Noncovalent Interactions Overview

Overview
Examples

Noncovalent interactions are particularly important in biological chemistry. The binding of ligands to a receptor is usually via noncovalent interactions such as hydrogen bonding, pi-pi stacking, pi-cation interactions, and even halogen bonding. These weak interactions and their existence can be explored with the help of the electron density, via noncovalent interaction plots.

How do we know when there is a bond? For a normal, covalent sigma bond, we usually consider that there is a maximum in the electron density along the line that joins the two atoms in the bond. As we walk along this bond path (which need not be exactly straight) from one atom to the other, the electron density decreases along this line to some minimum, then increases again. Perpendicular to the line, the electron density decreases in any direction. This means that the gradient of the electron density is zero perpendicular to the bond path, and is also zero at one point along the path, where it stops decreasing and starts increasing again. This point is a "critical point" in the electron density. All covalent bonds have such a bond critical point, and this point has maxima in the two (orthogonal) directions perpendicular to the bond path and a minimum along the bond path. (Mathematically, it is a second-order saddle point, with two negative eigenvalues and one positive eigenvalue of the matrix of second derivatives of the density).

The same is true for weak interactions. Bonding occurs because the electron density increases between the bonded atoms. Hydrogen bonds have a bond critical point. Pi-pi interactions can have more than one bond critical point. For example, the pi-pi interaction between two benzene molecules has two bond critical points, between the 2 and 6 carbons of one ring and the 3 and 5 carbons of the other.

There are other kinds of critical points as well. Consider going along the line from the 1 carbon to the 4 carbon in a benzene ring. The density decreases to the middle, then increases again. The same is true for any other pair of carbons on opposite sides of the ring. However, if we go out from the middle of the ring in either direction perpendicular to the ring, the density decreases. The density gradient in the middle of the ring is another critical point, a ring critical point. This point has minima in two (orthogonal) directions across the ring and a maximum in the third direction perpendicular to the ring (it is a first-order saddle point, with one negative eigenvalue and two positive eigenvalues of the matrix of second derivatives of the density). A ring critical point exists if a hydrogen bond completes the ring, such as in the case of 3-hydroxypropanal. The location of the ring critical point depends on the strength of the bonds in the ring: it is closest to the weakest bond. So the distance between the ring critical point and the bond critical point of the weakest bond is a measure of the strength of the bond. The two points annihilate each other if the bond disappears.

As you might guess, there are two other kinds of critical points. One is a maximum in all three (orthogonal) directions: this critical point defines the position of an atom, where the density is a maximum at the nucleus. The remaining critical point is a minimum in all three directions. This kind of critical point occurs in a caged structure, like cubane. If you traverse a line that goes through the center of the cage in any direction — from opposite atoms, or from the midpoint of the bonds on opposite sides, or even the midpoint of the faces of the cube — the density goes up from the center of the cage. This is called a cage critical point.

The interpretation of the critical points is only valid at the equilibrium geometry, where there are no net forces. Away from the equilibrium, critical points still exist (they must), but they don't necessarily provide the kind of information that we want about the bonding.

Jaguar (and QSite) can create surfaces that enclose these critical points. It calculates the density, the (reduced) density gradient, and the density second derivatives on a grid, and locates regions that contain the critical points. To visualize noncovalent interactions (NCI), you can filter out the points at higher densities, so that only those for lower densities are mapped. To set up a calculation, you should do a geometry optimization. In the same calculation, you can choose Surfaces in the Properties tab, and select Noncovalent interactions in the Surfaces section. When the results are imported into Maestro, you should map the strength volume onto the reduced gradient surface in the Surface Display Options dialog box. The Red-White-Blue color ramp is a good choice for this surface: the red regions contain bond critical points, the blue regions contain ring critical points. In addition to the surfaces, the bond critical points are identified and marked with dummy atoms. The bond paths to the bonded atoms are represented by zero-order bonds. You can display and undisplay them with the Maestro command [un]display (atom.mtype Z0), which you can type into the Commands text box.

NCI plots can help resolve questions about whether bonding interations truly exist between atoms that are not considered to be covalently bound to each other. Hydrogen bonds, for example, are known to be dependent upon both the H-acceptor atom distance and the donor-H-acceptor angle. When these parameters are far from ideal, one may question whether a bonding interaction truly exists. In other cases, a pi-pi interaction between aromatic rings may be controversial because the rings are tilted with respect to one another, or a halogen-oxygen bond may be disputed because the X-O distance is so large. When a bonding interaction truly exists between atoms, a bond critical point forms between them, and this information appears in an NCI plot as a small isosurface of low density gradient colored to show that the interaction is favorable.

When there is a single bonding interaction between two molecules, as in the hydrogen bond in the water dimer, an NCI plot shows a single isosurface. In contrast, an NCI plot of a ligand in the active site of an enzyme shows many isosurfaces. Because a ligand in an enzyme active site is an atomically crowded system, and because the ligand usually makes several bonding interactions with its environment, you often see ring and cage critical points in addition to bond critical points, and these add to the complexity of the plots. Ring critical points form inside any closed loop of bond paths. In symmetrical rings like benzene, the ring critical point is in the center of the ring. But if one bond in the ring is weaker than the others, as in the case of an intramolecular hydrogen bond, the ring critical point is off-center and closer to the critical point in the weak bond. The weaker this bond is, the closer the ring and bond critical points are to each other. Sometimes you see that a ring and bond critical point are close enough together that they appear in the same isosurface. In this case, part of the isosurface will be colored to show the favorable interaction indicated by the bond critical point, while the rest of the isosurface will be colored to show the unfavorable interaction indicated by the ring critical point.

Noncovalent Interactions Overview

Calculation of Molecular Properties Examples