How would you explain your work to someone who has no knowledge of chemistry?
Just like you can build many different structures from a pile of identical Legos, molecules can pack together in many different ways to form different crystal structures. These different structures can exhibit very different properties (colour, solubility, melting point, etc.) that can impact whether the pill you take dissolves in your stomach to give the proper dose of medicine or whether your chocolate tastes fresh. Understanding what crystal structures, or polymorphs, can occur and the conditions they are stable at is very important for designing crystals with desirable properties or avoiding problems arising from the unexpected appearance of a new, undesirable form once a product is on the market (see specific examples in question 2 below).
Exhaustively searching for crystal forms experimentally is difficult and time-consuming. W.C. McCrone wrote in 1965 that "The number of forms known for each compound is proportional to the time and money spent in research on that compound." Computational chemistry can help this search by predicting the possible crystal forms and their properties from the basic laws of physics and chemistry, without experimental input. However, one challenge is that while crystal structure prediction has been successful at enumerating and ranking potential structures, it does not provide information about the conditions under which those forms might actually occur in the lab/real world.
Our paper has taken the next major step: predicting the temperatures and pressures under which each polymorph of methanol will be stable, mapping out the so-called phase diagram for the α, β, and γ phases with unprecedented accuracy of 0.5 kJ/mol. That accuracy translates to predicting the phase transition temperatures and pressures to within 20–50 degrees C and a few tenths of a gigapascal. Errors of up to hundreds of degrees Celsius and many gigapascals were common in earlier studies. We achieved this starting only from the knowledge of the molecular packing from experimental crystal structures.
Successful phase diagram prediction means that if theory predicts a new structure, we can then inform our experimental colleagues how likely this new polymorph is to interfere with their desired one. In other cases, we might predict a previously unknown polymorph with particularly desirable properties, and we could tell the experimentalists the “where to look" if they want to make it –at what temperatures and pressures it would be most likely to be stable.
It’s only a side note in the paper, but we did something like this regarding a candidate structure that had recently been proposed for a newly discovered methanol polymorph. A 2013 experimental paper found evidence for a new “δ phase” whose structure remains unknown. A subsequent computational study proposed a structure that the authors suggested could be a candidate for the unknown δ polymorph. However, our calculations suggest that while the phase the earlier computational study predicted might exist under certain experimental conditions, it seems unlikely to occur under the temperatures and pressures at which the δ phase is observed experimentally. This suggests that more work will be needed to figure out what the structure of the δ phase is.
Achieving this successful phase diagram prediction required new computational techniques that we and others have been developing over the past decade. Half a kilojoule accuracy is very tough for computational chemistry (see answer to Q4 for more details). For comparison, a half kilojoule is only about enough energy to heat a 100 mL of water by 1 degree Celsius. But this high level of accuracy proves essential to predict the phase diagram correctly. Striving for that level of accuracy with straightforward brute force computational approaches would be utterly infeasible with current computational resources. Instead, we'fragment' the crystal into many smaller pieces. Each fragment (a single methanol molecule) and the interactions between pairs of fragments at a time can be treated much more accurately, and we can use more approximate strategies to handle the 'cooperative' contributions arising from beyond-pairwise interactions. We also had to account for how the atoms in the crystal vibrate, and how the crystal structure expands upon heating.
Methanol’s polymorphs are not of major commercial interest, but methanol provides a really good proving ground for the theoretical techniques. Methanol's seeming simplicity is deceiving. It actually exhibits many of the complexities found in crystals of more chemically relevant species: it has multiple polymorphs over a relatively narrow range of temperatures and pressures, one of the crystal forms exhibits disorder, and the particularly strong cooperative interactions between molecules in the crystal are challenging to model. At the same time, it is small enough that we could afford to perform very high-level calculations, both for the sake of getting the right answer and for benchmarking more approximate models to understand what model features are most important.
Why should an average person care about this research? What are some potential real-life applications?
The most important application of this research is the prediction of pharmaceutical polymorphs. There are numerous examples where the unexpected appearance of new polymorphs with undesirable properties have force drug recalls, including for the HIV drug Ritonavir in 1998 and for Neupro, a skin patch medicine for Parkinsons' disease, a decade later. In both cases, the formation of low-solubility polymorphs reduced the bioavailability of the drug molecules.
Pharmaceutical polymorphs are also considered intellectual property and can be patented. A few years ago, generic pharmaceutical manufacturer Natco discovered a new commercially viable polymorph of Celgene’s blockbuster multiple myeloma drug Revlimid ($8.2 billion USD in sales in 2017) which Celgene had missed. This would allow Natco to bring a generic version of the drug to market several years sooner than otherwise anticipated, potentially disrupting Celgene’s business plans. Lawsuits ensued, and the two companies settled in 2015.
Pharmaceutical companies expend significant time and money searching for polymorphs, since knowledge of the potential crystal forms is required for regulatory approval and to protect intellectual property. However, it is hard to rule out the potential for other, unknown forms that have not yet been discovered. Crystal structure prediction is increasingly used to help screen for potential polymorphs, identifying structures that might have been missed in the experiments and mitigating the risks associated with the unexpected discovery of new forms later in a product's life cycle. For example, computation helped identify a new polymorph for the pharmaceutical compound Dalcetrapib during the polymorph screening stage, before it went to market (DOI: 10.1038/ncomms8793). The predicted form was subsequently confirmed experimentally, and it turned out to be one that was unlikely to occur under normal conditions.
