Although most of the basic mathematical equations describing electronic structures have been known for a long time, they are too complex to solve in practice. This has hindered progress in physics, chemistry and materials science. Thanks to modern high-performance computer clusters and the creation of the density functional theory (DFT) simulation method, researchers were able to change this situation. But even with these tools, the modeled processes are still drastically simplified in many cases. Now physicists from the Center for Advanced Systems Understanding (CASUS) and the Institute of Radiation Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have succeeded in significantly improving the DFT method. This opens up new possibilities for experiments with ultra-high-intensity lasers, as the group explains in the *Journal of Chemical Theory and Computation*†

In the new publication, Young Investigator Group Leader Dr. Tobias Dornheim, lead author Dr. Zhandos Moldabekov (both CASUS, HZDR) and Dr. Jan Vorberger (Institute of Radiation Physics, HZDR) tackles one of the most fundamental challenges of our time : accurately describing how billions quantum particles like electrons interact. These so-called quantum many-body systems form the core of many research areas within physics, chemistry, materials science and related disciplines. indeed, most material properties: are determined by the complex quantum mechanical behavior of interacting electrons. Although the fundamental mathematical equations describing electronic structures have been known in principle for a long time, they are too complex to solve in practice. Therefore, the actual understanding of elaborately designed materials has been very limited.

This unsatisfactory situation has changed with the advent of modern high-performance computer clusters, leading to the new field of computational quantum many-body theory. Here, a particularly successful tool is density functional theory (DFT), which has provided unprecedented insights into the properties of materials. DFT is currently considered one of the most important simulation methods in physics, chemistry and materials science. It is especially adept at describing systems with many electrons. The number of scientific publications based on DFT calculations has grown exponentially over the past decade, and companies have used the method to calculate the properties of materials as accurately as never before.

**Overcoming a drastic simplification**

Many such properties that can be calculated with DFT are obtained within the framework of linear response theory. This concept is also used in many experiments in which the (linear) response of the system in question to an external disturbance such as a laser is measured. In this way, the system can be diagnosed and essential parameters such as density or temperature can be obtained. Linear response theory often makes experiment and theory feasible in the first place and is nearly ubiquitous in physics and related disciplines. However, it is still a drastic simplification of the processes and a strong limitation.

In their latest publication, the researchers break new ground by extending the DFT method beyond the simplified linear regime. For the first time, non-linear effects in quantities such as density waves, braking force and structure factors can be calculated and compared with experimental results of real materials.

Prior to this publication, these nonlinear effects were only reproduced by a series of comprehensive computational methods, namely quantum Monte Carlo simulations. Although this method provides exact results, it is limited to limited system parameters because it requires a lot of computing power. Therefore, there was a great need for faster simulation methods.

“The DFT approach we present in our paper is 1,000 to 10,000 times faster than quantum Monte Carlo computations,” says Zhandos Moldabekov. “In addition, we were able to demonstrate different temperature regimes ranging from ambient temperature to extreme conditionsthat this is not at the expense of accuracy. The DFT-based methodology of the nonlinear response characteristics of quantum correlated electrons opens up the tantalizing opportunity to study novel nonlinear phenomena in complex materials.”

**More possibilities for modern free electron lasers**

“We see that our new methodology fits very well with the capabilities of modern experimental facilities such as the Helmholtz International Beamline for Extreme Fields, which HZDR is participating in and has only recently been put into use,” explains Jan Vorberger. “With high-power lasers and free electron lasers, we can create exactly these nonlinear excitations that we can now theoretically study and investigate with unprecedented temporal and spatial resolution. Theoretical and experimental tools are ready to study new effects in matter under extreme conditions that have not been accessible before.”

“This article is a good example to illustrate the direction my recently created group is taking,” said Tobias Dornheim, head of the Young Investigator Group’s “Frontiers of Computational Quantum Many-Body Theory,” which was installed in early 2022. “We have been mainly active in the high energy density physics community in recent years. Now we are committed to pushing the boundaries of science by providing computational solutions to quantum many-body problems in many different contexts. We believe that current progress in electronic structure theory will be useful to researchers in a number of research areas.”

**More information:**

Zhandos Moldabekov et al, Density Functional Theory Perspective on the nonlinear response of correlated electrons across temperature regimes,

*Journal of Chemical Theory and Computation*(2022). DOI: 10.1021/acs.jctc.2c00012

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Helmholtz Association of German Research Centers

**Quote**: Advocating a New Paradigm for Electron Simulations (2022, July 1,), retrieved July 1, 2022 from https://phys.org/news/2022-07-advocating-paradigm-electron-simulations.html

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