Pi interactions, halogen and chalcogen bonding

Aromatic rings are everywhere in drug molecules, and what they do when they meet each other is more subtle than the word "stacking" suggests. This module ends on the sigma hole — an interaction most force fields cannot represent at all, which makes it a useful test of what your software knows.

A benzene ring has a quadrupole: the pi electron density sits above and below the ring, leaving the edge relatively positive and the faces relatively negative. So two rings stacked exactly face to face put negative against negative, and repel.

That is why perfect face-to-face stacking is rare. What you actually see is one of two geometries:

• Parallel-displaced — the rings are parallel but offset sideways, so each ring's face sits over the other's edge. This is the commonest arrangement, at about 3.4 to 3.8 Å between planes.
• Edge-to-face, or T-shaped — one ring's C-H points into the other's face. The positively polarised hydrogen meets the negative pi cloud, which is favourable.

Both are worth roughly 1 to 3 kcal/mol in a binding site — real, but less than people assume, and comparable to what a few good van der Waals contacts would give you anyway.

Substituents tune the quadrupole. An electron-withdrawing group — fluorine, nitro, cyano — pulls density out of the ring and makes the face less negative, which strengthens stacking with an electron-rich ring. An electron-donating group does the reverse.

The limiting case is instructive: hexafluorobenzene and benzene stack face-to-face very happily, because one ring's face is now positive and the other's negative. Two identical rings will not do this.

A cation over the face of an aromatic ring is attracted to that negative pi cloud, and the interaction is stronger than most people expect — comparable to a good hydrogen bond, sometimes better, in the range of 2 to 5 kcal/mol in a protein environment.

In proteins the partners are almost always the same: a lysine ammonium or an arginine guanidinium over a phenylalanine, tyrosine or tryptophan ring. Tryptophan is the best partner, having the largest and most electron-rich face.

The geometry requirement is that the cation must be over the face, roughly on the ring axis, at about 4 to 6 Å from the centre. A cation beside the ring edge is not making a cation-pi interaction; it is making an ordinary contact, and calling it cation-pi is a common overclaim.

The place this matters most in pharmacology is the acetylcholine binding site. Acetylcholine's quaternary ammonium is permanently cationic and binds into a box of aromatic residues — the recognition is largely cation-pi, and the same box is what tacrine exploits.

Stacking is not the exclusive property of aromatic rings. Any planar, conjugated system with pi density will do it. The backbone amide is the important case: peptide bonds stack against aromatic rings routinely, and guanidinium groups do the same — arginine can stack as well as make salt bridges, sometimes both at once.

This is worth knowing because analysis software that looks only for aromatic rings will not report these contacts, and they are genuinely there.

Now the interaction that seems, at first, to be impossible.

A halogen is electronegative, so a C-X bond is polarised with the halogen negative. How can that halogen attract an oxygen lone pair?

The answer is that the charge distribution around a bonded halogen is anisotropic. It is not a uniform negative sphere. There is a belt of negative charge around the halogen perpendicular to the bond — and a small electropositive cap directly opposite the C-X bond. That cap is the sigma hole.

So an acceptor approaching along the C-X axis meets a positive region and is attracted. An acceptor approaching from the side meets the negative belt and is repelled. The geometry is therefore extremely restrictive: the C-X⋯A angle must be near 180 degrees.

Two consequences follow directly:

• Strength increases down the group: chlorine < bromine < iodine. The larger, more polarisable halogen has a bigger sigma hole. Fluorine has essentially none and does not form halogen bonds in any useful sense.
• Strength is tunable by the rest of the molecule. Electron-withdrawing groups deepen the sigma hole, which is why halogen bonds are stronger on electron-poor aromatic rings.

A good halogen bond is worth 1 to 3 kcal/mol — comparable to a hydrogen bond after desolvation, and with a much lower desolvation penalty because a halogen is not well solvated to begin with.

Most classical force fields place a single, uniform negative point charge on a halogen. A point charge is spherically symmetric. It has no sigma hole, no anisotropy, and no way of representing an attraction along the C-X axis.

So a standard docking run cannot find a halogen bond. It will score that geometry as neutral at best and repulsive at worst — actively penalising the correct pose.

The fixes exist and are worth knowing by name: add an extra point — a massless positive pseudo-atom on the C-X extension — or use a polarisable or multipole force field. Several docking programmes now include a specific halogen bond term.

The general lesson is bigger than halogens. When your calculation disagrees with a crystal structure, one possibility is that the crystal structure is showing you an interaction your force field has no way of representing. Chalcogen bonds — the same sigma-hole physics on sulfur and selenium — are in exactly the same position, and so is pnictogen bonding on phosphorus.