Density functional theory (DFT) is a computational approach used in tens of thousands of applicative scientific papers every year. It exploits the fact that a lot can be learnt from the way the electrons get distributed in a material. But DFT is mostly useful for ground states – i.e., non-excited states. Now an international team of scientists from Griffith University (Australia), Vrije Universiteit (the Netherlands) and Cnr Nano demonstrate that Ensemble DFT (EDFT) – a statistical extension of DFT – can solve excited-state problems by interpolating solutions from the extreme, yet exact, cases of high electron densities, where the distribution of electrons is squeezed, and at low electron densities, where the electrons distribution is stretched.
The study led by Tim Gould, Griffith University, with Derk P. Kooi, Vrije Universiteit, Paola Gori-Giorgi, previously at Vrije Universiteit and now at Microsoft Quantum and Stefano Pittalis (Cnr Nano) has been published in Physical Review Letter and featured as Editor’s suggestion. It also has a limpid synopsis on the web magazine Physics.
“The result is a kind of breakthrough in many-body physics and computational physics: solutions of excited-state problems which were thought to be too difficult may instead soon become computable via EDFT routinely”, explains Stefano Pittalis.
“Our most surprising result is that at low electron densities, all complications for treating excitations by EDFT basically disappear”, continues Pittalis ,”everything we already know about low electron densities from DFT for ground states can directly be reused in EDFT for excited states. We also showed that a previous study published in 2017 [Gould and Pittalis, PRL 119, 243001] becomes exact in the high-density limit – a case for which solutions are also computable via EDFT”.
The most immediate implication of the study is that EDFT solutions for excited states can now be formulated by using the fundamental information on the high-density and low-density limits revealed by the reserachers. “Our work is of direct importance for traditional analytic-driven models of materials. It also provides constraints for modern data-driven methodologies based on machine learning. As such, our results promise to accelerate the development of new technologies through simulations, prediction, screening, and analysis of excited states in materials”, Pittalis says.
To illustrate the importance of their findings for applications, researchers showed that they could interpolate the low- and high-density cases to approximate the excitation energies of molecular hydrogen at all bond lengths. Next steps from the present results are to further develop sufficiently general solutions, implement the corresponding algorithms in software packages, and apply them to important yet unsolved problems.
Tim Gould, Derk P. Kooi, Paola Gori-Giorgi, and Stefano Pittalis, “Electronic excited states in extreme limits via ensemble density functionals,” Phys. Rev. Lett. 130, 106401 (2023).
Istituto nanoscienze del Cnr