Simulations of chromium molecules get a faster, sharper method

A chromium atom is small, and its electrons are packed so tightly into compact orbitals that, in Kay Carter-Fenk's words, they behave like residents of “tiny apartments.” For chemists trying to predict how such atoms bond inside a molecule, that crowding has long been the problem. Chromium is an essential ingredient of stainless steel, and it is also among the metals that standard simulation methods handle worst.

Two families of methods do most of the work. Coupled cluster theory, or CC, starts from each electron moving in the average field of all the others, then adds back, step by step, the energy of pairs of electrons interacting, then groups of three. For many molecules it is the “gold standard” of quantum chemistry, but its computing cost rises steeply as molecules grow. Density functional theory, or DFT, starts from a simpler picture of the overall electron density and is far cheaper, but it relies on approximations and parameters that are not fully settled, so its results can be off. Both perform poorly with abundant transition metals such as iron, cobalt and chromium.

John Keith and Barbaro Zulueta were looking for ways to model chromium in order to make better stainless steels for the Navy. Reading the literature, they found that DFT was sometimes, but not always, a better starting point than the one normally used with CC for these metals. Other researchers had reported this without a clear explanation. Carter-Fenk's group, which works on strongly correlated electrons, suggested that the cause lay in the underlying mathematics rather than in the orbitals themselves. The team then built a diagnostic that measures the gap between the two starting densities and turns it into one number. “The magnitude of that number can indicate whether the DFT starting point is beneficial or not,” said first author Abdulrahman Zamani.

With that rule in hand, the researchers reported that CC could reach chemical accuracy for many hard combinations of atoms, with results close to those of weeks or months of supercomputing, obtained in minutes to hours. The paper's title, “Improving coupled cluster theory for strongly correlated molecules with Kohn-Sham density encoding,” describes the method; the press material does not report tests on a wider set of molecules beyond those in the study.

For now, the most direct beneficiary is the machine-learning community. Models that predict molecular behaviour are usually trained on DFT data, and the team argues that those data are least reliable exactly where chromium is involved. A more accurate reference calculation gives those models better material to learn from. The longer-term gain, according to Keith, is a route to metals such as stainless steel and heavy lanthanides and actinides. Those applications, and the new materials and catalysts they might lead to, remain goals: the study is a computational result, and no new alloy or catalyst has been made from it.