### Aditi Krishnapriyan

Stanford University

If earning a doctoral degree is like running a marathon, Aditi Krishnapriyan is equipped to finish the race.

Krishnapriyan, a Department of Energy Computational Science Graduate Fellowship (DOE CSGF) recipient, was briefly on the track and cross-country team as an undergraduate at the University of California, Santa Barbara. “I will totally admit that, compared to some of the people who were on the team, I was nothing special,” Krishnapriyan laughs. Yet the hours she’s spent testing her physical boundaries provided lessons she’s relied on since starting a Ph.D. in condensed matter physics and materials science at Stanford University.

“Once you really push yourself in one area, it makes you realize you can do it in other areas,” says Krishnapriyan, who still runs as a hobby.

Working with advisor Evan Reed, Krishnapriyan is pushing computation’s limits in capturing how atoms behave in two-dimensional materials – sheets only one or two atoms thick. Graphene, for example, is a single layer of interlinked carbon atoms. The materials often possess unusual and desirable properties, like high strength or the ability to conduct electricity, making them useful for a variety of applications.

Krishnapriyan focuses on 2-D materials, such as molybdenum disulfide, that can change how their atoms are arranged. These phase changes also can alter a material’s properties, such as going from a metal to a semiconductor. She’s developing algorithms to illuminate these structural changes and their impact. “If we can describe how this phase change happens and the kinetics of it, then hopefully we can use that to find out all these new things about the systems” of atoms. Meanwhile, “there’s also a bunch of interesting mathematical properties about these systems” that could apply to other 2-D materials, “so the goal is to have a transferrable model.”

Algorithms must track what happens at the interface of the two phases, particularly the energy associated with the transformation as electrons form new bonds. “If you can solve for all of the interface energies at the phase boundary, you can describe how this phase change might happen,” Krishnapriyan says, including possible new configurations the atoms will settle into.

However, no one had known how to solve directly for these individual interface energies. Krishnapriyan and her colleagues used mathematical techniques to solve the problem and developed a generalized method that can be applied to a variety of similar systems. The method helps determine how atoms rearrange into a new alignment and their optimal interface configurations.

Krishnapriyan is augmenting her methods with research begun during her summer 2016 Los Alamos National Laboratory practicum. With Marc Cawkwell, she focused on two methods to calculate atomic interactions: density functional theory (DFT) and density functional tight-binding (DFTB) theory.

DFT maps the demanding interacting electron problem to an easier, non-interacting problem. It’s become the go-to method for calculating atomic interactions because it accounts for quantum mechanical conditions in which electrons behave as both particles and waves. It’s an ab initio method: present conditions or experimental data don’t inform the simulations.

DFT is accurate but slow, Krishnapriyan says. DFTB is a similar, quantum approximation method that is faster but less accurate. It relies on input parameters to calculate the interatomic potentials – the energy interactions between atoms as they form bonds.

Krishnapriyan and her colleagues are developing algorithms based on a statistical framework that trains on data from DFT energy calculations and uses that training to optimize DFTB parameters. “Once you have a decent model to do that, you copy that model onto a new data test set,” she says. “You’ll hopefully have much lower errors on your new data set,” enabling fast, more accurate DFTB calculations.

Krishnapriyan has applied the technique to simple systems and plans to use it for the 2-D materials she concentrates on in her thesis research. She returned to Los Alamos in summer 2017 to continue the collaboration. “The nice thing is I have some domain knowledge I can put into this to make sure we get all the physics right while also using statistics and computer science to improve performance.”

Krishnapriyan expects to graduate in two to three years and hopes to continue working in research, perhaps at a national laboratory or in industry. Beyond that, it’s unclear where her skills – and her running shoes – will take her.