Let's talk about Valence Bond Theory. So Valence Bond Theory is a theory of how bonds occur
between atoms of a molecule that's a little older than another theory we are going to
talk about, Molecular Orbital Theory, but it can give some great predictions about molecular
structure and chemical properties so without further ado, bonding occurs according to valence
bond theory where atomic or hybrid orbitals overlap. So you've talked about "s" and "p"
orbitals "d" orbitals hybrid orbitals "sp" "sp2" sp3" and the greatest interaction occurs
at the perfect bond length. And we can illustrate that using an energy diagram, so if we draw
an energy axis, and we'll say zero energy, zero change in energy is no interaction so
no interaction at all occurs when delta E is equal to zero and so if we look at the
x -axis, if we plot bond length as increasing as we go to the right, then way out on the
other end of the universe from one another 2 atoms have a zero interaction to one another,
say hydrogen atoms that are very very very far apart have no interaction and then as
we get closer, they have a favorable interaction that maximizes at the bond length, and then
as we get closer and closer so here at the perfect interaction we are now overlapping
one another and valence bond theory says the bond occurs where this overlap occurs, and
as we get too close together the nuclei get closer and closer and you go to an asymptote
of positive energy, ok negative energy is considered stable, stable and low energy,
and unstable/unfavorable energy interaction is generally a positive energy for an energy
diagram. So the nuclei are trying to overlap one another and the overlap is too great and
the repulsion of the 2 positive nuclei overwhelm any favorable interaction, so what happens
is that at the perfect bond length, the bond as we've illustrated here for the hydrogen
molecule, theres the Lewis structure, is at the perfect favorable interaction for bonding,
and that's valence bond theory pictorially. So let's talk about the single bond in an
alkane, so here's ethane, and this is a perspective diagram of the Lewis structure and so I've
highlighted 2 bonds that we are going to talk about in terms of valence bond theory, so
we've got overlap of orbitals here, but let's talk about what type of orbitals we have.
We've got four domains about each of these carbons and so that means we have tetrahedral
109.5 degree bond angles for each of these positions okay or very approximate to 109.5
for each of these carbons. And that means according to hybridization 4 electron domains,
that means we've got sp3 orbitals coming of each of these carbons. In the middle we've
got two carbons that are overlapping sp3 orbitals so valence bond theory says that this single
bond is actually made up of 2 sp3 orbitals overlapping one another, and the bond occurs
right there in the middle where the overlap occurs. And then in the other position, hydrogen
does not hybridize it is an "s" orbital overlapping the sp3 of carbon so we have an s to sp3 overlap
here and so this bond is represented by the overlap which occurs between the two atoms
in that position. So those in the Lewis structure that's what we mean. For single bonds when
we have hybrid or "s" orbital overlap, we get a sigma bond, OK so sigma bond, both of
these are sigma bonds, in fact ethane has 6 C-H sigma bonds. Ok they occur in cylindrical
symmetry ok they are like cylinders all the way through the middle and they occur on the
plane of the bond as we draw in the Lewis structure so on the line that we draw in the
line structure. That's what a single bond looks like for both the C-H and C-C. What
about a double bond. So what i've drawn here is an on it's side representation of ethene
and we've got the p orbitals highlighted because we know that carbon is sp2 hybridized because
we have 1,2,3 electron domains on each of these carbons, so 1,2,3...the sigma bonds
that I'll highlight in yellow here, they all look just like the previous bonds that we
looked at before, they are s orbitals of hydrogen overlapping sp2 orbitals now of carbon, and
then 2 sp2's in the middle overlap for sigma bonding and then the hydrogens overlap for
sigma bonds with the sp2 on the outside so we have 1,2,3,4,5 sigma bonds. And then the
p orbitals are not in the same plane as the atoms they are actually they actually have
a node at the nucleus of carbon that is perpendicular to these hydrogen bonds or C-H bonds or C-C
bonds and so what we have are the two lobes of the p orbitals that overlap above and below
the bond, and what that looks like if we look on its side is we've got p orbitals and I'll
make them nice and large so we can see a valence bond theory, we've got two orbitals that overlap
above and below, there's a p orbital and there's a p orbital, and as we've shown we've got
a top phase and we've got a bottom phase that I'll leave uncolored here. So top phase and
bottom phase the gray we could actually look at that in terms of how it might look if we
shaded it gray like we did in the previous example, ok and we still have the same phases
lined up but the orbital overlap occurs here and here, valence bond theory says we've got
the bond occurring there, and whenever we've got p orbitals overlapping we have a pi bond
instead so there's one pi bond that occurs in a double bond so this double bond is made
up of a sigma and a pi bond together one is composed of sp2 orbitals overlapping and one
is composed of p atomic orbitals that are unhybridized overalapping so pi bonds occur
when we have two p orbitals overlapping now for courses that get into the d orbitals and
pi bonding we are not going to mention those here just for organic compounds we have p
orbitals overlapping to form pi bonds. And so if we look at the triple bond we've got
the same situation going on. We've got now sp hybridized carbons, we have linear molecular
structure and so if we draw this in a lewis structure the triple bond of ethyne has 180
degree bond angles at both carbons so what does that mean? It means that we are sp hybridized
at both carbons so if we are sp hybridized we have the s orbital of hydrogen and the
sp hybrid orbital of carbon overlapping one another to form a sigma bond. Then we have
two sp orbitals overlapping to form a sigma bond, and then finally the reciprocal on the
other side the hydrogen-carbon bond sp overlapping with H so we end up with 3 sigma bonds in
the triple bond or at least in ethyne overall, but in the triple bond one sigma bond, so
what's left over the other two bonds turns out they are pi bonds just like we showed
before, so we have the py orbital that's strait up and down in the y axis that's overlapping
here and then we have the pz orbital for each of the carbons which is in a plane that comes
at us and away from us in the page here and they are overlapping one another they are
perpendicular to the py orbital so they overlap one another to form another pi bond to form
the overall triple bond. so one sigma and 2 pi bonds compose the triple bond. Overall
ethyne has 3 sigma bonds and 2 pi bonds which add up to the same number of lines we have
in our Lewis structure 1,2,3,4,5 so 3 plus 2 is five we are all covered