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We give a detailed presentation of the theory and numerical implementation of an expression for the adiabatic energy flux in extended systems, derived from density-functional theory. This expression can be used to estimate the heat conductivity from equilibrium ab initio molecular dynamics, using the Green-Kubo linear response theory of transport coefficients. Our expression is implemented in an open-source component of the QE suite of computer codes for quantum mechanical materials modelling, which is being made publicly available.

The recent explosion in applications of machine learning to satellite imagery often rely on visible images and therefore suffer from a lack of data during the night. The gap can be filled by employing available infra-red observations to generate visible images. This work presents how deep learning can be applied successfully to create those images by using U-Net based architectures. The proposed methods show promising results, achieving a structural similarity index (SSIM) up to 86\% on an independent test set and providing visually convincing output images, generated from infra-red observations.

In this work we address Li-ion diffusion in thio-LISICON materials and in their oxide counterparts, exploring both the orthorhombic and tetragonal phases of Li10GeP2S12(LGPS) and Li10GeP2O12(LGPO) through extended Car-Parrinello molecular dynamics in the canonical and isobaric-isothermal ensemble. The (quasi-)orthorhombic and tetragonal phases are studied both for the oxide and for the sulfide, with the aim of comparing their conductivity with the same approach; out of these four case studies, tetragonal LGPO has not been reported and, while dynamically stable, it sits (0.04 Ha/formula unit) above orthorhombic LGPO. We calculate activation energies for diffusion of 0.18 eV and 0.23 eV for tetragonal and orthorhombic LGPS, and of 0.22 eV and 0.34eV for tetragonal and orthorhombic LGPO. In line with experiments, we find orthorhombic LGPO orders of magnitude less conductive, at room temperature, than the two sulfide systems. However, this is not the case for tetragonal LGPO, which, although less stable than its orthorhombic allotrope, shows at room temperature a conductivity comparable to orthorhombic and tetragonal LGPS, and, if synthesized, could make a very attractive Li-ion conductor., Comment: 18 pages, 12 figures, Supplemental Material

Computation of correlated ionic transport properties from molecular dynamics in the Green-Kubo formalism is expensive as one cannot rely on the affordable mean square displacement approach. We use spectral decomposition of the short-time ionic displacement covariance to learn a set of diffusion eigenmodes that encode the correlation structure and form a basis for analyzing the ionic trajectories. This allows to systematically reduce the uncertainty and accelerate computations of ionic conductivity in systems with a steady-state correlation structure. We provide mathematical and numerical proofs of the method's robustness, and demonstrate it on realistic electrolyte materials.

We study the oxo-hexametallate Li$_7$TaO$_6$ with first-principles and classical molecular dynamics simulations, obtaining a low activation barrier for diffusion of $\sim$0.29 eV and a high ionic conductivity of $5.7 \times 10^{-4}$ S cm$^{-1}$ at room temperature (300 K). We find evidence for a wide electrochemical stability window from both calculations and experiments, suggesting its viable use as a solid-state electrolyte in next-generation solid-state Li-ion batteries. To assess its applicability in an electrochemical energy storage system, we performed electrochemical impedance spectroscopy measurements on multicrystalline pellets, finding substantial ionic conductivity, if below the values predicted from simulation. We further elucidate the relationship between synthesis conditions and the observed ionic conductivity using X-ray diffraction, inductively coupled plasma optical emission spectrometry, and X-ray photoelectron spectroscopy, and study the effects of Zr and Mo doping.

The recently published DeePMD model (https://github.com/deepmodeling/deepmd-kit), based on a deep neural network architecture, brings the hope of solving the time-scale issue which often prevents the application of first principle molecular dynamics to physical systems. With this contribution we assess the performance of the DeePMD potential on a real-life application and model diffusion of ions in solid-state electrolytes. We consider as test cases the well known Li10GeP2S12, Li7La3Zr2O12 and Na3Zr2Si2PO12. We develop and test a training protocol suitable for the computation of diffusion coefficients, which is one of the key properties to be optimized for battery applications, and we find good agreement with previous computations. Our results show that the DeePMD model may be a successful component of a framework to identify novel solid-state electrolytes.

Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we show how this gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of isolated atoms, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients can be evaluated. To this end, we make use of a variational principle that relies on the metric properties of the conserved currents, treated as elements of an abstract linear space. Different metrics would result in different variational principles. We finally show how a recently proposed data-analysis methodology based on the theory of transport in multi-component systems can be recovered by a suitable choice of this metric.

We present a computational screening of experimental structural repositories for fast Li-ion conductors, with the goal of finding new candidate materials for application as solid-state electrolytes in next-generation batteries. We start from ~1400 unique Li-containing materials, of which ~900 are insulators at the level of density-functional theory. For those, we calculate the diffusion coefficient in a highly automated fashion, using extensive molecular dynamics simulations on a potential energy surface (the recently published pinball model) fitted on first-principles forces. The ~130 most promising candidates are studied with full first-principles molecular dynamics, first at high temperature and then more extensively for the 78 most promising candidates. The results of the first-principles simulations of the candidate solid-state electrolytes found are discussed in detail.

Superior stability and safety are key promises attributed to all-solid-state batteries (ASSBs) containing solid-state electrolyte (SSE) compared to their conventional counterparts utilizing liquid electrolyte. To unleash the full potential of ASSBs, SSE materials that are stable when in contact with the low and high potential electrodes are required. The electrochemical stability window is conveniently used to assess the SSE-electrode interface stability. In the present work, we review the most important methods to compute the SSE stability window. Our analysis reveals that the stoichiometry stability method represents a bridge between HOMO-LUMO method and phase stability method (grand canonical phase diagram). Moreover, we provide computational implementations of these methods for SSE material screening. We compare their results for the relevant Li- and Na-SSE materials LGPS, LIPON, LLZO, LLTO, LATP, LISICON, and NASICON, and we discuss their relation to published experimental stability windows.

We introduce a simple and efficient model to describe the potential energy surface of lithium diffusing in a solid-state ionic conductor. First, we assume that the Li atoms are fully ionized and we neglect the weak dependence of the electronic valence charge density on the instantaneous position of the Li ions. Second, we freeze the atoms of the host lattice in their equilibrium positions; consequently, also the valence charge density is frozen. We thus obtain a computational setup (the "pinball model") for which extremely inexpensive molecular dynamics simulation can be performed. To assess the accuracy of the model, we contrast it with full first-principles molecular dynamics simulations performed either with a free or frozen host lattice; in this latter case, the charge density still readjusts itself self-consistently to the actual positions of the diffusing Li ions. We show that the pinball model is able to reproduce accurately the static and dynamic properties of the diffusing Li ions - including forces, power spectra, and diffusion coefficients - when compared to the self-consistent frozen-host lattice simulations. The frozen-lattice approximation itself is often accurate enough, and certainly a good proxy in most materials. These observations unlock efficient ways to simulating the diffusion of lithium in the solid state, and provide additional physical insight into the respective roles of charge-density rearrangements or lattice vibrations in affecting lithium diffusion., Comment: In press, Physical Review Materials (2018)

The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analysing molecular trajectories that are more than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods., Comment: 36 pages, 14 figures

The evaluation of transport coefficients in extended systems, such as thermal conductivity or shear viscosity, is known to require impractically long simulations, thus calling for a paradigm shift that would allow to deploy state-of-the-art quantum simulation methods. We introduce a new method to compute these coefficients from optimally short molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single and relatively short trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding conductivity. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple data-analysis protocol is proposed and validated with the calculation of thermal conductivities in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H$_2$O) and of crystalline and glassy solids (MgO and a-SiO$_2$). We find that simulation times of one to a few hundred picoseconds are sufficient in these systems to achieve an accuracy of the order of 10% on the estimated thermal conductivities., Comment: 12 pages, 5 figures; published version

Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green-Kubo formula. We discuss this independence in terms of a kind of gauge invariance resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity., Comment: 7 pages, 3 figures

Quantum simulation methods based on density-functional theory are currently deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the atomic scale. We show that, while this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a sort of gauge invariance resulting from energy extensivity and conservation. Based on these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab-initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions with those of classical equilibrium and ab-initio non-equilibrium (M\"uller-Plathe) simulations for a liquid-Argon model, and finally applied to heavy water at ambient conditions., Comment: 9 two-column pages, 4 figures