The image below exhibits three possible conformations of propene. To facilitate analysis, the carbons have been labelled 1-3 with blue in the drawings. In a propene molecule, there is free rotation about the 2-3 sigma bond and we can draw Newman projections much as we would for ethane by substituting a C-H bond with the C=C, and adjusting for the proper sp² bond angle of 120°. The lowest energy conformation is not staggered, as one might initially assume, but is eclipsed. The eclipsed conformation is impressively 1kcal/mol more stable than the staggered conformation. Rotations about the 2-3 sigma bond allow different eclipsed conformations. For conformer 1 is more stable than conformer 2.
To find the reason for these observations we must look to stabilizing features in the more stable conformers, NOT to destabilizing features (such as steric or torsional strain). The eclipsed form is more stable because it allows electron delocalization through hyperconjugation unlike the staggered confirmation. The pi* anti-bonding orbitals are two p-orbitals that come together out of phase, and are rarely populated by electrons due to their high energy level. The pi* anti-bonding as well can be thought to exist simultaneously next to the pi bonding orbitals of a double bond. This makes them accessible to electron donation from the C3-H sigma bonds of propene. In eclipsed conformation #1, as shown below, two of the sp³ C3-H bonds are aligned with the pi* anti-bonding orbitals of C2. The C3-H electrons help to stabilize the empty pi* orbitals, which outweighs the energetic penalty for an eclipsed interaction.
Why is eclipsed #2
1. It aligns the C3-H bonds with the C1 pi* anti-bonding orbitals, which are farther up and farther back, so electron sharing is not as effective.
2. The eclipsing C3-H bond of eclipsed #2 interacts with a substituent that is one bond away (vs 2 bonds away for eclipsed #1).
Steric interactions in eclipsed propenes become more important when we start replacing hydrogens with larger substituents. The rotomers (conformers that differ by bond rotation) below show the energy difference between methyl-methyl and methyl-hydrogen eclipsing interactions. This interaction is very similar to a syn-pentane interaction, but one of the 4 bonds is a double bond, which brings the eclipsing substituents even closer. This is because the double bond is shorter than the corresponding single bond in a syn-pentane formation. Therefore, this interaction is actually a little bit worse than syn-pentane. Substituents attached to C3 of propene are said to be in the allylic position (one away from a double bond), so we call this new interaction between the C1 and C3 substituents Allylic 1,3 strain, or A(1,3) for short. The A(1,3) strain causes about a 4kcal/mol increase in energy.
Conformation Analysis of the Amide Bond
An amide exists when there is a nitrogen alpha to a carbonyl.
The Amide bonds result from the dehydration of two amino acids as shown below. Water is lost and a bond between the carboxylate anion and the amine forms. Resonance makes this newly formed amide significantly more stable than a normal carbonyl.
Effects of Resonance
The Nitrogen's p-orbital lone pair resonates into the carbonyl pi system as shown below. The Nitrogen is sp² hybridized and planar to allow this resonance. Remember that the actual molecule is hybrid of the two NOT just one of the two representations.
This resonance decreases the energy of the molecule and makes it more stable. In a normal carbonyl, the C carries a significant partial positive charge because the O withdraws so much electron density via induction. The N lone pair helps quench this charge and makes the C=O less reactive towards nucleophiles. Stability is very important because proteins, which are vital in many cell functions, consists entirely of amino acid polymers.
The bond length of a typical C-N sigma bond is about 1.45Å and the bond length in a C=N is about 1.25Å. If the two resonance structures were equally favored, we would expect an amide bond length of about 1.35Å, but that is not the case. The measured bond length is about 1.32Å, closer to that of a C=N double bond. This demonstrates that the resonance hybrid is more similar to a C=N double bond than a C-N single bond. Why is the amide bond length important? Since the resonance hybrid bond length is closer to the C=N double bond length, O-C=N resonance form is really the more accurate representation of the functional group. It turns out that we can treat amides much like substituted propenes for conformational anaylsis.
Minimization of Strain
The H, R-group, and AA backbone are oriented such that the smallest substituent, H, eclipses the Oxygen and therefore minimizes A(1,3) strain. In every amide linkage, the main chain rotatable bonds will adopt conformations that minimize A(1,3) strain. This provides a significant amount of structural rigidity to polypeptides. The A(1,3) minimized conformation places the hydrogen in the same plane as the carbonyl for every amide in the chain and produces an extended strand.
We must consider another steric interaction for amino acid amide bonds, the substituents of C1 are not equivalent unlike our substituted propane. This in itself would not matter, but the C=N is just a resonance form, so, also unlike our substituted propene, it has enough sigma character to potentially rotate. It is helpful to remember some simple alkene energetic factors, and realize that we have 4 different substituents branching out from our C=N. The C has an oxygen and polypeptide backbone, and the N has a hydrogen and polypeptide backbone. The polypeptide backbone is easily the larger substituent in both cases. Any good alkene keeps its two larger substituents pointing away from each other (trans), and thats exactly what amide bonds will do, too. The allylic perspective gives us a new way to describe the what's wrong with the cis conformation. Since the painfully crowded polypeptide backbones are attached to the 1 and 2 positions (see the propene-AA comparison above), we say that they are creating lots of Allylic (1,2) strain or A(1,2) for short.
Energetics of Amide Bond Rotation
The difference in energy of the cis(Z) and trans(E) amide conformers is about 4 kcal/mol; this might not sound like a substantial amount, but "we are perched on the thermodynamic edge" and 4 kcal/mol "is a huge deal." To further understand why the cis(Z) conformer is not observed, we must look at the transition state between the two. There is not free rotation about the C-N bond and, thus, in order to rotate the bond, the pi-bond must be broken. The energetic consequence of this is an activation barrier of 20 kcal/mol. However it is not as bad as a true pi bond which needs 60 kcal/mol.
We have now attributed a good bit more rigidity to polypeptides. Describing it with the allylic numbering system, the 1-2 bond is pretty steady in the first place, and basically locked to prevent A(1,2) strain. The 2-3 bond is stuck in one place to maintain eclipsing hyperconjugation and minimize A(1,3) interactions, even though it has full sigma flexibility,.
Proline accesses the cis conformation another way. Instead of eliminating the A(1,2) strain in the cis conformation, it adds some to the trans conformation. Remember that for all other amino acids, trans is comfortable because a hydrogen is always hanging down from the nitrogen in the position where A(1,2) interactions might occur with the polypeptide backbone on the other side of the C=N. Proline's R group reaches around to that nitrogen and replaces the hydrogen with an aliphatic chain, which creates a pretty big A(1,2) strain in the trans position. The cis is not any better, but since it's not much worse, proline is pretty willing to go either way.
Flexibility at proline residues allows polypeptide chains to make "U-Turns" and fold back onto themselves. This allows for favorable Hydrogen bonding interactions which are worth about 1-4 kcal/mol each. This secondary structure is referred to as a "beta sheet." The Beta sheet still minimizes A(1,3) strain throughout the entire chain. Below is an example of a beta turn that lets beta sheets fold back.