Deep learning has led to a paradigm shift in artificial intelligence, including web, text and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning in general and deep learning in particular is ideally suited for representing quantum-mechanical interactions, enabling to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for \emph{molecules and materials} where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study of the quantum-mechanical properties of C$_{20}$-fullerene that would have been infeasible with regular ab initio molecular dynamics.

Polymorphs in molecular crystals are often very close in energy, yet they may possess markedly different physical and chemical properties. The understanding and prediction of polymorphism is of paramount importance for a variety of applications, including pharmaceuticals, non-linear optics, and hydrogen storage. Here, we show that the non-additive many-body dispersion (MBD) energy beyond the standard pairwise approximation is crucial for the correct qualitative and quantitative description of polymorphism in molecular crystals. This is rationalized by the sensitive dependence of the MBD energy on the polymorph geometry and the ensuing dynamic electric fields inside molecular crystals. We use the glycine crystal as a fundamental and stringent benchmark case to demonstrate the accuracy of the DFT+MBD method.

DFT is a widely used method to compute properties of materials, which are often collected in databases and serve as valuable starting points for further studies. In this article, we present the Materials Cloud Three-Dimensional Structure Database (MC3D), an online database of computed three-dimensional (3D) inorganic crystal structures. Close to a million experimentally reported structures were imported from the COD, ICSD and MPDS databases; these were parsed and filtered to yield a collection of 72589 unique and stoichiometric structures, of which 95% are, to date, classified as experimentally known. The geometries of structures with up to 64 atoms were then optimized using density-functional theory (DFT) with automated workflows and curated input protocols. The procedure was repeated for different functionals (and computational protocols), with the latest version (MC3D PBEsol-v2) comprising 32013 unique structures. All versions of the MC3D are made available on the Materials Cloud portal, which provides a graphical interface to explore and download the data. The database includes the full provenance graph of all the calculations driven by the automated workflows, thus establishing full reproducibility of the results and more-than-FAIR procedures.

We present an investigation of one-photon valence-shell photoelectron spectroscopy and photoelectron circular dichroism (PECD) for the chiral molecule (1R,4R)-3-(heptafluorobutyryl)-(+)-camphor (HFC) and its europium complex Eu(III) tris[3-(heptafluorobutyryl)-(1R,4R)-camphorate] (Eu-HFC$_{3}$), the latter of which constitutes the heaviest organometallic molecule for which PECD has yet been measured. We discuss the role of keto-enol tautomerism in HFC, both as a free molecule and complexed in Eu-HFC$_{3}$. PECD is a uniquely sensitive probe of molecular chirality and structure such as absolute configuration, conformation, isomerisation, and substitution, and as such is in principle well suited to unambiguously resolving tautomers; however modeling remains challenging. For small organic molecules, theory is generally capable of accounting for experimentally measured PECD asymmetries, but significantly poorer agreement is typically achieved for the case of large open-shell systems. Here, we report PECD asymmetries ranging up to $\sim8\%$ for HFC and $\sim7\%$ for Eu-HFC$_{3}$, of similar magnitude to those reported previously for smaller isolated chiral molecules, indicating that PECD remains a practical experimental technique for the study of large, complicated chiral systems.

We propose a novel direct detection concept to search for dark matter with 100~keV to 100~MeV masses. Such dark matter can scatter off molecules in a gas and transfer an $\mathcal{O}(1)$ fraction of its kinetic energy to excite a vibrational and rotational state. The excited ro-vibrational mode relaxes rapidly and produces a spectacular multi-infrared-photon signal, which can be observed with ultrasensitive photodetectors. We discuss in detail a gas target consisting of carbon monoxide molecules, which enable efficient photon emission even at a relatively low temperature and high vapor pressure. The emitted photons have an energy in the range 180~meV to 265~meV. By mixing together carbon monoxide molecules of different isotopes, including those with an odd number of neutrons, we obtain sensitivity to both spin-independent interactions and spin-dependent interactions with the neutron. We also consider hydrogen fluoride, hydrogen bromide, and scandium hydride molecules, which each provide sensitivity to spin-dependent interactions with the proton. The proposed detection concept can be realized with near-term technology and allows for the exploration of orders of magnitude of new dark matter parameter space.

Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many modern functional materials. Interestingly, there is no reliable measure to quantify anharmonicity so far. Thus, a systematic classification of materials in terms of anharmonicity and a benchmark of methodologies that may be appropriate for different strengths of anharmonicity is currently impossible. In this work, we derive and discuss a statistical measure that reliably classifies compounds across temperature regimes and material classes by their "degree of anharmonicity". This enables us to distinguish "harmonic" materials, for which anharmonic effects constitute a small perturbation on top of the harmonic approximation, from strongly "anharmonic" materials, for which anharmonic effects become significant or even dominant and the treatment of anharmonicity in terms of perturbation theory is more than questionable. We show that the analysis of this measure in real and reciprocal space is able to shed light on the underlying microscopic mechanisms, even at conditions close to, e.g., phase transitions or defect formation. Eventually, we demonstrate that the developed approach is computationally efficient and enables rapid high-throughput searches by scanning over a set of several hundred binary solids. The results show that strong anharmonic effects beyond the perturbative limit are not only active in complex materials or close to phase transitions, but already at moderate temperatures in simple binary compounds.

In order to commemorate Alfred Landé's unriddling of the anomalous Zeeman Effect a century ago, we reconstruct his seminal contribution to atomic physics in light of the atomic models available at the time. Landé recognized that the coupling of quantized electronic angular momenta via their vector addition within an atom was the origin of all the apparent mysteries of atomic structure as manifested by the anomalous Zeeman effect. We show to which extent Landé's ideas influenced the development of quantum physics, particularly Wolfgang Pauli's path to the exclusion principle. We conclude with Landé's brief biography.

Using the example of a proton adsorption process, we analyze and compare two prominent modelling approaches in computational electrochemistry at metallic electrodes - electronically canonical, constant-charge and electronically grand-canonical, constant-potential calculations. We first confirm that both methodologies yield consistent results for the differential free energy change in the infinite cell size limit. This validation emphasizes that, fundamentally, both methods are equally valid and precise. In practice, the grand-canonical, constant-potential approach shows superior interpretability and size convergence as it aligns closer to experimental ensembles and exhibits smaller finite-size effects. On the other hand, constant-charge calculations exhibit greater resilience against discrepancies, such as deviations in interfacial capacitance and absolute potential alignment, as their results inherently only depend on the surface charge, and not on the modelled charge vs. potential relation. The present analysis thus offers valuable insights and guidance for selecting the most appropriate ensemble when addressing diverse electrochemical challenges.

Site-specific information on how adenosine triphosphate in the aqueous phase (ATP$_{(aq)}$) interacts with magnesium (Mg$^{2+}_{(aq)}$) is a prerequisite to understanding its complex biochemistry. To gather such information, we apply liquid-jet photoelectron spectroscopy (LJ-PES) assisted by electronic-structure calculations to study ATP$_{(aq)}$ solutions with and without dissolved Mg$^{2+}$. Valence photoemission data reveal spectral changes in the phosphate and adenine features of ATP$_{(aq)}$ due to interactions with the divalent cation. Chemical shifts in Mg 2p, Mg 2s, P 2p, and P 2s core-level spectra as a function of the Mg$^{2+}$/ATP concentration ratio are correlated to the formation of [MgATP]$^{-2}_{(aq)}$ and Mg$_2$ATP$_{(aq)}$ complexes, demonstrating the element-sensitivity of the technique to Mg$^{2+}$-phosphate interactions. In addition, we report and compare P 2s data from ATP$_{(aq)}$ and adenosine mono- and di-phosphate (AMP$_{(aq)}$ and ADP$_{(aq)}$, respectively) solutions, probing the electronic structure of the phosphate chain and the local environment of individual phosphate units in ATP$_{(aq)}$. Finally, we have recorded intermolecular Coulombic decay (ICD) spectra initiated by ionization of Mg 1s electrons to probe ligand exchange in the Mg$^{2+}$-ATP$_{(aq)}$ coordination environment, demonstrating the unique capabilities of ICD for revealing structural information. Our results provide an overview of the electronic structure of ATP$_{(aq)}$ and Mg$^{2+}$-ATP$_{(aq)}$ moieties relevant to phosphorylation and dephosphorylation reactions that are central to bioenergetics in living organisms.

