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We develop a probabilistic machine learning model and use it to screen for new hybrid organic-inorganic perovskites (HOIPs) with targeted electronic band gap. The data set used for this work is highly diverse, containing multiple atomic structures for each of 192 chemically distinct HOIP formulas. Therefore, any property prediction on a given formula must be associated with an irreducible "uncertainty" that comes from its unknown atomic details. As a result, dozens of new HOIP formulas with band gap falling between 1.25 and 1.50 eV were identified and validated against suitable first-principles computations. Through this demonstration we show that the probabilistic deep learning approach is robust, versatile, and can be used to properly quantify this uncertainty. In conclusion, the probabilistic standpoint and approach described herein could be widely useful for the very common and inevitable data uncertainty which is rooted at the incompleteness of information during experiments and/or computations.

The design/discovery of new materials is highly non-trivial owing to the near-infinite possibilities of material candidates, and multiple required property/performance objectives. Thus, machine learning tools are now commonly employed to virtually screen material candidates with desired properties by learning a theoretical mapping from material-to-property space, referred to as the \emph{forward} problem. However, this approach is inefficient, and severely constrained by the candidates that human imagination can conceive. Thus, in this work on polymers, we tackle the materials discovery challenge by solving the \emph{inverse} problem: directly generating candidates that satisfy desired property/performance objectives. We utilize syntax-directed variational autoencoders (VAE) in tandem with Gaussian process regression (GPR) models to discover polymers expected to be robust under three extreme conditions: (1) high temperatures, (2) high electric field, and (3) high temperature \emph{and} high electric field, useful for critical structural, electrical and energy storage applications. This approach to learn from (and augment) human ingenuity is general, and can be extended to discover polymers with other targeted properties and performance measures.

Artificial intelligence (AI) based approaches are beginning to impact several domains of human life, science and technology. Polymer informatics is one such domain where AI and machine learning (ML) tools are being used in the efficient development, design and discovery of polymers. Surrogate models are trained on available polymer data for instant property prediction, allowing screening of promising polymer candidates with specific target property requirements. Questions regarding synthesizability, and potential (retro)synthesis steps to create a target polymer, are being explored using statistical means. Data-driven strategies to tackle unique challenges resulting from the extraordinary chemical and physical diversity of polymers at small and large scales are being explored. Other major hurdles for polymer informatics are the lack of widespread availability of curated and organized data, and approaches to create machine-readable representations that capture not just the structure of complex polymeric situations but also synthesis and processing conditions. Methods to solve inverse problems, wherein polymer recommendations are made using advanced AI algorithms that meet application targets, are being investigated. As various parts of the burgeoning polymer informatics ecosystem mature and become integrated, efficiency improvements, accelerated discoveries and increased productivity can result. Here, we review emergent components of this polymer informatics ecosystem and discuss imminent challenges and opportunities.

The family of binary compounds composed of magnesium and silicon is rather rich. In addition to the well-known magnesium silicide Mg$_2$Si, other compounds, including MgSi$_2$, Mg$_4$Si$_7$, Mg$_5$Si$_6$, MgSi, and Mg$_9$Si$_5$, have also been identified and/or proposed in precipitated Al-Mg-Si solid solutions. Nevertheless, computational studies show that only Mg$_2$Si is thermodynamically stable at ambient conditions while certain non-zero hydrostatic pressure can stabilize Mg$_9$Si$_5$ so that it can co-exist with Mg$_2$Si. We conduct a comprehensive search for viable binary compounds of Mg$_x$Si$_{1-x}$ ($1/3\leq x \leq 2/3$), discovering numerous new structures for all the compounds. On the one hand, we find that MgSi$_2$, MgSi, and Mg$_9$Si$_5$ are likely pressure-stabilized materials, while, on the other hand, supporting previous studies, raising doubt on the existence of Mg$_5$Si$_6$, and claiming that the existence of Mg$_4$Si$_7$ remains an open question. Therefore, we recommend that (hydrostatic and/or non-hydrostatic) pressure should be explicitly considered when discussing the stability of these solids (and maybe other solids as well) by computations. We also find that MgSi$_2$ can potentially exhibit superconducting behaviors within a wide range of pressure with the critical temperature of up to $7$ K.

