Kurt Lejaeghere

Reproducibility in density functional theory calculations of solids

A comparison of DFT methods Density functional theory (DFT) is now routinely used for simulating material properties. Many software packages are available, which makes it challenging to know which are the best to use for a specific calculation. Lejaeghere et al. compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT codes employing 40 different potentials (see the Perspective by Skylaris). Although there were variations in the calculated values, most recent codes and methods converged toward a single value, with errors comparable to those of experiment. Science, this issue p. 10.1126/science.aad3000; see also p. 1394 A survey of recent density functional theory methods shows a convergence to more accurate property calculations. [Also see Perspective by Skylaris] INTRODUCTION 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. Recent DFT methods yield reproducible results. Whereas older DFT implementations predict different values (red darts), codes have now evolved to mutual agreement (green darts). The scoreboard illustrates the good pairwise agreement of four classes of DFT implementations (horizontal direction) with all-electron results (vertical direction). Each number reflects the average difference between the equations of state for a given pair of methods, with the green-to-red color scheme showing the range from the best to the poorest agreement. The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data. These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist—experimental or theoretical—to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state elemental crystals (except most lanthanides). For several properties of each crystal, the difference between DFT results and experimental values is assessed. We discuss trends in these deviations and review explanations suggested in the literature. A prerequisite for such an error analysis is that different implementations of the same first-principles formalism provide the same predictions. Therefore, the reproducibility of predictions across several mainstream methods and codes is discussed too. A quality factor Δ expresses the spread in predictions from two distinct DFT implementations by a single number. To compare the PAW method to the highly accurate APW+lo approach, a code assessment of VASP and GPAW (PAW) with respect to WIEN2k (APW+lo) yields Δ-values of 1.9 and 3.3 meV/atom, respectively. In both cases the PAW potentials recommended by the respective codes have been used. These differences are an order of magnitude smaller than the typical difference with experiment, and therefore predictions by APW+lo and PAW are for practical purposes identical.

First-Principles Study of Antisite Defect Configurations in ZnGa2O4:Cr Persistent Phosphors.

Zinc gallate doped with chromium is a recently developed near-infrared emitting persistent phosphor, which is now extensively studied for in vivo bioimaging and security applications. The precise mechanism of this persistent luminescence relies on defects, in particular, on antisite defects and antisite pairs. A theoretical model combining the solid host, the dopant, and/or antisite defects is constructed to elucidate the mutual interactions in these complex materials. Energies of formation as well as dopant, and defect energies are calculated through density-functional theory simulations of large periodic supercells. The calculations support the chromium substitution on the slightly distorted octahedrally coordinated gallium site, and additional energy levels are introduced in the band gap of the host. Antisite pairs are found to be energetically favored over isolated antisites due to significant charge compensation as shown by calculated Hirshfeld-I charges. Significant structural distortions are found around all antisite defects. The local Cr surrounding is mainly distorted due to a ZnGa antisite. The stability analysis reveals that the distance between both antisites dominates the overall stability picture of the material containing the Cr dopant and an antisite pair. The findings are further rationalized using calculated densities of states and Hirshfeld-I charges.

Understanding Intrinsic Light Absorption Properties of UiO-66 Frameworks: A Combined Theoretical and Experimental Study

A combined theoretical and experimental study is performed in order to elucidate the effects of linker functional groups on the photoabsorption properties of UiO-66-X materials. This study, in which both mono- and difunctionalized linkers (with X = OH, NH2, or SH) are investigated, aims to obtain a more complete picture of the choice of functionalization. Static time-dependent density functional theory calculations combined with molecular dynamics simulations are performed on the linkers, and the results are compared to experimental UV/vis spectra in order to understand the electronic effects governing the absorption spectra. The disubstituted linkers show larger shifts than the monosubstituted variants, making them promising candidates for further study as photocatalysts. Next, the interaction between the linker and the inorganic part of the framework is theoretically investigated using a cluster model. The proposed ligand-to-metal-charge transfer is theoretically observed and is influenced by the differences in functionalization. Finally, the computed electronic properties of the periodic UiO-66 materials reveal that the band gap can be altered by linker functionalization and ranges from 4.0 down to 2.2 eV. Study of the periodic density of states allows the band gap modulations of the framework to be explained in terms of a functionalization-induced band in the band gap of the original UiO-66 host.

