Sigma bonds and bond
rotation
Groups bonded by only a sigma bond can
undergo rotation about that bond with respect
to each other,The temporary molecular shapes
that result from rotation of groups about single
bonds are called conformations of a molecule,Each
possible structure is called a conformer,An analysis
of the energy changes associated with a molecule
undergoing rotation about single bonds is called
conformational analysis.
When we do conformational analysis,we will find
that certain types of structural formulas are
especially convenient to use,One of these types is
called a Newman projection formula and another
type is a sawhorse formula,Sawhorse formula are
much like other three-dimensional formulas we have
used so far,In conformational analyses,we will make
substantial use of Newman projections.
To write a Newman projection formula,we
imagine ourselves taking a view from one
atom (usually a carbon) directly along a
selected bond axis to the next atom (also
usually a carbon atom),The front carbon
and its other bonds are represented as
and those of the back carbon as,
The rotation around the single bond in
ethane,while not obviously hindered,does
generate conformational isomers having
different potential energies,As shown
bellow,as the dihedral angle between the
ethane hydrogen atoms changes from 60 (a
staggered conformation) to 120 (an
eclipsed conformation),the potential
energy of the molecule increases by about
3 kcal/mole,As the methyl group continues
to rotate towards 180,the potential
energy again drops and rises again as the
next eclipsed structure is formed.
This can be contrasted,however,
with rotation around the central
carbon-carbon bond in butane,shown
below,in which two methyl groups
clearly overlap during a single
rotation (the van der Waals radii of
the methyl hydrogen atoms clearly
overlap).
The effect of rotation on the potential energy of
butane around the central carbon-carbon bond is
more significant,as shown above,The structure
shown at 0 is fully eclipsed,that is,both methyl
groups are aligned and are interacting maximally,As
the front methyl group is rotated 60,a gauche
conformation is produced in which the methyl group
is nestled between the back methyl and the adjacent
hydrogen atom,Another 60 rotation produces an
eclipsed version of the gauche conformation which is
approximately 2.4 kcal/mole less stable,At 180,the
anti conformation is formed in which the two methyl
groups are on opposite faces of the molecule and no
groups are eclipsed,This is the most stable
conformers and it differs from the fully eclipsed
conformers by about 5 kcal/mole in potential energy,
Further rotations regenerate an equivalent eclipsed
gauche conformer (at 240),another gauche form
(300) and finally,the eclipsed form at 360,
Rotations such as these are not possible in
cycloalkanes,where the ring constrains
the movements around the carbon-carbon
single bonds,Cyclopropane rings are
generally flat and have little
conformational flexibility,The flexibility
of four- and five-membered rings is
significantly greater and these molecules
exist as a dynamic equilibrium among
various "puckered" conformations,as
shown below,
The conformational flex ability of cyclohexane is
somewhat unique in that two equivalent structures
are involved which are linked by a process termed
"ring inversion",As shown in the figure above,the
lowest energy conformation of cyclohexane is one
in which each end of the molecule is "puckered",
relative to the plane of the ring,This form is
commonly called the "chair conformation",as it
somewhat resembles a reclined lawn chair,
Inspection of this structure shows that there are
two types of hydrogens in the molecule; a set that
is perpendicular to the plane of the ring (axial
hydrogens) and a set which are more-or-less in
the plane of the ring (equatorial hydrogens),
The chemical reactivity of cyclohexane,however,
is inconsistent with two types of hydrogens in a
stable form of the molecule (for example,there is
only one monochlorocyclohexane,not two,as would
be predicted if axial and equatorial hydrogens
could be replaced independently),The explanation
for this fact is that the flex ability of
cyclohexane allows for rapid ring inversion,in
which one chair conformation is replaced by a
second,Intermediate between these two chair
forms is an unstable conformation called "boat
cyclohexane",in which both ends of the molecule
are puckered in the same direction,
The important thing to note about
the process of ring inversion is that
during ring inversion,all axial
substituents are converted to
equatorial substituents,and all
equatorial substituents become
axial.
The axial hydrogens in cyclohexane
experience a slight amount of steric
repulsion,More bulky groups,however,can
interact strongly with other axial
substituents,making it energetically
unfavorable for these groups to occupy
axial positions,These unfavorable
interactions can be seen below in the
equatorial and axial representations of
bromocyclohexane.
In the equatorial conformation,the
bromine is "sticking out" from the plane of
the ring and is experiencing only minimal
steric interactions with neighboring groups,
In the axial conformation,however,the
van der Waals radii of the bromine
significantly overlaps with that of the two
axial hydrogens,This type of steric
interaction can also be clearly seen in the
models for ethylcyclohexane,shown below,
As stated above,steric interactions tend to make
conformations containing axial substituents energetically
unfavorable,relative to placing these substituents in
equatorial positions,Since axial and equatorial groups in
cyclohexane are linked via equilibria involving ring inversion,
the net effect is to force the equilibrium towards the more
stable form in which the bulky substituents are in equatorial
positions,as shown below,For very large substituents (i.e.,
the tert-butyl group) this equilibrium is so strongly shifted
so that ring inversion essentially never occurs,Such groups
are said to "lock" the ring into the energetically favorable
conformation,
rotation
Groups bonded by only a sigma bond can
undergo rotation about that bond with respect
to each other,The temporary molecular shapes
that result from rotation of groups about single
bonds are called conformations of a molecule,Each
possible structure is called a conformer,An analysis
of the energy changes associated with a molecule
undergoing rotation about single bonds is called
conformational analysis.
