Simple Solutions for Quantum Chemistry

In the early 2000s, Columbia professor Louis Brus, who won a 2023 Nobel prize for chemistry, observed that when solutions containing nanoparticles evaporated, they left behind thin films with curious patterns. Some were stripey, some splotched; others looked almost like the coat of a giraffe, recalls theoretical chemist David Reichman, who was a young professor at Harvard when he learned about Brus’ puzzling patterns. 

With colleagues Eran Rabani and Phillip Geissler, Reichman solved the puzzle: The patterns depend on the ratio of nanoparticles and how quickly the sample is dried. “It was a very, very simple model, but so beautiful. It described everything perfectly,” he said. 

Two decades later, Reichman, now the Centennial Professor of Chemistry at Columbia, still enjoys finding simplicity among his experimental colleagues' messy findings. In recognition of his work developing theoretical explanations for experimental observations, Reichman was this spring elected to the National Academy of Sciences. 

In particular, Reichman and his research group develop computational methods to solve quantum mechanical problems in chemistry and materials science. Whether one realizes it or not, this often counterintuitive collection of physics principles underpins all aspects of science. “Molecules wouldn’t exist without quantum mechanics. Electrostatically, it’s impossible,” Reichman says.

Reichman has been interested in the boundaries between chemistry and physics since he was an undergraduate at the University of Chicago, where he studied physics. He switched to chemistry for graduate school at MIT, though he took mostly physics courses. “I am a chemist, but I feel comfortable moving back and forth,” Reichman. “I can make very simple models, like a physicist, while understanding how chemical details can make a big difference.”

Molecules, materials, and the chemical reactions that shape them all come down to chemical bonds, which are determined by how electrons are shared between atoms. Each electron is governed by the infamous Schrödinger Equation, which describes the many possible locations and energies of these particles. The equation becomes harder and harder to solve as the number of electrons increases. And there can be a lot of electrons to keep track of—tens or even hundreds, depending on the particular elements and how many of each there are in a given sample. 

With solutions to the Schrödinger equation hard to come by, researchers are instead working towards making more accurate approximations. Reichman uses tools borrowed from other disciplines, like Monte Carlo simulations and neural networks, to make useful predictions and models.

One potential area where these mathematical approximations could be applied is in battery design, the focus of the Columbia Center for Computational Electrochemistry (CCCE). Reichman and collaborators in the chemistry department and at the software company Schrodinger (founded by Richard Friesner, Columbia’s Schweitzer Professor of Chemistry) are working to reveal the complicated chemical reactions inside lithium-ion batteries that determine their efficiencies and lifespans. “This is really a frontier application for translating our quantum mechanical knowledge,” he says. “Understanding how to solve the Schrödinger equation with high accuracy, which we do pretty much as well or even better than anyone else, is crucial.”

The CCCE team is made up of fellow theorists, but Reichman also enjoys running into his experimental and engineering colleagues. He notes recent work with chemist Milan Delor explaining the ultrafast movement of quantum quasiparticles called polaritons and with physicist Abhay Pasupathy on electron distribution patterns in a new material created by chemist Xavier Roy came from spontaneous conversations around campus. 

“There’s this wealth of tremendous experimental science in physics, chemistry, and engineering at Columbia, and what has always been exciting to me here is just talking to those colleagues about their interesting materials and experiments and the things they don’t understand,” he says. From there, he’s off to his blackboard and the world of quantum mechanics to explain their latest observations.