Although dopants have been extensively employed to promote ferroelectricity in hafnia films, their role in stabilizing the responsible ferroelectric non-equilibrium Pca21 phase is not well understood. In this work, using first principles computations, we investigate the influence of nearly 40 dopants on the phase stability in bulk hafnia to identify dopants that can favor formation of the polar Pca21 phase. Although no dopant was found to stabilize this polar phase as the ground state, suggesting that dopants alone cannot induce ferroelectricity in hafnia, Ca, Sr, Ba, La, Y and Gd were found to significantly lower the energy of the polar phase with respect to the equilibrium monoclinic phase. These results are consistent with the empirical measurements of large remnant polarization in hafnia films doped with these elements. Additionally, clear chemical trends of dopants with larger ionic radii and lower electronegativity favoring the polar Pca21 phase in hafnia were identified. For this polar phase, an additional bond between the dopant cation and the 2nd nearest oxygen neighbor was identified as the root-cause of these trends. Further, trivalent dopants (Y, La, and Gd) were revealed to stabilize the polar Pca21 phase at lower strains when compared to divalent dopants (Sr and Ba). Based on these insights, we predict that the lanthanide series metals, the lower half of alkaline earth metals (Ca, Sr and Ba) and Y as the most suitable dopants to promote ferroelectricity in hafnia.

Within the framework of density functional theory (DFT), the total energy of crystal structures is calculated at zero temperature. Herein, we briefly discuss the DFT-based lattice-dynamics approach for computing crystal free energy, the quantity needed in various non-zero-temperature contexts. We illustrate this well-established approach by examining the temperature-dependent thermodynamic stability of several crystalline materials, including ZrO$_2$, HfO$_2$, KBH$_4$, and Zn(BH$_4$)$_2$.

Organic-inorganic hybrid halide perovskites, in which the A cations of an ABX$_3$ perovskite are replaced by organic cations, may be used for photovoltaic and solar thermoelectric applications. In this contribution, we systematically study three lead-free hybrid perovskites, i.e., methylammonium tin iodide CH$_3$NH$_3$SnI$_3$, ammonium tin iodide NH$_4$SnI$_3$, and formamidnium tin iodide HC(NH$_2$)$_2$SnI$_3$, by first-principles calculations. We find that in addition to the commonly known motif in which the corner-shared SnI$_6$ octahedra form a three-dimensional network, these materials may also favor a two-dimensional (layered) motif formed by alternating layers of the SnI$_6$ octahedra and the organic cations. These two motifs are nearly equal in free energy and are separated by low barriers. These layered structures features many flat electronic bands near the band edges, making their electronic structures significantly different from those of the structural phases composed of three-dimension networks of SnI$_6$ octahedra. Furthermore, because the electronic structures of HC(NH$_2$)$_2$SnI$_3$ are found to be rather similar to those of CH$_3$NH$_3$SnI$_3$, formamidnium tin iodide may also be promising for the applications of methylammonium tin iodide., Comment: Last version, appeared in Phys. Rev. B

Data-driven approaches are particularly useful for computational materials discovery and design as they can be used for rapidly screening over a very large number of materials, thus suggesting lead candidates for further in-depth investigations. A central challenge of such approaches is to develop a numerical representation, often referred to as a fingerprint, of the materials. Inspired by recent developments in chem-informatics, we propose a class of hierarchical motif-based topological fingerprints for materials composed of elements such as C, O, H, N, F, etc., whose coordination preferences are well understood. We show that these fingerprints, when representing either molecules or crystals, may be effectively mapped onto a variety of properties using a similarity-based learning model and hence can be used to predict relevant properties of a material, given that its fingerprint can be defined. Two simple procedures are introduced to demonstrate that the learning model can be inverted to identify the desired fingerprints and then, to reconstruct molecules which possess a set of targeted properties.

