What do Coal and Christmas Pie have to do with Computational Chemistry?

“Scrooge had a very small fire, but the clerk’s fire was so very much smaller that it looked like one coal. But he couldn’t replenish it, for Scrooge kept the coal-box in his own room; and so surely as the clerk came in with the shovel, the master predicted that it would be necessary for them to part.”

Charles Dickens, A Christmas Carol

“Little Jack Horner
, sat in the corner, eating a Christmas pie;
He put in his thumb, and pulled out a plum, and said ‘What a good boy am I!”

Traditional English

As you’re reading this, you may be wondering about whether the Cresset team might have been into the eggnog again. What do coal and Christmas pie have to do with computational chemistry?

Aromatic compounds, like those produced during incomplete coal combustion, can be complex in how they interact with one another. Key to those non-covalent intermolecular interactions are π-electrons (get it? Pie?); and these types of non-covalent interactions are extremely common in protein-ligand interactions and self-assembled systems.

Despite the common occurrence of π-cloud electrostatic interactions, traditional atom-centered force fields (with atom-centered charges) are incomplete in their description of these types of dichotomous (simultaneously both electrostatic and hydrophobic) interactions. And while traditional approaches will get you some of the way to truth, it misses induction and other through-bond / through-space interactions that result from the electronic anisotropy.

π-π interactions take on a number of motifs (edge-to-face, offset parallel stacking, etc.) in both small-molecule crystals and protein-ligand crystal structures. Traditional MM force field calculations predict these interactions to be face-to-face. To replicate what is seen experimentally (e.g., edge-to-face), an electronic structure method (i.e., QM) or an “electron-aware” force field would be required.

Incorrect field pattern around benzene
Figure 1: Incorrect field pattern around benzene; results in incorrect stacking (face-to-face).
In 2002, Chessari et al. published a paper that evaluated how various force field treatments of aromatic interactions stacked up. It was found that while conventional MM force fields (AMBER, MM2, OPLS) performed poorly, Cresset’s XED force field reproduced the trends in interaction energies and the predicted 3D structures quite well.

Underlying all of Cresset’s software is the XED (eXtended Electron Distribution) force field. XED is now in its 3rd iteration, and has been a 30-year work-in-progress for Cresset’s founder, Andy Vinter.

The XED approach is unique in that it explicitly represents electron anisotropy by using a distribution of charged “orbital points” around the molecule (depending on atom hybridizations), effectively moving the negative charge OFF the nucleus. Each XED point can thus be seen as p-orbital electrons (lone pairs, or Π-cloud delocalized pairs; and these points are included in the MM optimization.


Figure 2a: Field points and XED’s (the purple bits, corresponding to p-orbital electrons) for benzene, demonstrating both hydrophobic and electrostatic nature of the aromatic ring. Blue field points = negative; red field points = positive; orange = hydrophobic; yellow = accessible van der Waals surface.
Correct field pattern around benzene
Figure 2b: Correct predicted aromatic stacking (edge-to-face) from XED/Cresset calculations.
Obviously, folks (including myself!) could make the argument that a conventional force field method could be augmented by fitting the electrostatic potential from QM calculations to the charge terms. However, this might be an unrealistic endeavor, as each fragment would need to be assessed independently as the charge distribution is dependent on the neighboring atoms. This approach would be likely to stumble in systems with high degrees of rotational freedom, where energies and electronic distribution are tightly linked to conformation.

XED, with its off-nucleus charges, avoids the pitfalls of the electrostatic potential fitting approach. The XED charges are set using an empirical charge generator that takes into consideration both electronegativity and electron drift. When you think of what atoms are really like, it makes sense that the positive charge is on the nucleus, and the negative charge is not!

While enjoying a nice glass of eggnog, I encourage you to take a peek at the following papers:

Extended electron distributions applied to the molecular mechanics of intermolecular interactions
Vinter. J., CompAided Mol Des., 1994, 8, 653-668.

An Evaluation of Force-Field Treatments of Aromatic Interactions
Chessari et al., Chem. Eur. J., 2002, 8 (13), 2860-2867

Happy Holidays!

Rae Lawrence
Rae Lawrence
Account Manager, North America (West)