In this work, we present a general machine learning approach for full-dimensional potential energy surfaces for tetra-atomic systems. Our method employs an active learning scheme trained on {\it ab initio} points, which size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As an example, we provide the full-dimensional AlF-AlF potential energy surface, requiring $\lesssim 0.1\%$ of the configurations to be calculated {\it ab initio}. Furthermore, we analyze the general properties of the AlF-AlF system, finding key difference with other reported results on CaF or bi-alkali dimers.

The coupled transport of charge and orbital angular momentum (OAM) lies at the core of orbitronics. Here, we examine the reciprocal relation in orbital-charge-coupled transport in thin films, treating bulk and surface contributions on equal footing. We argue that the conventional definition of orbital current is ill-defiled, as it violates reciprocity due to the nonconservation of OAM. This issue is resolved by adopting the so-called \emph{proper} orbital current, which is directly linked to orbital accumulation. We establish the reciprocal relation for the \emph{global} (spatially integrated) response between orbital and charge currents, while showing that their \emph{local} (spatially resolved) responses can differ significantly. In particular, we find large surface contributions that may lead to nonreciprocity when currents are measured locally. These findings are supported by first-principles calculations on W(110) and Pt(111) thin films. In W(110), orbital-charge interconversion is strongly nonreciprocal at the layer level, despite exact reciprocity in the integrated response. Interestingly, spin-charge interconversion in W(110) remains nearly reciprocal even locally. In contrast, Pt(111) exhibits local nonreciprocity for both orbital-charge and spin-charge conversions, which we attribute to strong spin-orbit coupling. We propose that such local distinctions can be exploited to experimentally differentiate spin and orbital currents.

Here we report on spectroscopic measurements of the aluminum monofluoride molecule (AlF) that are relevant to laser cooling and trapping experiments. We measure the detailed energy level structure of AlF in the X$^1\Sigma^+$ electronic ground state, in the A$^1\Pi$ state, and in the metastable a$^3\Pi$ state. We determine the rotational, vibrational and electronic branching ratios from the A$^1\Pi$ state. We also study how the rotational levels split and shift in external electric and magnetic fields. We find that AlF is an excellent candidate for laser cooling on any Q-line of the A$^1\Pi$ - X$^1\Sigma^+$ transition and for trapping at high densities.

The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount to a sizeable fraction of the whole numerical calculation. For researchers in the field of computational materials science, an efficient and scalable solution of the eigenvalue problem is thus of major importance. The ELPA-library is a well-established dense direct eigenvalue solver library, which has proven to be very efficient and scalable up to very large core counts. In this paper, we describe the latest optimizations of the ELPA-library for new HPC architectures of the Intel Skylake processor family with an AVX-512 SIMD instruction set, or for HPC systems accelerated with recent GPUs. We also describe a complete redesign of the API in a modern modular way, which, apart from a much simpler and more flexible usability, leads to a new path to access system-specific performance optimizations. In order to ensure optimal performance for a particular scientific setting or a specific HPC system, the new API allows the user to influence in straightforward way the internal details of the algorithms and of performance-critical parameters used in the ELPA-library. On top of that, we introduced an autotuning functionality, which allows for finding the best settings in a self-contained automated way. In situations where many eigenvalue problems with similar settings have to be solved consecutively, the autotuning process of the ELPA-library can be done "on-the-fly". Practical applications from materials science which rely on so-called self-consistency iterations can profit from the autotuning. On some examples of scientific interest, simulated with the FHI-aims application, the advantages of the latest optimizations of the ELPA-library are demonstrated.

