Reading Notes
for Chapter 8
These are Dr. Bodwin's reading notes for Chapter 8 of "Chemistry
2e" from OpenStax.
I am using a local .pdf copy that was downloaded in May 2020.
Chapter
Summary:
As with many topics, there are a variety of different ways we can
envision and explain chemical bonding. Many of these "competing"
theories exist and are valid within their limitations. In general,
always use the "simplest" theory to explain whatever you are trying to
explain; just because a theory or model is more complex, doesn't mean
it does a better job of explaining an observation.
Valence
Bond Theory:
When orbitals on adjoining atoms overlap, they allow sharing of the
electrons between them and form a bond.
VB theory treats orbitals on atoms as distinct and fully "belonging" to
one atom, although the electrons that are shared can bounce back and
forth between the atoms.
"Stronger" bonds have more "effective" overlap.
The energy well graph in Figure 8.2 is a very important concept in
chemistry. It is widely used to describe energy-based interactions
between charged particles.
There are a number of different ways that orbitals can overlap simply
based upon their shape and orientation. This terminology is used common
in chemistry courses beyond General Chemistry, so it's important to
specify here:
- Sigma bond/interaction - these are the simplest overlaps where
there is one point of interactions. They're called "sigma" because this
is the only interaction that two "s" orbitals can have, as shown in
Figure 8.4a. All orbital types can form sigma interactions. In a
molecule or polyatomic ion, the first interaction between any 2 atoms
is almost always a sigma interaction.
- Pi bond/interaction - This is a two-point overlap as shown in
Figure 8.5. This type of overlap is a "side-by-side" interaction that
can take place between two "p" orbitals, or a "p" and a "d" orbital, or
two "d" orbitals. When we form double or triple bonds in molecules and
polyatomic ions, the second and third interactions between any 2 atoms
is almost always a pi interaction.
- Delta bond/interaction - These aren't discussed in your textbook,
but as long as we're looking at interactions, we might as well include
this one. A delta overlap is a "face-to-face" interaction that can take
place between two "d" orbitals. Since both orbitals have to be "d"
orbitals, this type of interaction only occurs between transition
metals, so it is a less common interaction when we are looking at
"simple" molecules. For some good pictures and further description of
delata interactions, check out:
- https://www.quora.com/What-is-a-delta-bond-and-how-do-d-orbitals-form-a-delta-bond
What is an "orbital"? As we get deeper into our discussion of bonding
and bonding theories, let's not forget what an orbital is. An orbital
is a visual representation of a mathematical probability surface where
we are most likely to find an electron or electron "pair". The red/blue
shading in your textbook represents the "sign" of each lobe of an
orbital, and effective overlap can only occur between lobes of the same
sign. That's why the pi interaction is specifically shown with the blue
lobes of the p-orbitals lined up and the red lobes lined up. This is an
important concept that we'll get back to soon...
Hybrid
Orbitals:
The cartesian geometry of atomic orbitals causes some problems when we
look at the geometry of actual molecules. We could explain that away by
just saying the orbitals overlap at an angle, but it's hard to come up
with a good reason for that. Since orbitals are just visualizations of
a mathematical relationship, it seems reasonable that we can combine
those orbitals to form new
orbitals that retain some character of the old ones. These are hybrid
orbitals
and can be used to explain a much wider range of molecular geometries
than the standard "s", "p", "d", and "f" orbital set we have already
developed.
Forming hybrids - We can think in simple visual math terms. Orbitals
are added and subtracted to give a new set of shapes. The number of
atomic orbitals that go in to
making the hybrids must equal the number of hybrids we get out.
Look at the left side of Figure 8.8. Remember, we said that the red and
blue color represent the +/- "sign" of the orbital. If we superimpose
the "s" and "p" orbital shown in the picture, where blue overlaps with
blue, the blue part gets bigger; where blue overlaps with red, the red
part gets smaller. That's the first hybrid orbital shown on the right
side of the picture. Now, if we "subtract" these instead of "adding"
them, change the color of the s-orbital to red (the "negative" of blue)
and repeat the process. That gives the 2nd hybrid orbital on the right
side of the figure. Two "standard" orbitals go in, two hybrid orbitals
come out!
Hybrid Orbital Types:
-
"sp" - one s and one p orbital form 2 "sp" hybrid orbitals. These
orbitals are 180° apart and result in linear electronic geometry.
-
"sp2" - one s and two p orbitals form 3 "sp2" hybrid orbitals. These
orbitals are 120° apart and result in trigonal planar electronic geometry.
-
"sp3" - one s and three p orbitals form 4 "sp3" hybrid orbitals. These
orbitals are 109.5° apart and result in tetrahedral geometry.
-
"sp3d" - one s, three p, and one d orbital form 5 "sp3d" hybrid orbitals. These
orbitals are 180°/120°/90° apart and result in trigonal bipyramidal electronic geometry.
-
"sp3d2" - one s, three p, and two d orbitals form 6 "sp3d2" hybrid orbitals. These
orbitals are 180°/90° apart and result in octahedral electronic geometry.
Those bond angles are the ideal angles in a "perfect" shape... bond
type, bond length, bond strength, atom type, and other things can cause
deviations.
Hybrid orbitals work the same way as "standard" s/p/d/f orbitals, they just allow different bond angles and interactions.
Molecular
Orbital Theory:
Linear Combination of Atomic Orbitals (LCAO) - in some resources,
Molecular Orbital Theory ("MO Theory" of just "MO") is explicitly
called "LCAO-MO" because we get molecular orbitals by taking linear combinations of atomic orbitals. It's similar to the method we used to "make" hybrid orbitals, but now it's done on the molecule as a whole.
Your textbook shows some nice pictures of simple MOs. Start with the simple ones because some MOs can get pretty complex!
The pictures can sometimes get a little ponderous, so it's also
important to start to think about these as energy level diagrams.
You've seen some simple electron-filling diagrams before, a MO energy
level diagram if just a little extension of that. Check out Figure 8.34
for a nice example.
These energy level diagrams can also get pretty complex, but the simple
ones aren't too ponderous and give us a good foundation for how they
work.
MO diagrams are extremely powerful tools, but again, don't use a more
complicated tool if you don't need to. You don't need to take a Ferrari
or a semi tractor-trailer to the grocery store for a loaf of bread, use
something simpler. Same thin here. If all you want to do is look at the
bonding an carbon dioxide, Valence Bond theory works great! If you need
to understand why molecule oxygen behaves as if it has unpaired
electrons, you might need to step up to MO theory.
Return to ChemBits
General Chemistry Index.
All information on this page is produced by Jeffrey
Bodwin,
Copper Sun Creations, or curated from the attributed source.
This work is licensed under a Creative
Commons Attribution-NonCommercial-ShareAlike 4.0 International License.