1. Covalent Bonding: Orbitals
DE Chemistry
Dr. Walker

2. Hybridization and the Localized Electron Model
The mixing of two or more atomic orbitals of similar energies on the same atom to produce new orbitals of equal energies
Mixes s, p, and/or d orbitals when covalently bonded
Hybrid Orbitals
Orbitals of equal energy produced by the combination of two or more orbitals on the same atom

3. Hybridization - The Blending of Orbitals+ =
Poodle +
Cocker Spaniel =
Cockapoo + =
s orbital +
p orbital =
sp orbital

4. Why Hybridization? Think of the electrons involved in bonding….
Typically, most bonding occurs between electrons in s and p orbitals
These orbitals are all valence electrons, so all are involved in bonding

5. Why Hybridization? Think about carbon….
We know carbon needs to make four covalent bonds to complete its octet and become stable
Two electrons are at one energy level and two electrons are at another energy level

6. Things we know….
In methane, the electrons in hydrogen’s 1s orbital bond with the orbitals in the second energy level of carbon

7. Houston, we have a problem….
We know that all of the C-H bonds in methane are identical
If two bonds are made with electrons in 2s and two with electrons in 2p, these bonds SHOULD be at different energies….
How can we explain this?

8. The Rationalization How can we explain this?
Hybridization is the combining of two or more orbitals of nearly equal energy within the same atom into orbitals of equal energy.

9. In the case of methane, they call the hybridization
sp3, meaning that an s orbital is combined with three
p orbitals to create four equal hybrid orbitals.
2sp3
2sp3
2sp3
2sp3 1s
These new orbitals have slightly MORE energy than
the 2s orbital…
… and slightly LESS energy than the 2p orbitals.

11. Notice the tetrahedral arrangement of sp3 orbitals on the
right correspond with the molecular geometry of methane
and other AX4 type molecules, with bond angles of 109o
(assuming no unbonded electron pairs).

12. sp2 Hybridization
Another hybrid is the sp2, which combines two orbitals from a p sublevel with one orbital from an s sublevel.
One of the p orbitals is not used in hybridization
Energy diagram of sp2 orbitals

13. sp2 Hybridization
This hybridization results in bond angles of 120o, consistent with trigonal planar geometries

14. sp2 Hybridization
3 effective pairs of electrons surround the carbon (double bond treated as one effective pair)
In boron compounds, the unused p orbital is empty

15. s and p bonds s bonds p bonds Occupies space directly between atoms
Occupies space above and below atoms from the overlap between two p orbitals
The picture on the left represents a double bond, which uses one s and one p bond

16. Notice the sp2 geometry on the left. The single bonds in
ethene are s bonds. Notice the unhybridized p orbital on
the left, which forms the p bond shown in the previous slide.

17. sp Hybridization
As you can probably guess this is a hybrid of one s and one p orbital, with 2 p orbitals remaining unhybridized.
In the previous example, the unhybridized p orbitals made the double bond. In this case, two unhybridized p orbitals results in a triple bond between carbons (one s bond, two p bonds.

18. sp Hybridization
The three different p orbitals (px, py, pz) are oriented on each axis of space.
If only one p orbital hybridizes, it results in a 180o angle. This is consistent with linear molecules.

19. sp Hybridization
sp Hybridization of carbon in ethyne.

20. sp Hybridization
sp Hybridization of carbon in carbon dioxide.

21. dsp3 Hybridization
Forms for central atoms requiring a trigonal bipyramidal arrangement
Examples PCl5, other pentavalent atoms that disobey the octet rule
Allows bonding of extra electrons that require more than the s and p orbitals (8 electrons) allow

23. d2sp3 Hybridization
Used for hexavalent atoms with 12 bonded electrons, requiring an octahedral arrangement

24. Hybridization and Molecular Geometry
Forms
Overall Structure
Hybridization of “A”
AX2
Linear sp
AX3, AX2E
Trigonal Planar
sp2
AX4, AX3E, AX2E2
Tetrahedral
sp3
AX5, AX4E, AX3E2, AX2E3
Trigonal bipyramidal
dsp3
AX6, AX5E, AX4E2
Octahedral
d2sp3
A = central atom
X = atoms bonded to A
E = nonbonding electron pairs on A

