Energy production and storage technologies have attracted a great deal of attention for day-to-day applications. In recent decades, advances in lithium-ion battery (LIB) technology have improved living conditions around the globe. LIBs are used in most mobile electronic devices as well as in zero-emission electronic vehicles. However, there are increasing concerns regarding load leveling of renewable energy sources and the smart grid as well as the sustainability of lithium sources due to their limited availability and consequent expected price increase. Therefore, whether LIBs alone can satisfy the rising demand for small- and/or mid-to-large-format energy storage applications remains unclear. To mitigate these issues, recent research has focused on alternative energy storage systems. Sodium-ion batteries (SIBs) are considered as the best candidate power sources because sodium is widely available and exhibits similar chemistry to that of LIBs; therefore, SIBs are promising next-generation alternatives. Recently, sodiated layer transition metal oxides, phosphates and organic compounds have been introduced as cathode materials for SIBs. Simultaneously, recent developments have been facilitated by the use of select carbonaceous materials, transition metal oxides (or sulfides), and intermetallic and organic compounds as anodes for SIBs. Apart from electrode materials, suitable electrolytes, additives, and binders are equally important for the development of practical SIBs. Despite developments in electrode materials and other components, there remain several challenges, including cell design and electrode balancing, in the application of sodium ion cells. In this article, we summarize and discuss current research on materials and propose future directions for SIBs. This will provide important insights into scientific and practical issues in the development of SIBs.

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Sodium-ion batteries: present and future

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

We review some recently published methods to represent atomic neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighborhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

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On representing chemical environments

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.

A random-sampling high dimensional model representation neural network for building potential energy surfaces.

Development and applications of neural network (NN)-based approaches for representing potential energy surfaces (PES) of bound and reactive molecular systems are reviewed. Specifically, it is shown that when the density of ab initio points is low, NNs-based potentials with multibody or multimode structure are advantageous for representing high-dimensional PESs. Importantly, with an appropriate choice of the neuron activation function, PESs in the sum-of-products form are naturally obtained, thus addressing a bottleneck problem in quantum dynamics. The use of NN committees is also analyzed and it is shown that while they are able to reduce the fitting error, the reduction is limited by the nonrandom nature of the fitting error. The approaches described here are expected to be directly applicable in other areas of science and engineering where a functional form needs to be constructed in an unbiased way from sparse data. © 2014 Wiley Periodicals, Inc.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/qua.24795

Neural network‐based approaches for building high dimensional and quantum dynamics‐friendly potential energy surfaces

It is shown that neural networks (NNs) are efficient and effective tools for fitting potential energy surfaces. For H2O, a simple NN approach works very well. To fit surfaces for HOOH and H2CO, we develop a nested neural network technique in which we first fit an approximate NN potential and then use another NN to fit the difference of the true potential and the approximate potential. The root-mean-square error (RMSE) of the H2O surface is 1 cm-1. For the 6-D HOOH and H2CO surfaces, the nested approach does almost as well attaining a RMSE of 2 cm-1. The quality of the NN surfaces is verified by calculating vibrational spectra. For all three molecules, most of the low-lying levels are within 1 cm-1 of the exact results. On the basis of these results, we propose that the nested NN approach be considered a method of choice for both simple potentials, for which it is relatively easy to guess a good fitting function, and complicated (e.g., double well) potentials for which it is much harder to deduce an approp...

A nested molecule-independent neural network approach for high-quality potential fits.

In the last few years, organic–inorganic halide perovskites (OIHP) have gained significant attention in the optoelectronics community and become one of the most popular research topics. Due to their fascinating properties, including wide-range tunable band gap, long charge carrier diffusion length, high absorption coefficient, and easy solution processability, they have become one of the most promising classes of low-cost and easily scalable semiconductor materials for application in various optoelectronic devices such as solar cells, photodetectors, and light-emitting diodes. To achieve the best performance and viable technologies for future energy harvesting, display and light sensing prototypes, in addition to the OHIP active layer, the use of interfacial charge transporting layers is crucial. These interfacial charge-transporting layers not only enhance the performance of optoelectronic devices but also effectively protect the active environmentally unstable OHIP layer. In this review, we summarize the development and utilization of organic interfacial materials and OIHP in solar cells, photodetectors and light-emitting diodes. In each section, the working principle and the development of a wide range of hole/electron transporting materials are discussed. Finally, an outlook and further research directions as well as useful rules for the design of novel hole/electron transporting materials are proposed.

Organic interfacial materials for perovskite-based optoelectronic devices

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.

Sergei Manzhos

Papers

A random-sampling high dimensional model representation neural network for building potential energy surfaces.

Neural network‐based approaches for building high dimensional and quantum dynamics‐friendly potential energy surfaces

A nested molecule-independent neural network approach for high-quality potential fits.

Organic interfacial materials for perovskite-based optoelectronic devices

Using neural networks to represent potential surfaces as sums of products.