Chemical defects in polyethylene (PE) can deleteriously downgrade its electrical properties and performance. Although these defects usually leave spectroscopic signatures in terms of characteristic luminescence peaks, it is nontrivial to make unambiguous assignments of the peaks to specific defect types. In this work, we go beyond traditional density functional theory calculations to determine defect-derived emission and absorption energies in PE. In particular, we characterize PE defect levels in terms of thermodynamic and adiabatic charge transition levels that involve total energy calculations of neutral and charged defects. Calculations are performed at several levels of theory including those involving (semi)local and hybrid electron exchange-correlation functionals, and many-body perturbation theory. With these critical elements, the calculated defect transition levels are in excellent correspondence to observed luminescence spectra of PE, thus clarifying and confirming the origins of the observed peaks. Based on this work, a prescription with a reasonable computational expense is proposed to accurately predict and assign spectroscopic signatures of defects in other organic polymers as well.

Metal sulfate formation is one of the major challenges to the emissions aftertreatment catalysts. Unlike the incredibly sulfation prone nature of Pd to form PdSO$_4$, no experimental evidence exits for the PtSO$_4$ formation. Given the mystery of nonexistence of the PtSO$_4$, we explore the PtSO$_4$ using a combined approach of evolutionary algorithm based search technique and quantum mechanical computations. Experimentally known PdSO$_4$ is considered for the comparison and validation of our results. We predict many possible low-energy phases of the PtSO$_4$ and PdSO$_4$ at 0K, which are further investigated under wide range of temperature-pressure conditions. An entirely new low-energy (tetragonal $P4_2/m$) structure of the PtSO$_4$ and PdSO$_4$ is predicted, which appears to be the most stable phase of the PtSO$_4$ and a competing phase of the experimentally known monoclinic $C_2/c$ phase of PdSO$_4$. Phase stability at finite temperature is further examined and verified by free energy calculations of sulfates towards their possible decomposition products. Finally, temperature-pressure phase diagrams are computationally established for both PtSO$_4$ and PdSO$_4$.

The question of whether one can systematically identify (previously unknown) ferroelectric phases of a given material is addressed, taking hafnia (HfO$_2$) as an example. Low free energy phases at various pressures and temperatures are identified using a first-principles based structure search algorithm. Ferroelectric phases are then recognized by exploiting group theoretical principles for the symmetry-allowed displacive transitions between non-polar and polar phases. Two orthorhombic polar phases occurring in space groups $Pca2_1$ and $Pmn2_1$ are singled out as the most viable ferroelectric phases of hafnia, as they display low free energies (relative to known non-polar phases), and substantial switchable spontaneous electric polarization. These results provide an explanation for the recently observed surprising ferroelectric behavior of hafnia, and reveal pathways for stabilizing ferroelectric phases of hafnia as well as other compounds., Comment: There are 6 pages of main text (5 figures) and 3 pages of supplemental material (2 figures & 1 table)

According to previous interpretations of experimental data, sodium-scandium double-cation borohydride NaSc(BH$_4$)$_4$ crystallizes in the crystallographic space group $Cmcm$ where each sodium (scandium) atom is surrounded by six scandium (sodium) atoms. A careful investigation of this phase based on \textit{ab initio} calculations indicates that the structure is dynamically unstable and gives rise to an energetically and dynamically more favorable phase with $C222_1$ symmetry and nearly identical x-ray diffraction pattern. By additionally performing extensive structural searches with the minima-hopping method we discover a class of new low-energy structures exhibiting a novel structural motif in which each sodium (scandium) atom is surrounded by four scandium (sodium) atoms arranged at the corners of either a rectangle with nearly equal sides or a tetrahedron. These new phases are all predicted to be insulators with band gaps of $7.9-8.2$ eV. Finally, we estimate the influence of these structures on the hydrogen-storage performance of NaSc(BH$_4$)$_4$., Comment: Version published

