Extrapolation to complete basis-set limit in density-functional theory by quantile random-forest models

The numerical precision of density-functional-theory (DFT) calculations depends on a variety of computational parameters, one of the most critical being the basis-set size. The ultimate precision is reached with an infinitely large basis set, i.e., in the limit of a complete basis set (CBS). Our aim in this work is to find a machine-learning model that extrapolates finite basis-size calculations to the CBS limit. We start with a data set of 63 binary solids investigated with two all-electron DFT codes, exciting and FHI-aims, which employ very different types of basis sets. A quantile-random-forest model is used to estimate the total-energy correction with respect to a fully converged calculation as a function of the basis-set size. The random-forest model achieves a symmetric mean absolute percentage error of lower than 25% for both codes and outperforms previous approaches in the literature. Our approach also provides prediction intervals, which quantify the uncertainty of the models' predictions

Electronic structure of MoS2_2 revisited: a comprehensive assessment of G0W0G_0W_0 calculations

Two-dimensional MoS$_2$ combines many interesting properties that make the material a top candidate for a variety of applications. It exhibits a high electron mobility comparable to graphene, a direct fundamental band gap, relatively strongly bound excitons, and moderate spin-orbit coupling. For a thorough understanding of all these properties, an accurate description of the electronic structure is mandatory. Surprisingly, published band gaps of MoS$_2$ obtained with $GW$, the state-of-the-art in electronic-structure calculations, are quite scattered, ranging from 2.31 to 2.97 eV. The details of $G_0W_0$ calculations, such as the underlying geometry, the starting point, the inclusion of spin-orbit coupling, and the treatment of the Coulomb potential can critically determine how accurate the results are. In this manuscript, we employ the linearized augmented planewave + local orbital method to systematically investigate how all these aspects affect the quality of $G_0W_0$ calculations, and also provide a summary of literature data. We conclude that the best overall agreement with experiments and coupled-cluster calculations is found for $G_0W_0$ results with HSE06 as a starting point including spin-orbit coupling, a truncated Coulomb potential, and an analytical treatment of the singularity at $q=0$

Numerical Quality Control for DFT-based Materials Databases

Electronic-structure theory is a strong pillar of materials science. Many different computer codes that employ different approaches are used by the community to solve various scientific problems. Still, the precision of different packages has only recently been scrutinized thoroughly, focusing on a specific task, namely selecting a popular density functional, and using unusually high, extremely precise numerical settings for investigating 71 monoatomic crystals. Little is known, however, about method- and code-specific uncertainties that arise under numerical settings that are commonly used in practice. We shed light on this issue by investigating the deviations in total and relative energies as a function of computational parameters. Using typical settings for basis sets and k-grids, we compare results for 71 elemental and 63 binary solids obtained by three different electronic-structure codes that employ fundamentally different strategies. On the basis of the observed trends, we propose a simple, analytical model for the estimation of the errors associated with the basis-set incompleteness. We cross-validate this model using ternary systems obtained from the NOMAD Repository and discuss how our approach enables the comparison of the heterogeneous data present in computational materials databases.Comment: 7 pages, 4 figure

Maxquant software for ion mobility enhanced shotgun proteomics

Ion mobility can add a dimension to LC-MS based shotgun proteomics which has the potential to boost proteome coverage, quantification accuracy and dynamic range. Required for this is suitable software that extracts the information contained in the four-dimensional (4D) data space spanned by m/z, retention time, ion mobility and signal intensity. Here we describe the ion mobility enhanced MaxQuant software, which utilizes the added data dimension. It offers an end to end computational workflow for the identification and quantification of peptides and proteins in LC-IMS-MS/MS shotgun proteomics data. We apply it to trapped ion mobility spectrometry (TIMS) coupled to a quadrupole time-of-flight (QTOF) analyzer. A highly parallelizable 4D feature detection algorithm extracts peaks which are assembled to isotope patterns. Masses are recalibrated with a non-linear m/z, retention time, ion mobility and signal intensity dependent model, based on peptides from the sample. A new matching between runs (MBR) algorithm that utilizes collisional cross section (CCS) values of MS1 features in the matching process significantly gains specificity from the extra dimension. Prerequisite for using CCS values in MBR is a relative alignment of the ion mobility values between the runs. The missing value problem in protein quantification over many samples is greatly reduced by CCS aware MBR.MS1 level label-free quantification is also implemented which proves to be highly precise and accurate on a benchmark dataset with known ground truth. MaxQuant for LC-IMS-MS/MS is part of the basic MaxQuant release and can be downloaded from http://maxquant.org

Reproducibility in density functional theory calculations of solids

NTRODUCTION The reproducibility of results is one of the underlying principles of science. An observation can only be accepted by the scientific community when it can be confirmed by independent studies. However, reproducibility does not come easily. Recent works have painfully exposed cases where previous conclusions were not upheld. The scrutiny of the scientific community has also turned to research involving computer programs, finding that reproducibility depends more strongly on implementation than commonly thought. These problems are especially relevant for property predictions of crystals and molecules, which hinge on precise computer implementations of the governing equation of quantum physics. RATIONALE This work focuses on density functional theory (DFT), a particularly popular quantum method for both academic and industrial applications. More than 15,000 DFT papers are published each year, and DFT is now increasingly used in an automated fashion to build large databases or apply multiscale techniques with limited human supervision. Therefore, the reproducibility of DFT results underlies the scientific credibility of a substantial fraction of current work in the natural and engineering sciences. A plethora of DFT computer codes are available, many of them differing considerably in their details of implementation, and each yielding a certain “precision” relative to other codes. How is one to decide for more than a few simple cases which code predicts the correct result, and which does not? We devised a procedure to assess the precision of DFT methods and used this to demonstrate reproducibility among many of the most widely used DFT codes. The essential part of this assessment is a pairwise comparison of a wide range of methods with respect to their predictions of the equations of state of the elemental crystals. This effort required the combined expertise of a large group of code developers and expert users. RESULTS We calculated equation-of-state data for four classes of DFT implementations, totaling 40 methods. Most codes agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Even in the case of pseudization approaches, which largely depend on the atomic potentials used, a similar precision can be obtained as when using the full potential. The remaining deviations are due to subtle effects, such as specific numerical implementations or the treatment of relativistic terms. CONCLUSION Our work demonstrates that the precision of DFT implementations can be determined, even in the absence of one absolute reference code. Although this was not the case 5 to 10 years ago, most of the commonly used codes and methods are now found to predict essentially identical results. The established precision of DFT codes not only ensures the reproducibility of DFT predictions but also puts several past and future developments on a firmer footing. Any newly developed methodology can now be tested against the benchmark to verify whether it reaches the same level of precision. New DFT applications can be shown to have used a sufficiently precise method. Moreover, high-precision DFT calculations are essential for developing improvements to DFT methodology, such as new density functionals, which may further increase the predictive power of the simulations