Self-interaction correction in density functional theory is relaxed in transition metals, in the study

Density-Sensory Theory (DFT) is a fundamental tool in modern physics, chemistry and engineering used to explore the behavior of electrons. It is essential for modeling systems with many electrons, but suffers from a well-known defect called self-interaction errors. Recent research has identified new areas where corrections for this error collapse.

The research team will be accompanied by Professor J Karl Johnson of the University of Pittsburgh and his graduate student Priyanka Bholanath Shukla, graduate student Rohan Maniar of Tulane University, and Professor Koblar Alan Jackson of Michigan Central University.

This study, which strengthens DFT and has practical impacts on areas such as catalytic conversion, is published in the Proceedings of the National Academy of Sciences

Since its inception in the 1970s, DFT has been an incomplete but essential tool for scientists. “This theory has improved over the years, but there are some flaws that many researchers overlook,” said Shukla, Ph.D. Chemistry and Petroleum Engineering student at Pitt’s Swanson School of Engineering. “One defect is a self-interaction error that occurs when an electron interacts with itself.”

Professor John likens self-interaction errors to billiards. The electrons in the material should work somewhat like a billiard ball. The movement of one ball should only change due to interaction and collision with the other ball. Self-interaction errors are like billiard balls that collide with itself.

DFTs create problems because DFTs believe that electrons are interacting with another electron that is actually itself. This error can create incorrect modeling. To correct the error, dew with fellow theoretical physicist Alex Zunger developed computational corrections in 1981.

This advancement has improved DFT, but as Johnson said, self-interaction correction (sic) can “make things wrong.”

Perdew and fellow researchers developed the Flosic (Fermi-Löwdin Orbital Self-Interaction Correction) Center. Scholars from five universities are working to identify SIC problems and develop solutions to improve DFT. For the past eight years, Johnson of Pitt has been part of this team and in 2021 he invited Shukla.

A new approach to finding transition metal imbalances.

Recent research in DFT and SICs focuses on transition metals, which are essential for the development of catalysts, electronic equipment, and new materials. Specifically, the researchers looked at how DFT handles electrons of different types, electrons in the outermost “S” orbitals, and more closely coupled “D” orbitals of metals such as chromium, copper and cobalt.

A well-known problem with DFTs is the imbalance of SD energy. This is the relative error that DFT makes for with respect to the energy of D electrons when compared to S electrons. DFTs must provide a balanced description of S and D electrons to accurately describe the energy of transition metals.

Previous methods for measuring this imbalance rely on the calculation of excited states outside the formal region of the DFT, and therefore are problematic. However, this study introduced a new method to assess this imbalance using ionization energy (the energy required to remove electrons from atoms).

Through computational studies conducted in part at the University of Pittsburgh research computing and data center, the team discovered that Perdew-Zunger’s self-interaction correction method struggles to find the correct energy balance of S and D electrons. They found that local scaling of corrections provides a better balance by reducing corrections for areas of spatial where they can be predicted to require little or no correction.

This study opens ways to identify obstacles to existing SIC methods and refine DFTs. “Transition metals are essential to our lives, and as we increase the accuracy of modeling through density functional theory, we can improve our catalysts. We can design better catalysts,” Johnson said. “In our world, we rely heavily on catalysis. To uncover and correct these defects has a real impact on everything from the food we eat to the techniques we use every day.”