if a compound has one chiral center
it's chiral overall and will exist as a pair of
enantiomers, one having R configuration the other having S.
but if a compound has two or more chiral centers
we're going to have to analyze a little bit further to tell if a molecule is
chiral or achiral
overall. so let's take a look at something like this, we have
two chiral centers here, because
each of these carbons is connected to four different groups, for example a chlorine
the implied hydrogen, and then two different carbon chains
around each side because in this direction there's a chlorine atom that
is not present in that direction
so those are different groups. now if we reflect this across a mirror plane
this is what we're gonna get and then if we rotate this
180 degrees in the plane on the board to try to be able to place it back on the original
we are gonna see that it is not going to work, this is not gonna fit because
a dash chlorine will be on a wedge and a wedge chlorine will be on a dash
therefore these are non superposable mirror images
they are enantiomers of one another, therefore this molecule
is chiral but what if we do something as simple
as just changing this dash to this wedge. now what we're gonna see is if we
reflect across the mirror plane this is what we're gonna get, we turn this
180 degrees and we find that this
is flawlessly superposable so the mirror image
is identical to the original therefore by definition
this is achiral or not chiral.
however it does still have two
chiral centers and you ought to be able to assign
absolute configuration to these two chiral centers
so this means that it can be possible for a molecule to have two or more chiral centers
with their own absolute configurations but be
achiral overall, and in fact there are special terms to designate why
and in this case it is because this
is something called a meso compound.
a meso compound is
a compound that has an internal plane
of symmetry. what that means is because the top half of this molecule
when reflected across the central line or plane
does in fact give accurately the other half of the molecule
that means that this is a plane of symmetry therefore it is a meso
compound and any meso compound
is achiral or not chiral, so if you want to see whether molecule with two or more
chirall centers
is chiral overall or not you can
either examine for any kind of planes of symmetry
or as always you can simply
go ahead and reflect across the mirror plane see what you get
and then investigate as to whether the result can be
superposable on the original. so there's another kind of internal
symmetry that will allow for a molecule with multiple chiral centers
to be achiral overall, it's a little bit different from a meso compound because
it's not a plane of symmetry it's actually more like a point of symmetry
called an inversion center. so let's take a look at what this is doing
so if you reflect every atom in the molecule
across the inversion center at the center the molecule
this is what happens, so A will see
A on the other side of the molecule, those are both in the plane of the board
now B here is extending
out of the board and that is gonna go through the center
to the dash B on the other side
so that's passing through the center and through the board on to the other side
and then likewise the C that is coming from the other side past the board
will travel through the center and then to the C
on the wedge over here, so if it is the case
that every atom in the molecule can be reflected
across an inversion center and see itself on the other side
that molecule has an inversion center
and is therefore achiral overall or not chiral
even though there could be
just as in this case two chiral centers
so there's another stereoisomeric relationship that we need to be aware of
and that is that of diastereomers. diastereomers
are stereoisomers that are not
specifically enantiomers. in other words
they are molecules that are stereoisomers of one another
but they're not specifically mirror images of each other.
so let's take a look at a molecule that has two chiral centers
so here we have an R and we have an S
we know very well that if we take the mirror image of that
that we're gonna get the enantiomer
so that would be this, and at home if you want you can go ahead
and draw this across that mirror plane and then flip it over
and you will see that you would get the same group but now those would be
on the dash bonds. when you take the mirror image of something or if you're
drawing the
enantiomer of a molecule it is essentially the inversion of
every stereocenter so whereas this
is R and S this is S and R
so these are enantiomers because they have precisely
the inversion of each chiral center
now a diastereomer of this molecule
would be one in which one but not both
of the stereocenters are inverted, so down here
if we swap the wedged hydroxyl for a dash
we're going to get a different stereoisomer
because these are not the same molecule
they differ in how they are oriented in three-dimensional space
but they are not specifically mirror images of each other
they do not have a mirror image relationship so they can not be
enantiomers of one another, so that's what diastereomers are
these are different diastereomeric relationships
because they are stereoisomers of one another
but not specifically the mirror image
so basically what we want to understand is that
any molecule no matter how many stereocenters it has, let's say there's a
compound with
10 chiral centers, that means it could have many many many different
diastereomers
because if you invert only one or two or three or four or up to nine
of those stereocenters in any combination you can think of
you would generate a different diastereomer
of that molecule however there can only be one
enantiomer of any given molecule because
it is specifically the mirror image
of that molecule or the molecule in which
every single one of those chiral centers
is inverted to the opposite absolute configuration
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