Amino acids and other small chiral molecules play key roles in biochemistry. However, in order to understand how these molecules behave in vivo, it is necessary to study them under aqueous-phase conditions. Photoelectron circular dichroism (PECD) has emerged as an extremely sensitive probe of chiral molecules, but its suitability for application to aqueous solutions had not yet been proven. Here, we report on our PECD measurements of aqueous-phase alanine, the simplest chiral amino acid. We demonstrate that the PECD response of alanine in water is different for each of alanine's carbon atoms, and is sensitive to molecular structure changes (protonation states) related to the solution pH. For C~1s photoionization of alanine's carboxylic acid group, we report PECD of comparable magnitude to that observed in valence-band photoelectron spectroscopy of gas-phase alanine. We identify key differences between PECD experiments from liquids and gases, discuss how PECD may provide information regarding solution-specific phenomena -- for example the nature and chirality of the solvation shell surrounding chiral molecules in water -- and highlight liquid-phase PECD as a powerful new tool for the study of aqueous-phase chiral molecules of biological relevance.

We demonstrate rapid loading of a magneto-optical trap (MOT) of cadmium atoms from a pulsed cryogenic helium buffer gas beam, overcoming strong photoionization losses. Using the $^1S_0 \rightarrow{} ^1P_1$ transition at 229 nm, we capture up to $1.1(2) \times 10^7$ $^{112}$Cd atoms in 10 ms, achieving a peak density of $2.5 \times 10^{11}$cm$^{-3}$ and a phase-space density of $2 \times 10^{-9}$. The large scattering force in the deep ultraviolet enables Zeeman slowing within 5 cm of the trap, yielding a capture velocity exceeding 200 m/s. We measure the MOT trap frequency and damping constant, and determine the absolute photoionization cross section of the $^1P_1$ state. Photoionization losses are mitigated via dynamic detuning of the trapping light's frequency, allowing efficient accumulation of multiple atomic pulses. Our results demonstrate the benefits of deep-UV (DUV) transitions and cryogenic beams for loading high-density MOTs, especially for species with significant loss channels in their main cooling cycle. The cadmium MOT provides a robust testbed that benchmarks our DUV laser cooling system and establishes the foundation for trapping and cooling polar AlF molecules, which share many optical and structural properties with Cd.

The electron-phonon coupling and the corresponding energy exchange was investigated experimentally and by ab initio theory in non-equilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean squared displacement in laser-excited thin free-standing films was monitored by femtosecond electron diffraction. The electron-phonon coupling strength was obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics (DFT-MD) simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a two-temperature model (TTM) deviates significantly from the ab initio values. We introduce a non-thermal lattice model (NLM) for describing non-thermal phonon distributions as a sum of thermal distributions of the three phonon branches. The contributions of individual phonon branches to the electron-phonon coupling are considered independently and found to be dominated by longitudinal acoustic phonons. Using all material parameters from first-principle calculations besides the phonon-phonon coupling strength, the prediction of the energy transfer from electrons to phonons by the NLM is in excellent agreement with time-resolved diffraction data. Our results suggest that the TTM is insufficient for describing the microscopic energy flow even for simple metals like aluminium and that the determination of the electron-phonon coupling constant from time-resolved experiments by means of the TTM leads to incorrect values. In contrast, the NLM describing transient phonon populations by three parameters appears to be a sufficient model for quantitatively describing electron-lattice equilibration in aluminium. We discuss the general applicability of the NLM and provide a criterion for the suitability of the two-temperature approximation for other metals.

Science is and always has been based on data, but the terms "data-centric" and the "4th paradigm of" materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of Artificial Intelligence (AI) and its subset Machine Learning (ML), has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research, and experimental techniques like photoemission, atom probe tomography, and electron microscopy. While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research.