Metal halide perovskites are a promising class of materials for next-generation photovoltaic and optoelectronic devices. The discovery and full characterization of new perovskite-derived materials are limited by the difficulty of growing high quality crystals needed for single-crystal Xray diffraction studies. We present the first automated, high-throughput approach for metal halide perovskite single crystal discovery based on inverse temperature crystallization (ITC) as a means to rapidly identify and optimize synthesis conditions for the formation of high quality single crystals. Using this automated approach, a total of 1928 metal halide perovskite synthesis reactions were conducted using six organic ammonium cations (methylammonium, ethylammonium, nbutylammonium, formamidinium, guanidinium, and acetamidinium), increasing the number of metal halide perovskite materials accessible by ITC syntheses by three and resulting in the formation of a new phase, [C2H7N2][PbI3]. This comprehensive dataset allows for a statistical quantification of the total experimental space and of the likelihood of large single crystal formation. Moreover, this dataset enables the construction and evaluation of machine learning models for predicting crystal formation conditions. This work is a proof-of-concept that combining high throughput experimentation and machine learning accelerates and enhances the study of metal halide perovskite crystallization. This approach is designed to be generalizable to different synthetic routes for the acceleration of materials discovery.

Abstract

This report describes a combined experimental and computational investigation of the mechanism of C(sp(3))-N bond-forming reductive elimination from sulfonamide-ligated Pd(IV) complexes. After an initial experimental assessment of reactivity, we used ZStruct, a computational combinatorial reaction finding method, to analyze a large number of multistep mechanisms for this process. This study reveals two facile isomerization pathways connecting the experimentally observed Pd(IV) isomers, along with two competing SN2 pathways for C(sp(3))-N coupling. One of these pathways involves an unanticipated oxygen-nitrogen exchange of the sulfonamide ligand prior to an inner-sphere SN2-type reductive elimination. The calculated ΔG(⧧) values for isomerization and reductive elimination with a series of sulfonamide derivatives are in good agreement with experimental data. Furthermore, the simulations predict relative reaction rates with different sulfonamides, which is successful only after considering competition between the proposed operating mechanisms. Overall, this work shows that the combination of experimental studies and new computational tools can provide fundamental mechanistic insights into complex organometallic reaction pathways.

Racemates have recently received attention as nonlinear optical and piezoelectric materials. Here, a machine-learningassisted composition space approach was applied to synthesize the missing M = Ti, Zr members of the Δ,Λ-[Cu(bpy) 2 (H 2 O)] 2 [MF 6 ] 2 • 3H 2 O (M = Ti, Zr, Hf; bpy = 2,2′-bipyridine) family (space group: Pna2 1 ). In each (CuO, MO 2 )/bpy/HF(aq) (M = Ti, Zr, Hf) system, the polar noncentrosymmetric racemate (M-NCS) forms in competition with a centrosymmetric one-dimensional chain compound (M-CS) based on alternating Cu(bpy)(H 2 O) 2 2+ and MF 6 2− basic building units (space groups: Ti-CS (Pnma), Zr-CS (P1̅ ), Hf-CS (P2/n)). Machine learning models were trained on reaction parameters to gain unbiased insight into the underlying statistical trends in each composition space. A human-interpretable decision tree shows that phase selection is driven primarily by the bpy:CuO molar ratio for reactions containing Zr or Hf, and predicts that formation of the Ti-NCS compound requires that the amount of HF present be decreased to raise the pH, which we verified experimentally. Predictive leave-one-metal-out (LOO) models further confirm that behavior in the Ti system is distinct from that of the Zr and Hf systems. The chemical origin of this distinction was probed via fluorine K-edge X-ray absorption spectroscopy. Pre-edge features in the F1s X-ray absorption spectra reveal the strong ligand-to-metal π bonding between Ti(3d − t 2g ) and F(2p) states that distinguishes the TiF 6 2− anion from the ZrF 6 2− and HfF 6 2− anions.

In this paper, we derive several differential Harnack estimates (also known as Li-Yau-Hamilton-type estimates) for positive solutions of Fisher's equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions and to construct classical Harnack inequalities.Date: October 7, 2016. 1 2 XIAODONG CAO, BOWEI LIU, IAN PENDLETON, AND ABIGAIL WARD Our work introduces and proves three Li-Yau-Hamilton-type Harnack inequalities which constrain positive functions satisfying the Fisher-KPP equation on an arbitrary Riemannian manifold M n . Depending on the setting we obtain different inequalities. The study of differential Harnack inequalities was first initiated by P. Li and S.-T. Yau in [10] (also see [1]). Harnack inequalities have since played an important role in the study of geometric analysis and geometric flows (for example, see [7,13]). Applications have also been found to the study of nonlinear parabolic equations, e.g. in [8]. One of these is a recent reproof of the classical result of H. Fujita [6], which states that any positive solution to the Endangered Species Equation in dimension n,blows up in finite time provided 0 < n(p − 1) < 2; see [3].When the dimension falls into a certain range we can integrate our differential Harnack inequality along any space-time curve to obtain a classical Harnack inequality which allows us to compare the values of positive solutions at any two points in space-time when time is large.The organization for the paper is as follows: In Section 2 we present the precise formulations and the proofs of our two inequalities governing closed manifolds. In Section 3 we state and prove a similar Harnack inequality for complete noncompact manifolds. In Section 4, we end the paper with the aforementioned results on the minimum speed of traveling wave solutions and classical Harnack inequalities.