When we do conformational analysis,we will find
that certain types of structural formulas are
especially convenient to use,One of these types is
called a Newman projection formula and another
type is a sawhorse formula,Sawhorse formula are
much like other three-dimensional formulas we have
used so far,In conformational analyses,we will make
substantial use of Newman projections.
To write a Newman projection formula,we
imagine ourselves taking a view from one
atom (usually a carbon) directly along a
selected bond axis to the next atom (also
usually a carbon atom),The front carbon
and its other bonds are represented as
and those of the back carbon as,
The rotation around the single bond in
ethane,while not obviously hindered,does
generate conformational isomers having
different potential energies,As shown
bellow,as the dihedral angle between the
ethane hydrogen atoms changes from 60 (a
staggered conformation) to 120 (an
eclipsed conformation),the potential
energy of the molecule increases by about
3 kcal/mole,As the methyl group continues
to rotate towards 180,the potential
energy again drops and rises again as the
next eclipsed structure is formed.
This can be contrasted,however,
with rotation around the central
carbon-carbon bond in butane,shown
below,in which two methyl groups
clearly overlap during a single
rotation (the van der Waals radii of
the methyl hydrogen atoms clearly
overlap).
The effect of rotation on the potential energy of
butane around the central carbon-carbon bond is
more significant,as shown above,The structure
shown at 0 is fully eclipsed,that is,both methyl
groups are aligned and are interacting maximally,As
the front methyl group is rotated 60,a gauche
conformation is produced in which the methyl group
is nestled between the back methyl and the adjacent
hydrogen atom,Another 60 rotation produces an
eclipsed version of the gauche conformation which is
approximately 2.4 kcal/mole less stable,At 180,the
anti conformation is formed in which the two methyl
groups are on opposite faces of the molecule and no
groups are eclipsed,This is the most stable
conformers and it differs from the fully eclipsed
conformers by about 5 kcal/mole in potential energy,
Further rotations regenerate an equivalent eclipsed
gauche conformer (at 240),another gauche form
(300) and finally,the eclipsed form at 360,
Rotations such as these are not possible in
cycloalkanes,where the ring constrains
the movements around the carbon-carbon
single bonds,Cyclopropane rings are
generally flat and have little
conformational flexibility,The flexibility
of four- and five-membered rings is
significantly greater and these molecules
exist as a dynamic equilibrium among
various "puckered" conformations,as
shown below,
The conformational flex ability of cyclohexane is
somewhat unique in that two equivalent structures
are involved which are linked by a process termed
"ring inversion",As shown in the figure above,the
lowest energy conformation of cyclohexane is one
in which each end of the molecule is "puckered",
relative to the plane of the ring,This form is
commonly called the "chair conformation",as it
somewhat resembles a reclined lawn chair,
Inspection of this structure shows that there are
two types of hydrogens in the molecule; a set that
is perpendicular to the plane of the ring (axial
hydrogens) and a set which are more-or-less in
the plane of the ring (equatorial hydrogens),
The chemical reactivity of cyclohexane,however,
is inconsistent with two types of hydrogens in a
stable form of the molecule (for example,there is
only one monochlorocyclohexane,not two,as would
be predicted if axial and equatorial hydrogens
could be replaced independently),The explanation
for this fact is that the flex ability of
cyclohexane allows for rapid ring inversion,in
which one chair conformation is replaced by a
second,Intermediate between these two chair
forms is an unstable conformation called "boat
cyclohexane",in which both ends of the molecule
are puckered in the same direction,
The important thing to note about
the process of ring inversion is that
during ring inversion,all axial
substituents are converted to
equatorial substituents,and all
equatorial substituents become
axial.
The axial hydrogens in cyclohexane
experience a slight amount of steric
repulsion,More bulky groups,however,can
interact strongly with other axial
substituents,making it energetically
unfavorable for these groups to occupy
axial positions,These unfavorable
interactions can be seen below in the
equatorial and axial representations of
bromocyclohexane.
In the equatorial conformation,the
bromine is "sticking out" from the plane of
the ring and is experiencing only minimal
steric interactions with neighboring groups,
In the axial conformation,however,the
van der Waals radii of the bromine
significantly overlaps with that of the two
axial hydrogens,This type of steric
interaction can also be clearly seen in the
models for ethylcyclohexane,shown below,
As stated above,steric interactions tend to make
conformations containing axial substituents energetically
unfavorable,relative to placing these substituents in
equatorial positions,Since axial and equatorial groups in
cyclohexane are linked via equilibria involving ring inversion,
the net effect is to force the equilibrium towards the more
stable form in which the bulky substituents are in equatorial
positions,as shown below,For very large substituents (i.e.,
the tert-butyl group) this equilibrium is so strongly shifted
so that ring inversion essentially never occurs,Such groups
are said to "lock" the ring into the energetically favorable
conformation,