25. Shortcomings of the Localized Electron Model
Assumes electrons are localized (thus the name…)
Doesn’t really explain resonance
Doesn’t work well for unpaired electrons
Doesn’t give any indication of bond energy

26. Molecular Orbital (MO) Theory
Molecular Orbitals
Similar to atomic orbitals, but for molecules
Can hold two electrons with opposite spins
Square of the orbital's wave function indicates electron probability

27. Hydrogen Two possible bonding orbitals, shapes determine by Y2
Bonding takes place in MO1 in which electrons achieve lower energy (greater stability), with electrons between the two nuclei

28. Hydrogen
Both orbitals are in line with the nuclei, so they are s (same as in localized model) molecular orbitals
Higher energy orbital is designated as antibonding (*)
Electron configuration of H2 can be written as s1s2

29. Bond Order
Bond order is the difference between the number of bonding electrons and the number of antibonding electrons, divided by two
Larger bond order =
greater bond strength
greater bond energy
shorter bond length
Typically, molecules with a bond order = 0 don’t actually exist

30. Bonding in Homonuclear Diatomic Molecules
In order to participate in molecular orbitals, atomic orbitals must overlap in space
Larger bond order is favored
When molecular orbitals are formed from p orbitals, s orbitals are favored over p orbitals (s interactions are stronger than p interactions)
Electrons are closer to the nucleus = lower energy

31. Note Regarding MO Theory
In the localized electron model, hybrid orbitals are formed by mixing s, p, and d orbitals for bonding
There is no hybridization in MO theory. Electrons in s orbitals bond with each other (forming s bonds) and electrons in p orbitals bond with each other (forming s and p bonds)

32. B2 Molecule
Notice that s and p orbitals do not mix when bonding to form molecular orbitals
There are 4 total bonding electrons and 2 antibonding electrons
Bond order = (4-2)/2 = 1, making this a stable molecule
The figure shown on the right is the expected arrangement, but fails to account for certain physical properties of B2.

33. Paramagnetism
Magnetism can be induced in some nonmagnetic materials when in the presence of a magnetic field
Paramagnetism causes the substance to be attracted into the inducing magnetic field
Associated with unpaired electrons
Diamagnetism causes the substance to be repelled from the inducing magnetic field
Associated with paired electrons

35. Observations Regarding Paramagnetism
Bond order does not necessarily equal number of bonds, as B2 has a triple bond, yet its bond order is 1.
If you’re paying attention, the s and p molecular orbital energies are reversed from the expected arrangement shown previously for B2.
This alteration to the model explains B2’s paramagnetic behavior.
In the expected arrangement shown earlier, B2 should have been diamagnetic….but it isn’t.

36. Bonding in Heteronuclear Diatomic Molecules
Similar, but not identical atoms
Use molecular orbital diagrams for homonuclear molecules
Significantly different atoms
Each molecule must be examined individually
There is no universally accepted molecular orbital energy order

37. Bonding in Heteronuclear Diatomic Molecules
Example: NO
Nitrogen has 5 valence electrons, oxygen has 6, giving 11 total
Bond order = (8-3)/2 = 2.5
With an unpaired electron we expect this to be paramagnetic (and it is)

38. Bonding in Heteronuclear Diatomic Molecules
Example: CN
Carbon has 4 valence electrons, oxygen has 6, giving 10 total
Bond order = (8-2)/2 = 3
With no unpaired electrons we expect this to be diamagnetic (and it is)

39. Combining Models Resonance
Attempt to draw localized electrons in a structure in which electrons are not localized
s bonds can be described using localized electron model
p bonds (delocalized) must be described using the molecular orbital model

40. Benzene s bonds (C - H and C - C) are sp2 hybridized
Uses localized model
p bonds are a result of remaining p orbitals above and below the plane of the benzene ring
Uses delocalized model (MO)

41. Representations of Benzene
The s bonding system with carbon’s sp2 orbital system demonstrates the localized bonding model

42. Representations of Benzene
The non-hybridized p orbitals used to make p bonds above and below the ring show the need for a delocalized model where resonance is necessary