ energy than the original atomic orbitals Antibonding Molecular Orbital
s*, p*
most of the electron density outside the nuclei
nodes between nuclei
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55. Interaction of 1s Orbitals: Bonding vs. Antibonding
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56. Molecular Orbital Theory
Electrons in bonding MOs are stabilizing
lower energy than the atomic orbitals
Electrons in antibonding MOs are destabilizing
higher in energy than atomic orbitals
electron density located outside the internuclear axis
electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals
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57. Energy Comparisons of Atomic Orbitals to Molecular Orbitals
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58. MO and Properties
Bond Order = difference between number of electrons in bonding and antibonding orbitals
only need to consider valence electrons
may be a fraction
higher bond order = stronger and shorter bonds
if bond order = 0, then bond is unstable compared to individual atoms and no bond will form
Paramagnetic: unpaired electrons in MO
if all electrons paired it is diamagnetic
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59. Because more electrons are in
Dihydrogen, H2
Molecular
Orbitals
Hydrogen
Atomic
Orbital
Hydrogen
Atomic
Orbital s* 1s 1s s
Because more electrons are in
bonding orbitals than are in antibonding orbitals,
net bonding interaction
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60. H2 s* Antibonding MO LUMO s bonding MO HOMO
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61. Because there are as many electrons in
Dihelium, He2
Molecular
Orbitals
Helium
Atomic
Orbital
Helium
Atomic
Orbital s* 1s 1s s
BO = ½(2-2) = 0
Because there are as many electrons in
antibonding orbitals as in bonding orbitals,
there is no net bonding interaction
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62. therefore only need to consider valence shell
Dilithium, Li2
Molecular
Orbitals
Lithium
Atomic
Orbitals
Lithium
Atomic
Orbitals s* 2s 2s s
Any fill energy level will generate filled bonding and antibonding MO’s;
therefore only need to consider valence shell s*
BO = ½(4-2) = 1 1s 1s s
Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction
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63. Li2 s* Antibonding MO LUMO s bonding MO HOMO
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64. Interaction of p Orbitals
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65. Interaction of p Orbitals
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67. O2 Dioxygen is paramagnetic
Paramagnetic material has unpaired electrons
Neither Lewis theory nor valence bond theory predict this result
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68. O2 as Described by Lewis and VB Theory
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69. 2 x unpaired electrons in the
Oxygen
Atomic
Orbitals
Oxygen
Atomic
Orbitals p* 2p
O2 MO’s 2p
more electrons are in bonding orbitals than are in antibonding orbitals: net bonding interaction p s
2 x unpaired electrons in the
antibonding orbitals,
O2 as paramagnetic s*
BO = ½(8 be – 4 abe)
BO = 2 2s 2s s
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70. Example: N2− : bond order and magnetic properties
Bond order = (#bonding electrons - #antibonding electrons) ÷ 2
Presence of unpaired electrons  paramagnetic
BO = ½(8 be – 3 abe)
BO = 2.5
This is lower than BO of N2 (3), the bond should be weaker
s2s
s*2s
p2p
s2p
p*2p
s*2p ↑ ↑ ↓ ↑ ↓ ↑ ↓
Unpaired electrons: paramagnetic ↑ ↓ ↑ ↓
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71. Heteronuclear Diatomic Molecules & Ions
When the combining atomic orbitals are identical and equal energy, the contribution of each atomic orbital to the molecular orbital is equal
When the combining atomic orbitals are different types and energies, the atomic orbital closest in energy to the molecular orbital contributes more to the molecular orbital
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72. Heteronuclear Diatomic Molecules & Ions
The more electronegative an atom is, the lower in energy are its orbitals
Lower energy atomic orbitals contribute more to the bonding MOs
Higher energy atomic orbitals contribute more to the antibonding MOs
Nonbonding MOs remain localized on the atom donating its atomic orbitals
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73. Example: Draw a molecular orbital diagram of N2− ion and predict its bond order and magnetic properties
Write a MO diagram for N2− using N2 as a base
Count the number of valence electrons and assign these to the MOs following the aufbau principle, Pauli principle & Hund’s rule
s2s
s*2s
p2p
s2p
p*2p
s*2p
N has 5 valence electrons
2 N = 10e−
(−) = 1e−
total = 11e− ↑ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓
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74. NO a free radical s2s Bonding MO
shows more electron density near O because it is mostly O’s 2s atomic orbital
BO = ½(6 be – 1 abe)
BO = 2.5
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75. Practice – Draw a molecular orbital diagram of C2+ and predict its bond order and magnetic properties
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76. Practice – Draw a molecular orbital diagram of C2+ and predict its bond order and magnetic properties
C has 4 valence electrons
2 C = 8e−
(+) = −1e−
total = 7e−
s2s
s*2s
p2p
s2p
p*2p
s*2p
BO = ½(5 be – 2 abe)
BO = 1.5 ↑ ↓ ↑
Because there are unpaired electrons, this ion is paramagnetic ↑ ↓ ↑ ↓
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77. HF
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78. Polyatomic Molecules
When many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals, which are delocalized over the entire molecule
Gives results that better match real molecule properties than either Lewis or valence bond theories
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79. Ozone, O3 MO Theory: Delocalized p bonding orbital of O3
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