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Register a new userOpening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations
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The recent TASK meta-GGA density functional [Phys. Rev. Research, 1, 033082 (2019)] is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme, and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. The reduced screening of these materials results in larger band gaps compared to their bulk counterparts, as an additional barrier to overcome. In this work, we demonstrate how the alteration of exact physical constraints in this functional affects the band gaps of monolayers and nanoribbons, and present accurate band gaps competing with the HSE06 approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper-bound for one or two-electron systems ($h_X^0$) from 1.174 to 1.29 (b) by changing the limit of interpolation function $f_X (alpha rightarrow infty$) of the TASK functional that interpolates the exchange enhancement factor $F_X (s,alpha)$ from $alpha=$ 0 to 1. The resulting modified TASK (mTASK) was tested for various materials from 3D to 2D to 1D (nanoribbons), and was compared with the results of the higher-level hybrid functional HSE06 or with the G$_0$W$_0$ approximation within many-body perturbation theory. We find that mTASK greatly improves the band gaps and band structures of 2D and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared to the PBE-GGA and SCAN meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of TMD nanoribbons with respect to various bending curvatures.
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Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Moller-Plesset perturbation theory (MP2) significantly underestimates band gaps. Here, we evaluate the band gap predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to equation-of-motion coupled-cluster theory with single and double excitations. On a test set of elemental and binary semiconductors and insulators, we find that P-EOM-MP2 overestimates band gaps by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on average exhibited by the G0W0 approximation with a PBE reference. We show that P-EOM-MP2, when interpreted as a Greens function-based theory, has a self-energy that includes all first- and second- order diagrams and a few third-order diagrams. We find that the GW approximation performs better for materials with small gaps and P-EOM-MP2 performs better for materials with large gaps, which we attribute to their superior treatment of screening and exchange, respectively.
Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is non-multiplicative, which prevents systematic comparison of meta-GGA bandstructures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.
Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGA functionals for magnetism, we extend the assessment to more functionals, but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice-versa. We also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.
Recent advances in scanning transmission electron microscopy (STEM) instrumentation have made it possible to focus electron beams with sub-atomic precision and to identify the chemical structure of materials at the level of individual atoms. Here we discuss the dynamics that are observed in the structure of low-dimensional materials under electron irradiation, and the potential use of electron beams for single-atom manipulation. As a demonstration of the latter capability, we show how momentum transfer from the electrons of a 60-keV {AA}ngstrom-sized STEM probe can be used to move silicon atoms embedded in the graphene lattice with atomic precision.
Computational virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for the cases with challenging electronic structure (e.g., open shell transition metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families and rungs (e.g., semi-local to double hybrid) and basis sets on over 2,000 TMCs. Although computed properties (e.g., spin-state ordering and frontier orbital gap) naturally differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance; these features thus provide DFA-invariant, universal design rules. We devise a strategy to train ML models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 182k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of these computational lead compounds with literature-mined, experimental compounds over the single-DFA approach typically employed. Both feature analysis and consensus-based ML provide efficient, alternative paths to overcome accuracy limitations of practical DFT.
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