In the old days, in the really old days, the task of designing materials was laborious. Researchers, for more than 1,000 years, attempted to produce gold by combining elements such as lead, mercury and sulfur, mixed in what they hoped were the right proportions. Even famous scientists like Tycho Brahe, Robert Boyle, and Isaac Newton tried their hand at the fruitless endeavor we call alchemy.
Of course, materials science has come a long way. For the past 150 years, researchers have been able to turn to the periodic table of elements, which tells them that different elements have different properties and that one cannot magically transform into another. Furthermore, in the last decade, machine learning tools have greatly increased our ability to determine the structure and physical properties of various molecules and substances. New research by a group led by Ju Li, Tokyo Electric Power Company professor of nuclear engineering at MIT and professor of materials science and engineering, offers the promise of a giant leap in capabilities that can facilitate material design. The results of their research are presented in a December 2024 issue of Computational Nature Science.
Currently, most machine learning models used to characterize molecular systems are based on density functional theory (DFT), which offers a quantum mechanical approach to determining the total energy of a molecule or crystal. observing the distribution of electron density. – which is basically the average number of electrons located in a unit volume around each given point in space near the molecule. (Walter Kohn, who co-invented this theory 60 years ago, received the Nobel Prize in Chemistry for it in 1998.) While the method has been very successful, it has some drawbacks, according to Li: “First, the precision is not uniformly brilliant. And secondly, it only tells you one thing: the lowest total energy of the molecular system.”
“Couples therapy” to the rescue
His team now relies on a different computational chemistry technique, also derived from quantum mechanics, known as coupled cluster theory or CCSD(T). “This is the gold standard of quantum chemistry,” says Li. The results of CCSD(T) calculations are much more accurate than those obtained with DFT calculations and can be as reliable as those currently obtained through experiments. The problem is that performing these calculations on a computer is very slow, he says, “and the scaling is bad: if you double the number of electrons in the system, the calculations become 100 times more expensive.” For that reason, CCSD(T) calculations have typically been limited to molecules with a small number of atoms, on the order of 10. Anything much beyond that would simply take too long.
That's where machine learning comes into play. CCSD(T) calculations are first performed on conventional computers and then the results are used to train a neural network with a novel architecture specially designed by Li and his colleagues. After training, the neural network can perform these same calculations much faster by taking advantage of approximation techniques. What's more, their neural network model can extract much more information about a molecule than just its energy. “In previous work, people have used multiple different models to evaluate different properties,” says Hao Tang, a doctoral student in materials science and engineering at MIT. “Here we use a single model to evaluate all these properties, so we call it a 'multitasking' approach.”
The “multitask electronic Hamiltonian network,” or MEHnet, sheds light on a number of electronic properties, such as dipole and quadrupole moments, electronic polarizability, and optical excitation gap: the amount of energy required to take an electron from the ground state to lowest excited state. “The excitation gap affects the optical properties of materials,” explains Tang, “because it determines the frequency of light that can be absorbed by a molecule.” Another advantage of their model trained with CCSD is that it can reveal properties of not only the ground states, but also the excited states. The model can also predict the infrared absorption spectrum of a molecule in relation to its vibrational properties, where the vibrations of atoms within a molecule couple with each other, leading to various collective behaviors.
The robustness of their approach owes much to the architecture of the network. Building on the work of MIT assistant professor Tess SmithThe team is using a so-called E(3) equivalent graph neural network, Tang says, “in which the nodes represent atoms and the edges connecting the nodes represent the bonds between the atoms. “We also use custom algorithms that incorporate principles from physics (related to how people calculate molecular properties in quantum mechanics) directly into our model.”
Tests, 1, 2 3
When tested in their analysis of known hydrocarbon molecules, the model of Li et al. outperformed its DFT counterparts and closely agreed with experimental results taken from published literature.
Qiang Zhu, a materials discovery specialist at the University of North Carolina at Charlotte (who was not involved in this study), is impressed by what has been accomplished so far. “Their method enables efficient training with a small data set, while achieving superior accuracy and computational efficiency compared to existing models,” he says. “This is exciting work that illustrates the powerful synergy between computational chemistry and deep learning, and offers new ideas for developing more accurate and scalable electronic structure methods.”
The MIT-based group first applied their model to small, nonmetallic elements (hydrogen, carbon, nitrogen, oxygen and fluorine, from which organic compounds can form) and has since moved on to examine heavier elements: silicon, phosphorus, sulfur, chlorine and even platinum. After training on small molecules, the model can be generalized to increasingly larger molecules. “Previously, most calculations were limited to analyzing hundreds of atoms with DFT and only tens of atoms with CCSD(T) calculations,” says Li. “Now we're talking about handling thousands of atoms and, eventually, maybe tens of thousands.”
For now, researchers are still evaluating known molecules, but the model can be used to characterize molecules that have not been seen before, as well as to predict the properties of hypothetical materials consisting of different types of molecules. “The idea is to use our theoretical tools to select promising candidates, satisfying a particular set of criteria, before suggesting them to an experimenter for review,” Tang says.
It's about the applications
Looking ahead, Zhu is optimistic about potential applications. “This approach has potential for high-throughput molecular screening,” he says. “That's a task where achieving chemical precision may be essential to identifying new molecules and materials with desirable properties.”
Once they demonstrate the ability to analyze large molecules with perhaps tens of thousands of atoms, Li says, “we should be able to invent new polymers or materials” that could be used in drug design or semiconductor devices. Examination of heavier transition metal elements could lead to the arrival of new battery materials, an area that is currently in great need.
The future, as Li sees it, is wide open. “It's not just one area anymore,” he says. “Our ambition, ultimately, is to cover the entire periodic table with CCSD(T) level precision, but at a lower computational cost than DFT. This should allow us to solve a wide range of problems in chemistry, biology and materials science. “It is difficult to know, at present, how wide that range could be.”
This work was supported by the Honda Research Institute. Hao Tang acknowledges the support of the Mathworks Engineering Fellowship. The calculations in this work were performed, in part, on the Matlantis high-speed universal atomistic simulator, the Texas Advanced Computing Center, the MIT SuperCloud, and the National Energy Research Scientific Computing.
