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Machine learning (ML) has become a part of the fabric of high-throughput screening and computational discovery of materials. Despite its increasingly central role, challenges remain in fully realizing the promise of ML. This is especially true for the practical acceleration of the engineering of robust materials and the development of design strategies that surpass trial and error or high-throughput screening alone. Depending on the quantity being predicted and the experimental data available, ML can either outperform physics-based models, be used to accelerate such models, or be integrated with them to improve their performance. We cover recent advances in algorithms and in their application that are starting to make inroads toward ( a) the discovery of new materials through large-scale enumerative screening, ( b) the design of materials through identification of rules and principles that govern materials properties, and ( c) the engineering of practical materials by satisfying multiple objectives. We conclude with opportunities for further advancement to realize ML as a widespread tool for practical computational materials design. 

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization and static correlation errors. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization and static correlation errors within a non-empirical framework.