1. Molecular Orbitals in Chemical Bonding
Chapter 9

2. Valence Bond Theory
Explains the structures of covalently bonded molecules
‘how’ bonding occurs
VSEPR is part of VB theory
Principles of VB Theory
Bonds form from overlapping atomic orbitals and electron pairs are shared between two atoms
A new set of hybridized orbitals can form
Lone pairs of electrons are localized on one atom

3. Molecular Orbital(MO) Theory
Explains the distributions and energy of electrons in molecules
Useful for describing properties of compounds
Bond energies, electron cloud distribution, and magnetic properties
Basic principles of MO Theory
Atomic orbitals combine to form molecular orbitals
Molecular orbitals have different energies depending on type of overlap
Bonding orbitals (lower energy than corresponding AO)
Nonbonding orbitals (same energy as corresponding AO)
Antibonding orbitals (higher energy than corresponding AO)

4. Formation of Molecular Orbitals
Recall than an electron in an atomic orbital can be described as a wave function utilizing the Schröndinger equation. The ‘waves’ have positive and negative phases. To form molecular orbitals, the wave functions of the atomic orbitals combine. How the phases or signs combine determine the energy and type of molecular orbital.
Look at Figure 9-1 to see how the phases combine.

5. Formation of Molecular Orbitals
Bonding orbital – the wavefuntions are in-phase and overlap constructively (they add).
Bonding orbitals are lower in energy than AOs
Antibonding orbital – the wavefunctions are out-of-phase and overlap destructively (they subtract)
Antibonding orbitals are higher in energy than the AO’s
When two atomic orbitals combine, one bonding and one antibonding MO is formed.

6. Overlap of Two 1s Atomic Orbitals
Two MO’s are formed when the two 1s atomic orbitals overlap
The in-phase combination produces a 1s molecular bonding orbital.
Has lower energy than corresponding AO’s
The out-of-phase contribution produces a molecular antibonding orbital
Has higher energy than corresponding AO’s

7. Overlap of Two 1s Atomic Orbitals
2 1s orbitals that are far apart
Constructive interference from the 1s orbitals (1s)
Destructive inteference form the 1s orbitals ( )
The molecular orbital has a nodal plane bisecting the internuclear axis. A node or nodal plan is a region in which the probability of finding an electron is zero.

8. Overlap of 2px Orbitals
Head-on overalp produces a p (actually ) and a (actually ). These are also termed as sigma orbitals since they are cylindrically symmetric about the internuclear axis.
Constructive interference from the 2px orbitals
Destructive interference for the 2px orbitals

9. Overlap of 2px Orbitals
Page 356

10. Overlap of 2py Orbitals
These atomic orbitals overlap ‘side-on’ forming  molecular orbitals
The bonding combination is
The antibonding combination is
Termed as  molecular orbitals because they have a nodal plane along the internuclear axis
The antibonding combination also has a nodal plane bisecting the internuclear axis

11. Overlap of 2py Orbitals
Constructive interference from the 2py orbitals
Destructive interference from the 2py orbitals

12. Overlap of 2pz Orbitals
The 2pz atomic orbitals can overlap in the same fashion except that the orientation in space is different
The 2pz atomic orbitals overlap ‘side-on’ to produce a bonding and an antibonding  orbital
Together, the 2pz and the 2py atomic orbitals produce two bonding orbitals and two antibonding orbitals. MO theory commonly illustrates these orbitals as the same.

13. Molecular Orbital Filling-Energy Diagram
Order of filling of MO’s obeys same rules as for atomic orbitals.
Including
Aufbau principle
Hund’s Rule
Recall that bonding orbitals have lower energies than the corresponding atomic orbitals and antibonding orbitals have higher energies than corresponding atomic orbitals

14. Molecular Orbital Filling-Energy Diagram for Homonuclear Molecules
Page 357

15. Using Energy Diagrams in MO Theory
Draw (or select) the appropriate molecular orbital energy level diagram
Determine the total number of electrons in the molecule.
In MO theory, this includes all the electrons
Add these electrons to the energy level diagram, putting each electron into the lowest energy level available
Only two electron can be in a given orbital
Electrons must occupy all the orbitals of the same energy singly before pairing

16. Bond Order and Bond Stability
Usually, the bond order corresponds to the number of bonds described by the VB theory
A bond order equal to zero indicates that there are the same number of electron in bonding and antibonding orbitals
The greater the bond order, the more stable the molecule or ion. Also, the greater the bond order, the shorter the bond length and the greater the bond energy. Bond energy is the amount of energy necessary to break a mole of bonds.

17. Homonuclear Diatomic Molecules
Draw the energy level diagrams and write the MO electron configurations H2
He2 B2 N2
O2 and O2-
Notice the differences in the energy diagrams (it switches)

18. Homonuclear Diatomics
Look at Table 9-1
Trends in bond order versus bond length and bond energy
A few diatomics have unpaired electrons in the MO’s. These diatomics would be classified as being paramagnetic. Diamagnetic species have no unpaired electrons.
What molecules (or ions) form the previous slide are paramagetic?

19. Heavier Homonuclear Diatomic Molecules
Many heavy atoms such as S2 are instable due to inability to form strong  bonds
Bond length is too great for effective ‘side-on’ overlap of p orbitals.
N2 is much more stable than P2
The effectiveness of the ‘side-on’ overlap decreases much quicker than the ‘head-on’ overlap

20. Heteronuclear Diatomic Molecules
Molecular orbital diagrams for heteronuclear molecules have skewed energies for the combining atomic orbitals to take into account the differing electronegativities.
The more electronegative elements are lower in energy than those of the less electronegative element.

21. Heteronuclear Diatomic Molecules
Let’s examine the energy level diagram for NO (in your books on page 363)
The closer the energy of a MO is to the one of the AO from which it is formed, the more of the character of that atomic orbital it shows
Illustrate with NO

22. Energy Level Diagram for NO

23. Heteronuclear Diatomic Molecules
The energy differences between bonding orbitals depend on the electronegativity differences between the two atoms
The larger the difference the more polar the bond that is formed (ionic character increases)
The difference reflects the amount of overlap between the bonding orbitals. If the difference is too great the orbitals cannot overlap effectively and nonbonding orbitals will be formed.

24. Formation of MO’s in HF
The bond in HF involves the 1s electron of H and the 2p orbital of F
A bonding and antibonding MO are produced
sp and MO’s
The remaining 2p orbitals on F have no overlap with H orbitals. They are termed as ‘nonbonding’ orbitals. These orbitals retain the characteristics of the F 2p atomic orbitals.
Lack of overlap to produce nonbonding orbitals is much more pronounced for side-on bonding

25. The Energy Level Diagram for HF

26. Delocalization and Shapes of MO’s
Molecular orbital theory describes shapes in terms of delocalization of electrons.
All the contributing AO’s will be combined
Let’s look at the structure of benzene
VB theory indicates sp2 hybridization
There are sigma bonds from each C atom to the two adjacent C atoms and to one H atom. There is one unhybridized 2pz orbital on each C atom remaining

27. Benzene
Resonance structures with VB theory. MO theory, however, indicates that the electrons are delocalized. Experiemental data shows that all the C-C bond are equal.

28. Benzene
Overlap according to VB theory. This theory does not describe the molecule accurately.

29. Benzene
Structure according to MO theory. The electrons are delocalized over the 6 C-C bonds. The electrons contribute to bonding throughout the molecule as a whole.

30. Molecular Orbital Diagram for H2O

31. Molecular Orbital Diagram for Cr(Cl)63+