Researchers have created a new mathematical technique that predicts crystal structures quickly—within hours on a regular laptop—an improvement over the previous method, which relied on supercomputers and could take weeks or even months. This significant development is essential for the creation of various medications and electronic devices. The research findings were published in the journal Nature Communications.
Organic molecular crystals play a crucial role in multiple sectors, including pharmaceuticals, agriculture, electronics, and explosives. These crystals are key components of many products, ranging from over-the-counter and prescription medications to insect repellents, explosives like TNT, semiconductors, and the technology in screens and smartphones.
Despite their widespread use, predicting the three-dimensional structures of these molecular crystals can be quite difficult, especially when certain compounds can crystallize into different forms. A notable instance from the late 1990s showed the importance of crystal structure prediction: the HIV medication ritonavir unexpectedly changed from its known crystal form to a more stable but previously unknown one, which led to its ineffectiveness, forcing the drug off the market until a new formulation emerged.
Most existing methods for predicting crystal structures rely on physics-based techniques, which often have limitations; they can introduce biases and errors or may suggest more forms than what is actually observed in experimental settings. Additionally, these methods are computationally intensive and can take a considerable amount of time, from weeks to months, based on the complexity of the molecules involved.
Mark Tuckerman, a professor of chemistry and mathematics at NYU and senior author of the study, noted, “Current physics-based techniques are not only expensive and time-consuming but may also produce results that are limited by the accuracy of the physics used, which has prompted the need for computational methods that can mitigate these issues.”
To tackle this problem, Tuckerman and NYU postdoctoral researcher Nikolaos Galanakis have developed a mathematical framework called “Crystal Math.” This method predicts crystal structures governed by mathematical rules regarding how molecules are organized in crystals, alongside a few simple physical descriptors of the crystals’ environments. They identify 13 essential parameters linked to the arrangement of molecules—like their locations and orientations—and other geometric factors that help define the shape of each molecule within the crystal.
The researchers confirmed the rules of Crystal Math by utilizing the Cambridge Crystal Data Centre, which hosts a vast collection of known organic molecular crystal structures. They tested their mathematical rules against these structures to establish principles that were likely to hold true, and then translated these principles into equations capable of predicting the structures of molecular crystals not recorded in the database. They used well-known pharmaceuticals like aspirin and paracetamol as basic test cases.
Following the formulation of their equations, the researchers further applied Crystal Math to more complex molecular crystals that feature highly flexible molecules—structures not present in the database. Their predictions matched experimental results with a high degree of accuracy.
Tuckerman remarked, “Our equations seem to only yield experimentally realistic crystal structures, addressing the issue found in physics-based approaches, which often overshoot the number of potential structures, some of which may never be discovered through experimentation.”
A key advantage is that these solutions can now be reached in just a few hours using a standard laptop, unlike the lengthy processing times and advanced computing resources required by physics-based methods.
“We can now achieve solutions overnight instead of having to wait weeks or months, as solving the equations is quite rapid,” Tuckerman added.
Crystal Math is the result of seven years of dedication from Tuckerman and Galanakis to find a mathematical answer to this complex challenge. Tuckerman found inspiration in a 1967 paper by Swiss mathematician and crystallographer Johann Jakob Burckhardt, who proposed that mathematical methods could be utilized to predict crystal structures but did not provide a solution.
More than 55 years after Burckhardt’s suggestion, Tuckerman and Galanakis’s math-based method has attracted attention from the pharmaceutical industry and shows promise for exploring undiscovered compounds and predicting their crystal structures.
Tuckerman explained, “The ability to create new products is fundamentally dependent on understanding whether the compounds can crystallize, how many different forms they might have, and the stability of those forms. Our mathematical approach allows for the testing of numerous compounds for their crystallization potential and assesses the viability of these structures for market readiness.”
This research was funded by the National Science Foundation (CHE-1955381 and DMR-2118890).
