*Spectral properties of materials on accelerated architectures *

*PI: Nicola Marzari (EPFL)*

*Co-PIs: Nicola Colonna, Anton Kozhevnikov, Iurii Timrov *

*July 1, 2021 – June 30, 2024*

### Project Summary

This project aims to develop the capabilities to calculate very efficiently and automatically the spectral properties of materials using complex accelerated hardware architectures, as deployed in Piz Daint (Intel Xeon and Tesla P100), LUMI (AMD Epyc and Instinct), and in future pre- and exascale machines. Spectral properties are essential to understand or engineer materials: from photoemission spectra (widely used in recent years to characterise all possible topological properties) to transport (for ICT technologies) to light absorption (for energy harvesting) or emission (quantum technologies). Current electronic-structure approaches are either qualitatively incorrect and not appropriate to study band structures (e.g. density-functional theory (DFT)), or exceedingly expensive (GW, typically requiring both self-consistency and vertex corrections). We recently demonstrated the power of Kooopmans spectral functionals in providing spectral properties in materials with the same accuracy of these state-of-the-art GW calculations. These functionals have now been implemented, in the past 18 months, in periodic-boundary conditions in Quantum ESPRESSO. The most expensive step in the calculation is the linear-response algorithm, widely present in the code (for the calculations of phonons, magnetic response, Hubbard parameters, electron-phonon and phononphonon couplings), that is needed here to calculate the response function of a localized function to a change in occupation. In addition, extended Hubbard functionals (i.e. containing both on-site U interactions and inter-site V interactions) rely on a very similar linear-response formalism to determine the Hubbard interaction parameters from first-principles, and greatly improve the ground-state energetics of those functional materials (typically, transitionmetal/rare earth oxides, sulphides, nitrides, with localized d and f orbitals) that are so central to the scientific and technolgical areas metnioned above.

So, the core of the project is to implement in GPUs and other accelerated architectures a linear-response kernel (used for all the functionalities above) able to provide an integrated SIRIUS-enabled version of Quantum ESPRESSO that allows users to exploit the current capabilities (SIRIUS+QE running optimally on GPUs) by adding: 1) integration between SIRIUS and the Wannier90 code, for the localized response needed in the Koopmans and Hubbard functionals; 2) SIRIUS-enabled linear-response; and 3) symmetry operations in linear response. In addtion, 4) the GPU-enabled Koopmans and Hubbard capabilities will be made available as automated ”turnkey” workflows using AiiDA (Huber et al., 2020; Pizzi et al., 2016) and AiiDAlab (Yakutovich et al., 2020), greatly lowering the access barrier to these powerful tools while maintaining strict quality control on the computational protocols.

**Rationale of the project**: Electronic-structure simulations are having a transformational role in science and engineering, spanning fields that go from condensed-matter physics to chemistry, materials science, chemical and mechanical engineering, and earth sciences, to name just a few. At the core of this transformation has been the accuracy and efficiency of density-functional theory, coupled with the broad availability of robust computational codes that implement and make available to the community at large core or advanced functionalities. This accuracy and efficiency has nowadays reached the point where high-throughput simulations can routinely be employed to screen thousands of materials for optimal properties or performance. Nevertheless, and notwithstanding these successes, crucial limitations remain, and hinder accurate and efficient simulations on many materials or properties of fundamental importance for current scientific and technological applications, from energy harvesting and storage to quantum technologies. Some of these limitations are related to the accuracy of current approximations to the unknown exchange-correlation functional, while others are intrinsic to the theory itself, that, as a static functional of the local charge density, can only describe exactly (if the exact functional were known) the total energy of a system and its derivatives, precluding any access to spectroscopic information, except, at least in principle, the position of the highest occupied orbital. Our work in the past years has shown how one can define and apply a novel class of functionals (that we term Koopmans spectral functionals) that give access also to excited-state properties, with an accuracy that is currently comparable to the state-of-the-art in many-body perturbation theory (see narrative and figures below). In addition, Hubbard functionals, based on similar concepts and ideas, greatly improve the energetics and ground-state of materials that are challenging for DFT, such as those containing localized d or f electrons, that are ubiquitous in the cutting-edge scientific or technological applications mentioned.

**Methods to be used**: While the advances described above are general to density-functional theory and some of its extensions, and thus open to be implemented in the many codes available today, they will be implemented and disseminated by us into SIRIUS-enabled Quantum ESPRESSO, connecting thus naturally to a large community of users (Web of Science records more than 2500 papers published in 2019, making Quantum ESPRESSO the most used open-source code for quantum simulations of materials). A core underlying theme will be the use of linear-response techniques based on density-functional perturbation theory, to make the calculation of the screening/gauge parameters automatic, robust, and efficient: both the screening parameters of Koopmans-compliant functionals and the Hubbard on-site U and inter-site V parameters will be calculated automatically, and without the need to resort to expensive supercells’ calculations.

**Expected results and their impact**: First and foremost, the developments described above will bring pre-exascale and exascale capabilities for electronic-structure methods that allow to study the electronic structure of complex materials with prdictive accuracy. Since these functionals are tuned to the response functions of the system at hand, they bypass the need of employing more expensive (and somehow less satisfactory) hybrid functionals, while delivering the capability to describe spectroscopic properties (remarkably, the performance of Koopmans’ functionals is comparable or even slightly superior to the state-of-the-art in diagrammatic techniques, a much more involved and computationally expensive effort).