We study the thermodynamic stability at low temperatures of a series of alkali metal/zinc double-cation borohydrides, including LiZn(BH$_4$)$_3$, LiZn$_2$(BH$_4$)$_5$, NaZn(BH$_4$)$_3$, NaZn$_2$(BH$_4$)$_5$, KZn(BH$_4$)$_3$, and KZn$_2$(BH$_4$)$_5$. While LiZn$_2$(BH$_4$)$_5$, NaZn(BH$_4$)$_3$, NaZn$_2$(BH$_4$)$_5$ and KZn(BH$_4$)$_3$ were recently synthesized, LiZn(BH$_4$)$_3$ and KZn$_2$(BH$_4$)$_5$ are hypothetical compounds. Using the minima-hopping method, we discover two new lowest-energy structures for NaZn(BH$_4$)$_3$ and KZn$_2$(BH$_4$)$_5$ which belong to the $C2/c$ and $P2$ space groups, respectively. These structures are predicted to be both thermodynamically stable and dynamically stable, implying that their existence may be possible. On the other hand, the lowest-energy $P1$ structure of LiZn(BH$_4$)$_3$ is predicted to be unstable, suggesting a possible reason elucidating why this compound has not been experimentally identified. In exploring the low-energy structures of these compounds, we find that their energetic ordering is sensitive to the inclusion of the van der Waals interactions. We also find that a proper treatment of these interactions, e.g., as given by a non-local density functional such as vdW-DF2, is necessary to address the stability of the low-energy structures of these compounds., Comment: Final version

Low-energy structures of alanates are currently known to be described by patterns of isolated, nearly ideal tetrahedral [AlH$_4$] anions and metal cations. We discover that the novel polymeric motif recently proposed for LiAlH$_4$ plays a dominant role in a series of alanates, including LiAlH$_4$, NaAlH$_4$, KAlH$_4$, Mg(AlH$_4$)$_2$, Ca(AlH$_4$)$_2$ and Sr(AlH$_4$)$_2$. In particular, most of the low-energy structures discovered for the whole series are characterized by networks of corner-sharing [AlH$_6$] octahedra, forming wires and/or planes throughout the materials. Finally, for Mg(AlH$_4$)$_2$ and Sr(AlH$_4$)$_2$, we identify two polymeric phases to be lowest in energy at low temperatures., Comment: 9 pages, 8 figures, 2 tables, including supplemental material

We present a systematic study of the low-energy structures of zinc borohydride, a crystalline material proposed for the hydrogen storage purpose. In addition to the previously proposed structures, many new low-energy structures of zinc borohydride are found by utilizing the minima-hopping method. We identify a new dynamically stable structure which belongs to the $I4_122$ space group as the most stable phase of zinc borohydride at low temperatures. A low transition barrier between $I4_122$ and $P1$, the two lowest-lying phases of zinc borohydride is predicted, implying that a coexistence of low-lying phases of zinc borohydride is possible at ambient conditions. An analysis based on the simulated X-ray diffraction pattern reveals that the $I4_122$ structure exhibits the same major features as the experimentally synthesized zinc borohydride samples., Comment: Version accepted by Phys. Rev. B. Manuscript has 8 pages, 5 figures, 2 tables (with 6 pages, 5 figures, 2 tables in supplemental material)

We calculate the diffusion thermopower of the degenerate two-dimensional hole gas in a $p-$type Si/Si$_{1-x}$Ge$_x$ lattice mismatched heterostructure at low temperatures and zero magnetic field. The effects of possible scatterings, e.g. remote impurity, alloy disorder, interface roughness, deformation potential, and random piezoelectric on the hole mobility and the diffusion thermopower are examined. Calculated results are well fitted to the experimental data recently reported. In addition, we predict a possibility for the diffusion thermopower to change its sign as the SiGe layer thickness changes, the effect has not been discussed yet., Comment: This is the final version of the preprint arXiv:cond-mat/0603816