Transforming Equations into Materials
Imagine how handy it would be to have a magic crystal ball to answer any questions we might have. With the proper equations, we can similarly use computers to predict the properties of any given molecule or solid—existing or yet to be prepared. Researchers at two Energy Frontier Research Centers (EFRCs), the Center for the Computational Design of Functional Layered Materials (CCDM) and the Inorganometallic Catalyst Design Center (ICDC), have made enormous progress in developing new and efficient ways to accurately describe molecules and materials.
But why should we do math instead of simply going to the laboratory? Performing fewer experiments positively impacts the economy, by saving costs of expensive chemicals and instrumentation, the environment, by avoiding generating toxic waste every day, and safety, by minimizing exposure to dangerous substances. Computations also decrease the time involved by suggesting the most likely candidates to test experimentally. With these goals in mind, the use of computers becomes quite appealing to explore new materials for energy-related challenges.
Daily, fast, trustworthy (DFT). Quantum mechanics is the part of physics that describes matter at the atomic level. This field has developed very accurate and detailed ways to deal with atoms and molecules. However, they are tremendously costly and impossible to use for screening materials. On the other hand, density functional theory (DFT) significantly simplifies the complex system of equations, while maintaining physical accuracy! For example, “sticking” gases on metal surfaces are key processes during many chemical transformations in industry. The simulation of these phenomena may take several hours with DFT, but eons with more-detailed techniques—and we will get results of similar accuracy, especially with regards to trends. That is the beauty of DFT.
Forging new tools. In 1965, Walter Kohn and Lu Jeu Sham showed that we could obtain exact energies with DFT if we knew one key term, the exchange-correlation functional. This term is a relatively small portion of the total energy, but it’s nature’s glue—it binds one atom to another. But wait, don’t break out the champagne just yet—this mathematical expression is in essence unknowable. Researchers around the globe are developing equations to approach this term.
As one of those leading scientists, Don Truhlar says, “density functional theory is the most affordable way to get useful accuracy, and in fact in many cases of complex materials research, it is the only way to get reliable results for practical problems.” He continues, “the development of accurate density functionals has already revolutionized the practice of chemistry, and with the recent progress in the field I expect the revolution to be even more dramatic in the future.”
Getting everything at once. Each approximation, a.k.a. functional, is designed with different ingredients. As such, some flavors work very well for specific problems, but behave poorly for others. To design and predict new materials, these approximation methods must correctly model more than one property at a time. Despite the hard road, recent studies by scientists at EFRCs show promising results.
In this quest of searching accurate functionals, researchers at CCDM have developed the SCAN, Strongly Constrained and Appropriately Normed. By imposing certain physical constraints—with no input from experiments—they derived a mathematical form that can describe a diverse array of differently bonded molecules and solids.
One apparently simple but tricky system for DFT is the water hexamer. Water is ubiquitous, so we better get it right! Among the different ways we can connect six waters (see prism, cyclic, cage, and book in figure), the prism disposition is the most likely to happen. Water hexamers serve to evaluate the ability of a particular method to deal with weak interactions between molecules. SCAN passes this test with honors, predicting that the prism structure is the most favored.
Moving now to solid materials, another challenging trial is silicon, a celebrity material in electronics. Under great pressure, crystalline silicon transforms from an insulator to a conducting metal. Due to its ability to simultaneously describe very different connections between atoms, SCAN again perfectly captures the characteristics of this transition.
Along similar lines, researchers at ICDC have developed another set of equations called MN15 (Hybrid Meta Nonseparable Gradient Approximation 2015). By careful training against experimental data, they achieved an expression having accuracy for a broad set of chemical systems.
An excellent example to showcase the power of MN15 is photochemistry, that is, chemical transformations promoted by light. These processes are relevant in different areas such as photosynthesis or optical devices. The figure shows a general photochemical process to transform cheap chemicals into high-value products. Before irradiation, we need to calculate structures and energies to break and form chemical bonds. After the system experiences radiation, some electrons get excited and the behavior of molecules changes. An ongoing challenge for DFT is to accurately describe these systems before and after light irradiation, and MN15 appears as the most robust method in both situations. This exceptional performance extends to other properties in molecules, metals, and semiconductors.
From bottom to top, and beyond. The studies described show how rigorous calculations for small models can set the foundations to deal with big challenges. With these improved equations, we will accelerate the computational discovery of new materials for advancing energy technologies. For example, computer-driven research is currently targeting long-lived batteries for laptop computers and other devices and more efficient catalysts for industrial applications. However, how far are we from the exact universal functional, the holy grail of DFT? We may never get there, to be honest, but we may get close enough to warrant having a champagne bottle at hand, just in case.
Sun J, RC Remsing, Y Zhang, Z Sun, A Ruzsinszky, H Peng, Z Yang, A Paul, U Waghmare, X Wu, ML Klein, and JP Perdew. 2016. “Accurate First-Principles Structures and Energies of Diversely Bonded Systems from an Efficient Density Functional.” Nature Chemistry 8:831-836. DOI: 10.1038/nchem.2535
Yu HS, X He, SL Li, and DG Truhlar. 2016. “MN15: A Kohn–Sham Global-Hybrid Exchange–Correlation Density Functional with Broad Accuracy for Multi-Reference and Single-Reference Systems and Noncovalent Interactions.” Chemical Science 7:5032-5051. DOI: 10.1039/C6SC00705H
Sun et al. This research was supported as part of the Center for the Computational Design of Functional Layered Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0012575. Computer equipment in Temple’s High-Performance Computing (HPC) Center was supported by the National Science Foundation (NSF) under major research instrumentation grant no. CNS-09-58854. J.S., R.C.R., Y.Z., Z.S., A.R., and H.P. acknowledge support in the form of computer time from the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science user facility, and the HPC Center of Temple University. X.W. and Y.Z. acknowledge support from the American Chemical Society Petroleum Research Fund (ACS PRF) under grant no. 53482-DNI6.
Yu et al. This research is supported by the U.S. Department of Energy and the Inorganometallic Catalyst Design Center at the University of Minnesota under award DE-SC0012702. H.Y. acknowledges a Doctoral Dissertation Fellowship. S.L.L acknowledges support from the Frieda Martha Kunze Fellowship, University of Minnesota.