Missing Linkers: An Alternative Pathway to UiO-66 Electronic Structure Engineering

UiO-66 is a promising metal–organic framework for photocatalytic applications. However, the ligand-to-metal charge transfer of an excited electron is inefficient in the pristine material. Herein, we assess the influence of missing linker defects on the electronic structure of UiO-66 and discuss their ability to improve ligand-to-metal charge transfer. Using a new defect classification system, which is transparent and easily extendable, we identify the most promising photocatalysts by considering both relative stability and electronic structure. We find that the properties of UiO-66 defect structures largely depend on the coordination of the constituent nodes and that the nodes with the strongest local distortions alter the electronic structure most. Defects hence provide an alternative pathway to tune UiO-66 for photocatalytic purposes, besides linker modification and node metal substitution. In addition, the decomposition of MOF properties into node- and linker-based behavior is more generally valid, so we propose orthogonal electronic structure tuning as a paradigm in MOF design.

Quasi-1D physics in metal-organic frameworks: MIL-47(V) from first principles.

Summary The geometric and electronic structure of the MIL-47(V) metal-organic framework (MOF) is investigated by using ab initio density functional theory (DFT) calculations. Special focus is placed on the relation between the spin configuration and the properties of the MOF. The ground state is found to be antiferromagnetic, with an equilibrium volume of 1554.70 Å3. The transition pressure of the pressure-induced large-pore-to-narrow-pore phase transition is calculated to be 82 MPa and 124 MPa for systems with ferromagnetic and antiferromagnetic chains, respectively. For a mixed system, the transition pressure is found to be a weighted average of the ferromagnetic and antiferromagnetic transition pressures. Mapping DFT energies onto a simple-spin Hamiltonian shows both the intra- and inter-chain coupling to be antiferromagnetic, with the latter coupling constant being two orders of magnitude smaller than the former, suggesting the MIL-47(V) to present quasi-1D behavior. The electronic structure of the different spin configurations is investigated and it shows that the band gap position varies strongly with the spin configuration. The valence and conduction bands show a clear V d-character. In addition, these bands are flat in directions orthogonal to VO6 chains, while showing dispersion along the the direction of the VO6 chains, similar as for other quasi-1D materials.

Carbon capture turned upside down: high-temperature adsorption & low-temperature desorption (HALD)

Carbon capture & sequestration (CCS) could reduce CO2 emissions from large fossil-fuel power plants on the short term, but the high energy penalty of the process hinders its industrial deployment. Moreover, the utility of nanoporous materials, known to be selective for the CO2/N2 separation, is drastically reduced due to the competitive adsorption with H2O. Taking advantage of the power plants waste heat to perform CCS while at the same time surmounting the negative effect of H2O is therefore an attractive idea. We propose an upside-down approach for CCS in nanoporous materials, high-temperature adsorption & low-temperature desorption (HALD), that exploits the temperature-dependent competitive adsorption of CO2 and H2O. First, we provide a theoretical background for this entropy-driven behavior and demonstrate under what conditions competitive adsorption can be in favor of CO2 at high temperature and in favor of H2O at low temperature. Then, molecular simulations in all-silica MFI provide a proof of concept. The International Zeolite Association database is subsequently screened for potential candidates and finally, the most promising materials are selected using a post-Pareto search algorithm. The proposed post-Pareto approach is able to select the material that shows an optimal combination of multiple criteria, such as CO2/H2O selectivity, CO2/N2 selectivity, CO2 uptake and H2O uptake. As a conclusion, this work provides new perspectives to reduce the energy requirement for CCS and to overcome the competitive adsorption of H2O.

Exploring lanthanide doping in UiO-66 : a combined experimental and computational study of the electronic structure

Lanthanide-based metal-organic frameworks show very limited stabilities, which impedes their use in applications exploiting their extraordinary electronic properties, such as luminescence and photocatalysis. This study demonstrates a fast and easy microwave procedure to dope UiO-66, an exceptionally stable and tunable Zr-based metal-organic framework. The generally applicable synthesis methodology is used to incorporate different transition metal and lanthanide ions. Selected experiments on these newly synthesized materials allow us to construct an energy scheme of lanthanide energy levels with respect to the UiO-66 host. The model is confirmed via absolute intensity measurements and provides an intuitive way to understand charge transfer mechanisms in these doped UiO-66 materials. Density functional theory calculations on a subset of materials moreover improve our understanding of the electronic changes in doped UiO-66 and corroborate our empirical model.