1. Chapter 10 Chemical Bonding II

2. Valence Bond Theory
Valence Bond Theory: A quantum mechanical model which shows how electron pairs are shared in a covalent bond.
Bond forms between two atoms when the following conditions are met:
Covalent bonds are formed by overlap of atomic orbitals, each of which contains one electron of opposite spin.
Each of the bonded atoms maintains its own atomic orbitals, but the electron pair in the overlapping orbitals is shared by both atoms.
The greater the amount of overlap, the stronger the bond.

3. Orbital Interaction
In some cases, atoms use “simple” atomic orbital (e.g., 1s, 2s, 2p, etc.) to form bonds.
In other case, they use a “mixture” of simple atomic orbitals known as “hybrid” atomic orbitals.
as two atoms approached, the partially filled or empty valence atomic orbitals on the atoms would interact to form molecular orbitals
the molecular orbitals would be more stable than the separate atomic orbitals because they would contain paired electrons shared by both atoms

4. Valence Bond Theory - Hybridization
one of the issues that arose was that the number of partially filled or empty atomic orbital did not predict the number of bonds or orientation of bonds
C = 2s22px12py12pz0 would predict 2 or 3 bonds that are 90° apart, rather than 4 bonds that are 109.5° apart
to adjust for these inconsistencies, it was postulated that the valence atomic orbitals could hybridize before bonding took place
one hybridization of C is to mix all the 2s and 2p orbitals to get 4 orbitals that point at the corners of a tetrahedron

5. Valence Bond Theory Main Concepts
the valence electrons in an atom reside in the quantum mechanical atomic orbitals or hybrid orbitals
a chemical bond results when these atomic orbitals overlap and there is a total of 2 electrons in the new molecular orbital
the electrons must be spin paired
the shape of the molecule is determined by the geometry of the overlapping orbitals

6. The Phase of an Orbital
Orbitals are determined from mathematical wave functions.
A wave function can have positive or negative values.
As well as nodes where the wave function = 0
The sign of the wave function is called its phase.
When orbitals interact, their wave functions may be in phase (same sign) or out of phase (opposite signs).
This is important in bonding as will be examined in a later chapter.

7. Types of Bonds
a pi (p) bond results when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei
between unhybridized parallel p orbitals
the interaction between parallel orbitals is not as strong as between orbitals that point at each other; therefore s bonds are stronger than p bonds
a sigma (s) bond results when the bonding 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.

9. Hybridization some atoms hybridize their orbitals to maximize bonding
hybridizing is mixing different types of orbitals to make a new set of degenerate orbitals
sp, sp2, sp3, sp3d, sp3d2
more bonds = more full orbitals = more stability
better explain observed shapes of molecules
same type of atom can have different hybridization depending on the compound
C = sp, sp2, sp3

10. Hybrid Orbitals H cannot hybridize!!
the number of standard atomic orbitals combined = the number of hybrid orbitals formed
the number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals
the particular kind of hybridization that occurs is the one that yields the lowest overall energy for the molecule
in other words, you have to know the structure of the molecule beforehand in order to predict the hybridization

11. sp3 Hybridization of C

12. sp3 Hybridization atom with 4 areas of electrons tetrahedral geometry
109.5° angles between hybrid orbitals
atom uses hybrid orbitals for all bonds and lone pairs
Ammonia Formation with sp3 N

13. sp2 atom with 3 areas of electrons 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

14. 3-D representation of ethane (C2H4)

15. Bond Rotation
because orbitals that form the s bond point along the internuclear axis, rotation around that bond does not require breaking the interaction between the orbitals
but the orbitals that form the p bond interact above and below the internuclear axis, so rotation around the axis requires the breaking of the interaction between the orbitals

16. sp atom with 2 areas of electrons linear shape 180° bond angle
atom uses hybrid orbitals for s bonds or lone pairs, uses nonhybridized p orbitals for p bonds

17. sp3d atom with 5 areas of electrons around it trigonal bipyramid shape
See-Saw, T-Shape, Linear
120° & 90° bond angles
use empty d orbitals from valence shell
d orbitals can be used to make p bonds

18. sp3d2 atom with 6 areas of electrons around it octahedral shape
Square Pyramid, Square Planar
90° bond angles
use empty d orbitals from valence shell
d orbitals can be used to make p bonds

19. Predicting Hybridization and Bonding Scheme
Start by drawing the Lewis Structure
Use VSEPR Theory to predict the electron group geometry around each central atom
Use Table 10.3 to select the hybridization scheme that matches the electron group geometry
Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals
Label the bonds as s or p
# of e- groups around central atom
Hybrid orbitals used
Orientation of Hybrid Orbitals 2 sp 3
sp2 4
sp3 5
sp3d 6
sp3d2

20. Examples:
Predict the Hybridization and Bonding Scheme of All the Atoms in
Then sketch a σ framework and a π framework
CH3CHO
CH2NH
H3BO3

21. Problems with Valence Bond Theory
VB theory predicts many properties better than Lewis Theory
bonding schemes, bond strengths, bond lengths, bond rigidity
however, there are still many properties of molecules it doesn’t predict perfectly
magnetic behavior of O2

22. Molecular Orbital Theory
in MO theory, we apply Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals
in practice, the equation solution is estimated
we start with good guesses from our experience as to what the orbital should look like
then test and tweak the estimate until the energy of the orbital is minimized
in this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole molecule
unlike VB Theory where the atomic orbitals still exist in the molecule

23. 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

24. Molecular Orbitals
when the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals – it is called a Bonding Molecular Orbital
s, p
most of the electron density between the nuclei
when the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals – it is called a Antibonding Molecular Orbital
s*, p*
most of the electron density outside the nuclei
nodes between nuclei

25. Molecular Orbital Theory
Electrons in bonding MOs are stabilizing
Lower energy than the atomic orbitals
Electrons in anti-bonding MOs are destabilizing
Higher in energy than atomic orbitals
Electron density located outside the internuclear axis
Electrons in anti-bonding orbitals cancel stability gained by electrons in bonding orbitals H2
s bonding MO
HOMO
s* Antibonding MO
LUMO

26. 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 - no bond will form.
A substance will be paramagnetic if its MO diagram has unpaired electrons
if all electrons paired it is diamagnetic

27. Molecular Orbital Theory: The Hydrogen Molecule
Chapter 7: Covalent Bonds and Molecular Structure
Molecular Orbital Theory: The Hydrogen Molecule
5/29/2018
= 1 2
2 - 0
Bond Order =
Copyright © 2008 Pearson Prentice Hall, Inc.

28. What would happen if two helium atoms tried to form a bond by overlapping their two 1s orbitals?
The bonding picture is essentially the same as for the hydrogen molecule, except that each helium atom
brings two electrons to the molecular orbitals. There would be four electrons to fill into our molecular
orbital diagram and that would force us to fill in the bonding sigma MO and the anti-bonding sigma-star MO.
The bond order calculation equals zero, as expected for a diatomic helium molecule.
= 0 2
2 - 2
Bond order =

29. s* 2s 2s s s* 1s 1s s Dilithium, Li2 Molecular Orbitals Lithium Atomic
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
Since more electrons are in
bonding orbitals than are in antibonding orbitals, net bonding interaction

30. Examples
What would the MO pictures of H2+, H2-