A novel strategy for simulating molecules with quantum accuracy moves a step closer to disclosing the equation at the center of a prominent simulation method used in fundamental chemistry and materials science research.
The attempt to comprehend materials and chemical interactions consumes nearly one-third of national lab supercomputer time in the United States. The quantum many-body problem is the gold standard for precision, as it can reveal what is going on at the level of individual electrons. This is the key to chemical and material behavior since electrons are responsible for chemical reactivity and bonding, as well as electrical characteristics. However, quantum many-body computations are so complicated that scientists can only use them to compute atoms and molecules with a small number of electrons at a time.
Density functional theory, or DFT, is simpler since the computational resources required for its computations scale with the number of electrons cubed rather than increasing exponentially with each new electron. Instead of chasing each individual electron, this theory estimates electron concentrations, which indicate where electrons are most likely to be found in space. In this approach, it is possible to imitate the behavior of hundreds of atoms.
A major issue for DFT users is the exchange-correlation functional, which specifies how electrons interact with one another using quantum mechanical laws. So far, researchers have had to settle for approximating the XC functional for their specific application.
We know that there is a universal functional—it makes no difference whether the electrons are in a molecular system, a piece of metal, or a semiconductor. However, we do not know what its shape is, according to Vikram Gavini, a U-M mechanical engineering professor and corresponding author of the work published in Science Advances.
Because DFT is important for future materials as well as fundamental science, the Department of Energy donated cash and supercomputer time to the U-M team in their effort to achieve that universal XC functional.
To tackle the DFT problem, the researchers first studied individual atoms and tiny molecules using quantum many-body theory. Instead of utilizing the approximate XC functional to describe electron behavior in atoms and molecules, they use machine learning to determine which XC functional will describe electron behavior as estimated by quantum many-body theory.
“Many-body theories provide the correct solution for the right reasons, but at an unjustifiable computing expense. Our team has translated many-body results into a simpler, speedier form that preserves the majority of their correctness,” said Paul Zimmerman, a chemistry professor at the University of Michigan who conducted the quantum many-body calculations alongside chemistry Ph.D. student Jeffrey Hatch.
Zimmerman’s group generated a training data set of five atoms and two molecules: lithium, carbon, nitrogen, oxygen, neon, dihydrogen, and lithium hydride. They tried adding fluorine and water, but the XC function did not improve—the researchers feels it was already as excellent as it could be based on data on light atoms and molecules.
However, DFT computations employing that XC functional performed far better than predicted given their level of complexity. DFT accuracy is like a series of rungs on a ladder. In their most basic, first-rung form, electrons are considered as forming a uniform cloud. Gavini’s team employed the second-rung version, which shows the electron cloud changing density as a gradient.
For the third rung, researchers provide additional information about the electrons, such as their kinetic energies. This generally entails introducing simpler versions of the complex many-electron wavefunction, which can better represent what is happening with the electrons. However, by computing a superior XC functional, Gavini’s team was achieving third-tier accuracy.
“The use of an accurate XC functional is as varied as chemistry itself, precisely because it is material agnostic. It’s equally relevant for researchers looking for improved battery materials, those developing novel pharmaceuticals, and those creating quantum computers,” said Bikash Kanungo, U-M assistant research scientist in mechanical engineering and the study’s first author.
Researchers can utilize the XC functional found by the group directly or experiment with the team’s method. For example, Gavini says they began with light atoms and molecules and want to go on to solid materials.
Again, the XC functional is supposed to have a universal form; the difficult part is determining what it is. Will the XC function that his team found work well with solids? Would a new functional computed for solids be more effective? Could they create a combination functional that functioned well with both sets of materials?
Higher accuracies are another area of development the team want to explore. This would imply that instead of looking at electrons collectively as electron densities, they would need to consider the individual orbitals in which electrons flow. In such situation, inverting the issue to make the XC functional becomes a significantly more difficult computation. Even with density gradients, scientists had to perform the computations on one of the largest supercomputers in the United States, so this path would take more computing time.
