Conformational Analysis – Cyclohexanes
Cyclohexane is a lot more complicated than it looks at first. When we draw it quickly, for example when needed in a chemical equation, we draw the hexagon shown below. This, however, would infer that the molecule is flat and that each carbon has C-C-C bond angles of 120o. This would be very distorted and strained for sp3 hybrid carbons. The molecule actually relaxes, to the chair form shown in the (moveable) models below, in which each carbon atom is able to be an almost perfect tetrahedron with bond angles close to 109.5o. The shape is referred to as a chair conformation and the study of this kind of shape is essential for understanding concepts in Medicinal Chemistry and Structural Biology later.
Monosaccharide models are available here.
Since cyclohexane is 6 sp3 carbons joined together we must consider the consequences of that arrangement in terms of how the atoms will be organized and arranged in space relative to each other. To make sense, each tetrahedron must alternate in terms of being up or down relative to each other. This leads to the attached atoms having defined direction as shown in the (moveable) model. Orientate this model so that all green atoms are pointing straight up or straight down and you have a good idea of what the “side-on” chair picture looks like, which you will be drawing extensively in the Organic sequence. These atoms (or groups) are pointing along the north-south axis so we refer to them as being in axial positions. The red atoms are pointing out into space, from the equator of the molecule, so they are referred to as being in equatorial positions. You will find that atoms/groups bigger than H prefer to be equatorial.
While the C-C bonds in cyclohexane cannot rotate, the ring is still very flexible and the molecule may adopt many different shapes. The ring is so flexible in fact that it is usually capable of undergoing what is known as a ring-flip process in which the “head” and “foot” atoms (left-most and right most ring C atoms in A, below) change their positions relative to the other four carbon atoms in the “seat” of the chair. During the transformation to the other chair (B) many other shapes are adopted such as the half-chair (C). This is less stable than the chair since bond angles move away from ideal 109.5o and some of the atoms (or groups) attached to the cycle become eclipsed. Further movement produces the boat conformation (D) in which the bond angles are okay, eclipsing interactions are gone, but flagpole interactions appear. These can be alleviated by twisting the atoms in the so-called twist-boat conformations, before the system heads to chair B via half-chair E. The video below shows how this change occurs dynamically.
When only hydrogens are attached to the cyclohexane ring there is an equal distribution of chair forms since they have equal energy. If atoms or groups bigger than H are attached there tends to be one conformation preferred over others in which the larger substituent(s) prefer to go equatorial rather than axial. Unlike in acyclic systems the axial substituents will inevitably interact through destabilizing 1,3-diaxial interactions, for example in the first structure. This problem becomes more pronounced as the substituents get bigger and begins to cause strain within in the ring itself as seen in the second (moveable) structure. The axial substituent is able to become equatorial, via the ring-flip process, to to give the less-strained third (rotatable) structure.
While a large group on cyclohexane will prefer to be equatorial, placing a second substituent on the ring will require a consideration of where each group will want to be. We will need to analyze relative stabilities and compare different ring-flipped conformations to assess which is preferred. Beginning with isomeric di-bromocyclohexanes as examples, it will become obvious that the large Br groups will be equatorial whenever possible, however we must remember that a cis isomer cannot become a trans isomer (or vice versa) in any of these situations so Br may have to go axial depending on which isomer we are considering.
Caution: Keep in mind that rings can flip, so if the first structure drawn has a substituent axial, it could go equatorial by the ring flipping. For example, in the trans-1,4- isomer below, both Br atoms could be axial and pointing in opposite directions, which might suggest it is less stable than the cis isomer. However, the ring flip puts both atoms equatorial making it more stable. It is always better to work out which isomer is more stable than trying to memorize.
The 1,2-isomers: Isomers may be drawn starting with substituents placed anywhere on the cycle as long as they match the identity of the given molecule. Here we start at the top as, arbitrarily, carbon 1 and the Br is written as a dash, which suggests “down” and below the plane. It could also be written as a wedge as long as the next substituent is added so it points in the correct direction relative to the first one. The first image shows both Br atoms pointing in the same direction (cis) while the second has them in opposite directions (trans).
Play with the models below to view how the Br atoms are aligned. In the cis isomer (left) one Br atom is equatorial and fine while the other is axial and a problem. In the trans isomer, both Br atoms are able to be axial or, after the ring flip, both may be equatorial, which is the most stable conformation making trans the more stable isomer.
Moving to the 1,3-isomers, the cis must have the two Br atoms pointing in the same direction and in the trans isomer they must be opposite. Again, the cis isomer could be drawn with two wedges but we will end up in the same place regardless. The trans isomer requires one wedge and one dash but we must be careful not to rush to judgement as trans is not always the more stable isomer. A consideration of the orientations of the groups in each isomer is needed.
Move the models below around to view where the Br atoms are in each isomer. In the cis isomer they can both be equatorial while in the trans isomer one Br atom must be axial and therefore problematic. Notice that even if we flip the ring here, one Br atom is going to have to go axial, which makes this less stable than the cis isomer. For the cis isomer almost all molecules will have the Br atoms equatorial and there will be very few (if any) with both axial. The trans isomer will exist as an equal mix of interconverting chair conformations.
When considering the 1,4-isomers, the cis isomer may again be drawn with two dashes (Br atoms “down”) or two wedges (Br atoms “up”). It doesn’t matter as we will end up in the same place after looking at the possible chair forms. For the trans isomer we need one wedge and one dash; it doesn’t matter which is which. Again, we cannot assume which isomer is more stable, we should work it out by considering possible chair forms.
Moving the following molecules around reveals that in the cis isomer one of the Br atoms must be axial, regardless of which ring-flipped conformation is being assessed. In the trans isomer both Br atoms are able to be equatorial in the (much) more stable conformation. This results in the trans isomer being favoured in the 1,4-disubstituted configuration.