Potential functionals versus density functionals

Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between Thomas-Fermi theory as a density functional and as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially in their approach to the large particle number and classical continuum limits. The lack of ambiguity in the energy density of potential functional approximations is demonstrated. The density-density response function of the semiclassical approximation is calculated and shown to violate a key symmetry condition

Machine Learning-Driven Structure Prediction for Iron Hydrides

We created a computational workflow to analyze the potential energy surface (PES) of materials using machine-learned interatomic potentials in conjunction with the minima hopping algorithm. We demonstrate this method by producing a versatile machine-learned interatomic potential for iron hydride via a neural network using an iterative training process to explore its energy landscape under different pressures. To evaluate the accuracy and comprehend the intricacies of the PES, we conducted comprehensive crystal structure predictions using our neural network-based potential paired with the minima hopping approach. The predictions spanned pressures ranging from ambient to 100 GPa. Our results reproduce the experimentally verified global minimum structures such as \textit{dhcp}, \textit{hcp}, and \textit{fcc}, corroborating previous findings. Furthermore, our in-depth exploration of the iron hydride PES at different pressures has revealed complex alterations and stacking faults in these phases, leading to the identification of several new low-enthalpy structures. This investigation has not only confirmed the presence of regions of established FeH configurations but has also highlighted the efficacy of using data-driven, extensive structure prediction methods to uncover the multifaceted PES of materials

A Deep Dive into Machine Learning Density Functional Theory for Materials Science and Chemistry

With the growth of computational resources, the scope of electronic structure simulations has increased greatly. Artificial intelligence and robust data analysis hold the promise to accelerate large-scale simulations and their analysis to hitherto unattainable scales. Machine learning is a rapidly growing field for the processing of such complex datasets. It has recently gained traction in the domain of electronic structure simulations, where density functional theory takes the prominent role of the most widely used electronic structure method. Thus, DFT calculations represent one of the largest loads on academic high-performance computing systems across the world. Accelerating these with machine learning can reduce the resources required and enables simulations of larger systems. Hence, the combination of density functional theory and machine learning has the potential to rapidly advance electronic structure applications such as in-silico materials discovery and the search for new chemical reaction pathways. We provide the theoretical background of both density functional theory and machine learning on a generally accessible level. This serves as the basis of our comprehensive review including research articles up to December 2020 in chemistry and materials science that employ machine-learning techniques. In our analysis, we categorize the body of research into main threads and extract impactful results. We conclude our review with an outlook on exciting research directions in terms of a citation analysis

Machine learning the electronic structure of matter across temperatures

We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike other ML models that use DFT data, our models directly predict the local density of states (LDOS) of the electronic structure. This provides several advantages, including access to multiple observables such as the electronic density and electronic total free energy. Moreover, our models account for both the electronic and ionic temperatures independently, making them ideal for applications like laser-heating of matter. We validate the efficacy of our LDOS-based models on a metallic test system. They accurately capture energetic effects induced by variations in ionic and electronic temperatures over a broad temperature range, even when trained on a subset of these temperatures. These findings open up exciting opportunities for investigating the electronic structure of materials under both ambient and extreme conditions

Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within Kohn-Sham density functional theory (KS-DFT) for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of warm dense matter. Generated by laser-induced compression and heating in the laboratory, warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing to exact quantum Monte-Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response for partial degeneracy when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the previously reported results for the PBE, PBEsol, LDA, AM05, and SCAN functionals; B3LYP, on the other hand, does not perform well for the considered system. Together with the reduction of self-interaction errors, this seems to be the rationale behind the relative success of the HSE03 functional for the description of the experimental data on aluminum and liquid ammonia at WDM conditions