The context of our research is broader than just pharmaceuticals, however, extending also to the development of (i) new organic semi-conductor materials (flexible electronics, solar cells, etc), (ii) new explosives that are safer and more environmentally friendly, (iii) better-performing agrochemicals, (iv) improved understanding of common materials at extreme temperatures and pressures (e.g. what happens deep in the earth or in distant cosmic bodies), etc.
The next step in our research is to extend phase diagram predictions to polymorphs of small-molecule pharmaceuticals. Scaling up the calculations from methanol to say a small-molecule pharmaceutical like paracetamol (a.k.a. acetaminophen) or aspirin will require further approximations to make them computationally practical. Fortunately, some of our other recent research has figured out some new strategies that will make such calculations more feasible. We are optimistic that we can make meaningful progress on predicting molecular crystal phase diagrams for molecules with “real-world” interest over the next few years.
Why did you choose to research this topic?
Broadly speaking, I have been interested in accurate but computationally affordable electronic structure methods for years, and molecular crystals provide a really challenging proving ground for these techniques. Crystal packing is governed by a complex interplay among many different types of physical interactions, and even seemingly subtle problems in the models can lead to completely erroneous results. Only in the past decade have quantum mechanical techniques been developed that are sufficiently accurate and computationally feasible that we can make model these materials correctly.
After several years of focusing on the theoretical questions, I happened to read science fiction author Robert Heinlein.’s 1950 essay "Where To?" discussing what the year 2000 would be like. The following passage caught my attention:
"Chemistry is not a discipline today; it is a jungle. We know that chemical behavior depends on the number of orbital electrons in an atom and that physical and chemical properties follow the pattern called the Periodic Table. We don't know much else, save by cut-and-try, despite the great importance of the chemical industry. When chemistry becomes a discipline, mathematical chemists will design new materials, predict their properties, and tell engineers how to make them--without entering the laboratory. We've got a long way to go on that one."
These comments were incredibly prescient, and 70 years later, computational chemistry has finally reached the point where Heinlein's first two goals have become pretty routine and are having a large impact on many problems. In the context of molecular crystal polymorphism, recent years have seen dramatic improvements in the rate of successful crystal structure predictions in the Blind Tests of Crystal Structure prediction run every few years by the Cambridge Crystallographic Data Center. There are increasing examples in the literature where crystal structures that were first predicted have subsequently been discovered experimentally,* and various small companies like Avant-garde and XtalPi** are commercializing crystal structure prediction tools.
But achieving the third goal, the ability to not only predict possible structures and their properties, but to tell experimental researchers how to make them, has mostly eluded us and would be absolutely transformative if we could do it. Too often, actually realizing the structures predicted by computation experimentally proves hard or impossible.
Going beyond enumerating potential structures to actually predicting the temperature & pressure conditions under which they are stable was a way we could start trying to address that problem. For several years, I wanted to try to predict phase diagrams, but it was always such a daunting task that my group didn't make much progress on it for a while.
Then in 2016-17, Dr. Ctirad Červinka, a very talented Fulbright Scholar from the University of Chemistry and Technology in Prague, CZ, spent nine months in my research group. He had long been interested in first-principles quantum mechanical computations and modeling how interactions at the microscopic level translate into macroscopic physical and chemical properties. Ctirad brought a sharp understanding of the key thermodynamics parts of the calculations and critical assessment of the uncertainties in the relevant experimental data that I lacked, which was indispensable to the research. Combining Ctirad’s expertise and motivation with the computational techniques my group had been developing finally made this research possible. This research was an example of how international collaboration can really benefit science.
* I wrote a Nature Materials commentary about one such case 2017 that might give additional context if you want more info. DOI: 10.1038/nmat4913
** Disclosure: Xtalpi was co-founded by my former postdoc Shuhao Wen. I have no financial relationship with the company.
What is the most exciting thing about your results?
It represents a major step forward toward achieving Heinlein's third goal: not only can we predict what crystal structures might occur, but we can now predict the conditions under which those structures will be thermodynamically stable.
It was also hard to achieve. Computational chemists often strive for "chemical accuracy" of ~1 kcal/mol (about 4 kJ/mol) when modeling chemical reactions. To model the energy differences between crystal polymorphs and phase diagrams near ambient temperatures and pressures, that's not nearly accurate enough. Rather, one needs sub-kJ/mol accuracy in the relative free energy differences. Garnet Chan's group (currently at Caltech) managed to do that for the benzene crystal lattice energy at 0 K in 2014 (Science, DOI: 10.1126/science.1254419), but doing so for phase diagrams and free energies a real-world temperatures and pressures is even harder. It requires not only getting the lattice energy right in the absence of temperature, but also modeling how the atoms vibrate thermally and how the crystal volume expands with temperature and shrinks with pressure.
Our study has pushed the limits of what was previously considered feasible for quantum chemistry. Predicting polymorph phase diagrams near ambient temperatures and pressures has long been considered "too difficult." We hope the success of this study will change the minds of people working in this field, and will further convince experimentalists that theory can really make a useful contribution to this problem. The analysis included in the paper highlights the key ingredients behind the success. That will hopefully focus attention on how we can make further approximations that will make such predictions feasible for much larger molecular crystals, such as those for pharmaceuticals. Our results also reflect the tremendous advances that both the quantum chemistry and computational resources have undergone over the past 10-20 years.
Someday scientists would like to be able to go even further, and be able to predict the kinetic crystallization conditions (solvents, temperatures, etc) that could be used to actually grow those crystals, but that's an even harder problem that will require accurate models for crystal nucleation and growth and tools for modeling the energetics accurately with much lower computational cost than what we used. There has been progress in that direction from several research groups, but much work remains to be done.