Shows Orbital-Free Density Functional Theory Unlocks Electronic Structure under Extreme Conditions

Scientists are increasingly focused on understanding the behaviour of matter under the extreme pressures and temperatures found in environments like stellar interiors and fusion experiments. Cheng Ma, Qiang Xu, and Zhenhao Zhang, from the Key Laboratory of Material Simulation Methods & Software at Jilin University, alongside Ke Wang, Ying Sun, and Wenhui Mi, have developed a new computational framework to address the limitations of current methods. Their research introduces a Kohn-Sham-assisted orbital-free density functional theory that offers the efficiency of orbital-free methods, scaling linearly with system size, while achieving accuracy comparable to more computationally expensive Kohn-Sham density functional theory. This advance, validated against both Monte Carlo data and experimental measurements of beryllium, promises to significantly accelerate the analysis of experimental X-ray scattering data and unlock new insights into materials science under extreme conditions.

This breakthrough addresses a critical need for interpreting data obtained from advanced X-ray diagnostics, which are now capable of directly probing electronic structure at unprecedented resolutions.

The research team achieved KSDFT-level accuracy using orbital-free density functional theory (OFDFT), a method traditionally limited by its lower accuracy compared to the more computationally expensive Kohn-Sham density functional theory (KSDFT). The study unveils a non-empirical Kohn-Sham-assisted orbital-free density functional framework, termed SKANEX, that efficiently calculates electron densities, electron-ion structure factors, and equations of state across a broad range of pressures and temperatures.
This innovative approach overcomes the accuracy limitations of conventional OFDFT by optimizing the non-interacting free-energy functional, guided by low-cost KSDFT calculations performed on a minimal reference system. Experiments show that SKANEX delivers speedups of up to several hundred times compared with KSDFT, enabling efficient simulations of complex systems previously inaccessible to detailed electronic structure analysis.

Benchmark comparisons with Monte Carlo data for dense hydrogen and validation against Rayleigh weight measurements of hot dense beryllium demonstrate the reliability of the framework. The research establishes that even at temperatures as high as 100 eV, quantum non-locality remains essential for accurately describing the electronic structure of dense hydrogen.

This work opens new avenues for understanding the behavior of matter in extreme environments and for interpreting experimental results from facilities like the European XFEL and the National Ignition Facility. The ability to efficiently and accurately model electronic structure under these conditions is crucial for advancing inertial confinement fusion and for modelling astrophysical phenomena.

Benchmarking Kohn-Sham assisted orbital-free density functional theory against quantum Monte Carlo and Rayleigh weight data reveals promising accuracy

Scientists developed a novel Kohn-Sham-assisted orbital-free density functional framework to accurately simulate electronic structure under extreme conditions. The research addressed limitations in existing methods like Kohn-Sham density functional theory, which, despite its success in analysing X-ray scattering, suffers from high computational cost, hindering routine application.

This study pioneered a method to achieve efficient orbital-free DFT with KSDFT-level accuracy for electron densities, electron-ion structure factors, and equations of state across a broad range of conditions. Researchers benchmarked the framework against quantum Monte Carlo data for dense hydrogen, validating its reliability and demonstrating speedups of up to several hundred times compared with conventional KSDFT calculations.

Validation also included comparisons against Rayleigh weight measurements of hot dense beryllium, further confirming the accuracy of the approach. The team employed a non-empirical approach, avoiding approximations that could compromise the fidelity of the simulations at extreme pressures and temperatures.

Experiments utilised this framework to investigate the electronic structure of dense hydrogen at temperatures reaching 100 eV, revealing the continued importance of quantum non-locality for accurate description. The system delivers precise calculations of electron densities and structure factors, crucial for interpreting data from X-ray free-electron laser diagnostics used in studies of stellar interiors and inertial confinement fusion. This technique enables researchers to probe the electronic structure of matter under conditions previously inaccessible to accurate theoretical modelling, advancing understanding of warm dense matter and its behaviour.

SKANEX demonstrates high-accuracy warm dense matter simulations with substantial computational gains, achieving state-of-the-art performance

Scientists have developed a new Kohn-Sham-assisted orbital-free density functional framework designed for calculations under extreme conditions, achieving KSDFT-level accuracy with significantly improved efficiency. The research addresses limitations in existing orbital-free DFT methods, which, while computationally cheaper, often lack the necessary accuracy for describing electronic structure at high pressures and temperatures.

Experiments revealed speedups of up to several hundred times compared with traditional KSDFT calculations, enabling efficient analysis of electron densities, electron-ion structure factors, and equations of state. The team measured the performance of their SKANEX method against both KSDFT and path-integral Monte Carlo calculations across a wide range of temperatures and densities, demonstrating high accuracy for warm dense hydrogen.

Results demonstrate that even at temperatures around 100 eV, non-locality remains crucial for accurately describing the electronic structure of dense hydrogen. Data shows the framework reliably predicts electronic structure and the equation of state, crucial for understanding materials under extreme conditions like those found in stellar interiors and inertial confinement fusion experiments.

Analysis of commonly used functionals revealed that focusing solely on ionic structure and EOS properties does not guarantee accurate electronic structure description. Specifically, conventional finite-temperature functionals failed to accurately describe the electron, ion static structure factor for warm dense hydrogen across densities ranging from 0.08g/cm3 to 0.34g/cm3.

In contrast, SKANEX was specifically designed to provide accurate predictions for both the EOS and electronic structure, including the electron density distribution and the electron, ion static structure factor. The breakthrough delivers a non-local part of the non-interacting free-energy functional, defined by the equation FNL SKANEX[n; T] = FNL 0 [n; T] + βFNL 1 [n; T], where β is a system-dependent regularization factor.

Measurements confirm that this modification improves the description of density inhomogeneity and compensates for missing higher-order corrections. The parameter β is determined by minimizing the difference between OFDFT and KSDFT densities for a small reference system, incurring negligible computational overhead. Tests prove the framework’s accuracy for warm dense hydrogen, characterized by the coupling parameter rs and the degeneracy parameter θ, achieving KSDFT-level accuracy across a relevant temperature, density range.

SKANEX delivers efficient and accurate electronic structure modelling at extreme densities and temperatures, enabling new scientific discoveries

Scientists have developed a new computational framework, termed SKANEX, to model the electronic structure of matter under extreme conditions. This framework combines orbital-free density functional theory with Kohn-Sham density functional theory, achieving comparable accuracy to the latter while maintaining the computational efficiency of the former.

The research addresses a longstanding challenge in high-energy-density physics, where simulating materials at stellar-like temperatures and pressures demands both accuracy and speed. The SKANEX method demonstrates linear scaling with system size and minimal temperature dependence, offering speedups of up to several hundred times compared to traditional Kohn-Sham DFT calculations.

Validations using dense hydrogen and beryllium, benchmarked against Monte Carlo data and Rayleigh weight measurements, confirm the reliability of the approach. Importantly, the findings highlight the continued necessity of incorporating non-locality when modelling the electronic structure of dense hydrogen, even at temperatures reaching 100 eV.

The authors acknowledge limitations related to the complexity of extending the method to heavier elements, though they note recent progress in local pseudopotentials offers a pathway forward. Future work will focus on integrating SKANEX into the open-source code DFTpy, facilitating broader access and application within the warm dense matter and dense plasma research communities. This advancement promises to improve the interpretation of experimental data from facilities like the European XFEL by enabling more accurate and computationally feasible simulations across a wider range of conditions.