so let's take a moment to discuss the key differences between molecular orbital theory
and valence bond theory.
So valence bond theory we said that bonding was localized between atoms and that's just
not the case in molecular orbital theory.
So we would say that a single bond of a carbon carbon bond may look like this where we said
that the overlap say we have ethane the overlap of two sp3 orbitals is localized in the middle
between the two atoms.
this was called a sigma bond, it's got cylindrical symmetry um in the middle between two atoms.
We could have a pi bond in addition to this if we had a double bond to a carbon and so
we'd have the sigma bond in the middle and then additionally we show separately here
we have these p orbitals of carbon.
here the py orbital is emphasized and we'd say that the overlap is between the two above
and below so this would be what a pi bond would look like according to valence bond
theory.
Now molecular orbital theory would disagree and it would say that molecular orbitals exist
throughout the entire molecule not just in between two atoms and so we have this concept
of bonding and "antibonding" and with bonding orbitals what we have are the constructive
interference of atomic orbitals so just like two ocean waves that may come together and
double in size if they are in phase with one another you might add these two together and
come together constructively.
what we have is orbitals such as the s orbital of hydrogen that come together with the s
orbital of hydrogen and we constructively combine these two together to make a molecular
orbital that looks much like an addition of the two it's constructive interference of
the wave functions of the orbitals.
Ok and we are in phase with one another.
With the hydrogen atom we can pick one phase or the other and we'll see that in a moment
but s orbitals only have one phase at a time and so if we bring them together in phase
the same color as one another we get the bonding sigma molecular orbital, ok they are lower
in energy relative to comprising atomic orbitals as we'll see in a minute and the lowest energy
overall is when all s orbitals in a molecule are in phase with one another.
Ok so a sigma bond looks like this.
antibonding orbitals on the other hand are destructive interference so they are out of
phase interaction just like two ocean waves might be out of phase with one another.
ok so we would actually have downward peaks here in the places that we have ups and when
we add those together we would get a flat line nothing like the big wave we see cancels
out before it actually gets to us when the waves go away at the beach.
Destrcutive interference out of phase and we have more nodes with the hydrogen atom
this looks like two hydrogen atoms coming together one of which is out of phase with
the other so like i said before hydrogen has to pick a phase whether it picks one phase
or the other, the plus or minus phase, has nothing to do with charge, it's a mathematical
construct of waves and so we can pick either plus or minus and I'm using colors to denote
in phase or out of phase for one phase or the other so we just say they don't match
that means they cancel out where they touch so as we bring the hydrogen atom together
into the hydrogen molecule our molecular orbital has a node in the middle.
we are going to cancel out that node in between the atoms where they are closest together
and we will form an antibonding orbital that has a nodal plane down the middle of the molecule
and will have out of phase interaction so this an antibonding orbital that's worse higher
in energy relative to the atomic orbitals that bring it together and all s orbitals
out of phase or all p orbitals out of phase as we'll see in later examples can be the
highest energy molecular orbital we have to kind of do the calculation to see which is
which but it will be a candidate for that highest energy molecular orbital.
And so that leaves us with a few steps that you can just kind of jot down and we'll do
an example here in a moment, but what we are going to do for constructing the molecular
orbital diagram is we will mix atomic orbitals together and we'll list them on the left or
the right and leave a space in the middle.
and the orbitals should be labeled for example we label the 1s orbital.
We want to arrange orbitals vertically by relative energy "s" orbitals are lower than
"p" orbitals for the most part and electronegative atoms have lower energies than electropositive
atoms because they can handle electrons better than their electropositive counterparts, and
then we want to draw the MO's in the middle lower in energy for the bonding MO lower than
the lowest atomic orbital, and then we want to draw the antibonding MO higher than the
highest atomic orbital, and then we want to label those as sigma or pi bonding with a
star if we have an antibonding orbital and then we want to fill with valence electrons.
So let's look at the simplest example hydrogen.
we want to bring the 1s orbital in from a hydrogen so we bring two equivalent energy
orbitals together and we want these to mix to form molecular orbitals so we'll draw the
bonding sigma orbital that we just drew above slightly lower in energy or lower in energy
than the atomic orbitals so here's our energy axis zero energy here the atomic orbitals
have no interaction with each other at the zero line and so bonding has a delta E that
is negative and so this is a favorable interaction if we have a delta E that is positive for
the sigma star that we drew above, the antibonding orbital, we'll redraw it here with an out
of phase interaction its higher in energy than both the atomic orbitals and so it has
a delta E relative to the atomic orbitals that is positive so its an unfavorable interaction.
And so we connect the orbitals to indicate that we are mixing them together in case we
have more orbitals that we are mixing in larger diagrams.
So we connect those together and really and truly we are considering the orbitals in the
middle for the molecular orbitals.
So the molecular orbitals are in the box here they are in the middle, the atomic orbitals
on the outside.
So what else do we have to do?
We have to indicate what electrons are coming together from the atomic orbitals and so each
hydrogen a single dot for it's dot structure, we bring two together we form one bond according
to valence bond theory from our Lewis structure and so two electrons can fit in a single orbital.
That sigma bonding orbital fills for hydrogen.
Ok two electrons in and if we had a third electron we'd have to put it in up here but
we don't for the hydrogen atom, so this is H2 and that's equal to H to H. Ok last thing
is bond order and so bond order is going to equal the number of bonding electrons minus
the number of antibonding electrons, and all of this over 2.
And so for the hydrogen atom we have two in a bonding orbital and there they are right
there, and we have zero in an antibonding orbital, so 2 divided by 2 is one which matches
our Lewis structure for one bond so we agree there.
Ok so we'll do another video for more examples of more complicated molecular orbital theory
problems however, this is good for us getting started here.