Molecular Orbital Theory vs Valence Bond
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Molecular Orbital Theory vs Valence Bond

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.

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