Crystals Under Pressure Still Won’t Cooperate

OK, this one is going to be fairly geeky. But that’s almost inevitable when you start talking about some of the more exotic aspects of chirality, so read on if you dare.

For non-chemists reading this, chirality is “handedness”, the property some objects (like shoes and gloves) have of coming in either of two mirror-image forms. Meanwhile, other objects (a sheet pan, a can of tuna) don’t have right- and left-handed forms. (Generally speaking, if, if you can draw a line through an object that divides it into perfectly symmetrical halves, it can’t exist in mirror-image isomers). Molecules are the same way – some of them can exist in chiral forms and some of them can’t, and we call the right- and left-handed forms enantiomers. A perfectly balanced 50/50 mix of the two enantiomers is called a “racemic mixture”, and that’s what you’ll get if you make such a compound from a nonchiral source without any chiral reagents involved.

Biomolecules like proteins and carbohydrates are chiral, and so are many drugs. And a chiral drug will almost invariably act differently according to which enantiomer you take: one enantiomer of ibuprofen will relieve your headache, while the other will do nothing for it. One enantiomer of methamphetamine is a powerful addictive stimulant, while the other is an over-the-counter nasal decongestant. And so on! Producing pure enantiomers or separating them from racemic mixtures is thus of great interest.

What do you get when you take a racemic mixture and crystallize it? With about 90% of the compounds you try, you’ll make racemic crystals, in which the D- and L-forms are paired up one-to-one. The other ten per cent of compounds crystallize as a mixture of the two separate enantiomers, which is famously how Pasteur was able to understand the situation with tartaric acid when he examined the mixture of crystals under polarized light. The preference for crystallizing as a racemate is because there are just more ways to do it. Mathematics gives us a hard limit of 230 different space groups that crystals can use (well, in three dimensions, anyway), and racemates can use all of them. But just 65 space groups are chiral – which is why, for example, you will never get a protein to crystallize in a pure cubic form (like table salt). The highly symmetric cubic space group simply can’t accommodate a chiral packing.

But what are these crystals like? There’s an observation called “Wallach’s Rule” (although it probably wasn’t Wallach who did the work on it!) that the density of crystalline racemate is higher than the density of the crystals of the pure enantiomers. (This can also be a consequence of having more space groups to work with, giving more possibilities for denser packing). That rule-of-thumb holds a lot of the time, although there are plenty of exceptions. And those exceptions (denser chiral crystals) suggest a rather odd way to make pure enantiomers. It was first proposed in the 1980s, and has been re-investigated here by a group from Adam Mickiewicz University in Poznan.

Think about what it might be. . .if a particular crystalline form is denser, its formation should be more favored at higher pressure. They tried this out with crystals of sodium tartrate monohydrate, which is a well-known exception to Wallach’s rule. Running X-ray crystallography experiments under pressure confirmed that the enantiomeric crystals remain denser than the racemic crystals all the way up the 4.7 GPa, but to the authors’ surprise, those racemic crystals persisted in being more stable at those pressures, too. A close study of how the compound crystallizes inside the high-pressure diamond anvil cell revealed some odd behavior.

The racemic crystals can come in two polymorphs, alpha (monoclinic) and beta (triclinic), but both of these are still less dense than the enantiomeric crystals (in a orthorhombic space group). No matter how high the pressure (up to >4 GPa), though, no enantiomorph crystals ever emerged from the anvil cell – just racemic crystals, over and over (sometimes alpha, sometimes beta – the densities of those two become the same past about 0.5 GPa). On the face of it, this doesn’t seem like it should be happening.

But a close look at the crystals gave the answer. There aren’t any significant differences in the amount of disorder among the three kinds of crystal, nor in the amplitudes of the thermal vibrations of the atoms, so that tells you that the entropy term in the Gibbs free energy isn’t the source of the difference. That leaves you with enthalpy, the internal energy differences among the crystal forms, and two big contributions to that are the energy differences between the individual conformer states, and the differences between the Coulombic (charged) interactions between the tartrate anion and the sodium counterion. And as it turns out, both of those are much more favorable for the racemate crystals. The conformer differences favor the racemate form even more as the pressure goes up, while the Coulombic differences favor it slightly less under those conditions, but overall either the alpha or beta polymorphs win out at every pressure over the enantiomeric form.

In total, the racemate crystals involve the tartrate molecules fitting into conformers that make better hydrogen bonds with their neighbors, but these end up needing more space between the tartrates and water molecules than do the weaker H-bonds in the enantiomer crystals. As the authors note, the same effect is seen in water ice, where the ordered H-bond arrangement makes ice crystals less dense than liquid water. All in all, then, even though sodium tartrate monohydrate is a firm exception to Wallach’s rule, it was actually a poor candidate (in fact, an impossible one) to make this enantiomeric pressure crystallization actually work.

That doesn’t mean that it never can – the known examples of racemic crystals forming to greater or lesser extents with changes in temperature with some substances show you that such thermodynamic factors can have the influence that you’d need. But recent examples of high-pressure crystallization of some other compounds leading to lower-density crystals are a warning that you can’t take anything for granted, either. If this is going to work in a useful manner, it’s going to have to be on just the right system! And this wasn’t it. . .