Rotatable bonds and ring conformations

A structure drawn on paper is one shape. The molecule is a crowd of shapes, interconverting constantly. This module is about which bonds can turn, what it costs to turn them, and what shapes a ring can adopt — because a docking programme's first job is to enumerate exactly this.

The usual definition: a single, acyclic bond between two non-terminal heavy atoms. Single, because a double bond cannot rotate. Acyclic, because a bond inside a ring cannot rotate independently. Non-terminal, because turning a methyl group changes nothing you care about.

That sounds precise. It is not. Implementations disagree, which is why two programmes routinely report different rotatable bond counts for the same molecule. The commonest points of disagreement:

• Amide C-N bonds. Some definitions exclude them, because the partial double bond character means they barely rotate. Some include them.
• Terminal groups. Is a C-OH rotatable? Is a C-CF₃? Some say no because the rotation is symmetric and changes nothing.
• Bonds to sp carbons. Rotating about a linear centre is meaningless, but not every implementation excludes it.

This matters because the Veber criteria in module 20 put a threshold at ten rotatable bonds. A threshold is meaningless until you know which definition it was written against.

Rotating a bond is not free and it is not uniformly expensive. Plot energy against dihedral angle and you get a landscape with wells and barriers. Four cases cover most of drug chemistry.

Butane is the textbook case. The anti arrangement, with the two methyls opposite, is lowest. Two gauche wells sit a little higher. Between them are eclipsed barriers of a few kcal/mol — low enough that at body temperature the bond turns billions of times a second.

Two aromatic rings joined directly want to be flat, for conjugation, and cannot be, because the hydrogens next to the bond collide. The compromise is a twist of thirty to fifty degrees.

Now add a methyl next to the bond, and the barrier rises sharply.

The amide deserves its own treatment because it behaves like nothing else. You met the reason in module 2: the nitrogen lone pair delocalises onto the carbonyl, so the C-N bond has partial double bond character.

The consequences: the amide unit is planar, the rotation barrier is 15 to 20 kcal/mol — enough that at room temperature it rotates on a timescale of seconds, not picoseconds — and there are exactly two arrangements, cis and trans. For a secondary amide, trans is strongly preferred, which is why peptide backbones are what they are.

A six-membered ring drawn as a flat hexagon is a lie of convenience. Flat, its bond angles would be 120 degrees where sp³ carbon wants 109.5, and every pair of neighbouring hydrogens would be eclipsed. So it puckers.

• Chair — the minimum. All bond angles near ideal, all neighbours staggered. Cyclohexane is essentially always a chair.
• Twist-boat — about 5 to 6 kcal/mol up. A real but sparsely populated form.
• Boat — a transition state between twist-boats, not a resting place.

In a chair, each carbon has one axial position, pointing up or down roughly parallel to the ring axis, and one equatorial position, pointing outwards. A substituent prefers equatorial, because axial substituents collide with the other two axial groups on the same face. For a tert-butyl group that preference is worth about 5 kcal/mol, which is enough to lock the ring.

Five-membered rings pucker too, into envelope and half-chair forms, but the energy differences are much smaller and they interconvert freely. A cyclopentane ring is genuinely floppy in a way a cyclohexane is not.

This is worth stating plainly because it causes real errors. When you draw a ring flat and put two substituents on it, the drawing tells you nothing about how far apart they actually are. Two groups that look adjacent on paper may point in completely different directions in the puckered ring — and it is the puckered ring that meets the protein.

Strain is worth having a feel for, because the numbers turn up inside every scoring function.

• Butane gauche versus anti: about 0.9 kcal/mol.
• Axial versus equatorial methyl on cyclohexane: about 1.7 kcal/mol.
• Cyclohexane chair to twist-boat: about 5 to 6 kcal/mol.
• Amide rotation barrier: 15 to 20 kcal/mol.
• Cyclopropane ring strain: about 27 kcal/mol — which is why it opens.

Hold on to the first two. At body temperature, RT is about 0.62 kcal/mol. So a difference of 1 kcal/mol is a population ratio of roughly three to one, and a difference of 3 kcal/mol is roughly a hundred to one. That is the arithmetic behind everything in the next two modules.

When you press the button on a conformer generator, it is enumerating exactly what this module has described: it identifies the rotatable bonds, samples torsion angles for each — usually from a library of observed preferences rather than uniformly — chooses ring conformations from templates, builds the resulting geometries, minimises them, and discards duplicates.

Two settings control what you get, and both are worth understanding.

• The energy window discards conformers more than a stated amount above the minimum. Too tight and you lose the bioactive conformation; too loose and you keep thousands of structures that do not exist.
• The RMSD threshold decides when two conformers count as the same. Too tight and you keep near-duplicates; too loose and you throw away genuinely distinct shapes.

Neither has a universally right value, and the defaults were chosen for typical drug-sized molecules. A macrocycle or a very flexible ligand needs different ones.