Chris J. Pickard

First-principles simulation: ideas, illustrations and the CASTEP code

First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

First principles methods using CASTEP

Abstract The CASTEP code for first principles electronic structure calculations will be described. A brief, non-technical overview will be given and some of the features and capabilities highlighted. Some features which are unique to CASTEP will be described and near-future development plans outlined.

Electronic structure, properties, and phase stability of inorganic crystals: A pseudopotential plane‐wave study

Recent developments in density functional theory (DFT) methods applicable to studies of large periodic systems are outlined. During the past three decades, DFT has become an essential part of computational materials science, addressing problems in materials design and processing. The theory allows us to interpret experimental data and to generate property data (such as binding energies of molecules on surfaces) for known materials, and also serves as an aid in the search for and design of novel materials and processes. A number of algorithmic implementations are currently being used, including ultrasoft pseudopotentials, efficient iterative schemes for solving the one-electron DFT equations, and computationally efficient codes for massively parallel computers. The first part of this article provides an overview of plane-wave pseudopotential DFT methods. Their capabilities are subsequently illustrated by examples including the prediction of crystal structures, the study of the compressibility of minerals, and applications to pressure-induced phase transitions. Future theoretical and computational developments are expected to lead to improved accuracy and to treatment of larger systems with a higher computational efficiency. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 895-910, 2000

Ab initio random structure searching.

It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as density-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.

Towards crystal structure prediction of complex organic compounds – a report on the fifth blind test

The results of the fifth blind test of crystal structure prediction, which show important success with more challenging large and flexible molecules, are presented and discussed.

High-pressure phases of silane.

High-pressure phases of silane SiH4 are predicted using first-principles electronic structure methods. We search for low-enthalpy structures by relaxing from randomly chosen initial configurations, a strategy which is demonstrated to work well for unit cells containing up to at least ten atoms. We predict that silane will metallize at higher pressures than previously anticipated but might show high-temperature superconductivity at experimentally accessible pressures.

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.

Chemical shift computations on a crystallographic basis: some reflections and comments.

Computations for chemical shifts of molecular organic compounds using the gauge‐including projector augmented wave method and the NMR‐CASTEP code are reviewed. The methods are briefly introduced, and some general aspects involving the sources of uncertainty in the results are explored. The limitations are outlined. Successful applications of the computations to problems of interpretation of NMR results are discussed and the range of areas in which useful information is obtained is illustrated by examples. The particular value of the computations for comparing shifts between resonances where the same chemical site is involved is emphasised. Such cases arise for shifts between different crystallographically independent molecules of the same chemical species, between polymorphs and for shift anisotropies and asymmetries. Copyright

Reactions of xenon with iron and nickel are predicted in the Earth's inner core.

Studies of the Earths atmosphere have shown that more than 90% of xenon (Xe) is depleted compared with its abundance in chondritic meteorites. This long-standing missing Xe paradox has become the subject of considerable interest and several models for a Xe reservoir have been proposed. Whether the missing Xe is hiding in the Earths core has remained a long unanswered question. The key to address this issue lies in the reactivity of Xe with iron (Fe, the main constituent of the Earths core), which has been denied by earlier studies. Here we report on the first evidence of the chemical reaction of Xe and Fe at the conditions of the Earths core, predicted through first-principles calculations and unbiased structure searching techniques. We find that Xe and Fe form a stable, inter-metallic compound of XeFe3, adopting a Cu3Au-type face-centered cubic structure above 183 GPa and at 4470 K. As the result of a Xe ->Fe charge transfer, Xe loses its chemical inertness by opening up the filled 5p electron shell and functioning as a 5p-like element, whilst Fe is unusually negatively charged, acting as an oxidant rather than a reductant as usual. Our work establishes that the Earths core is a natural reservoir for Xe storage, and possibly provides the key to unlocking the missing Xe paradox.

Powder NMR crystallography of thymol

A protocol for the structure determination of powdered solids at natural abundance by NMR is presented and illustrated for the case of the small drug molecule thymol. The procedure uses proton spin-diffusion data from two-dimensional NMR experiments in combination with periodic DFT refinements incorporating (1)H and (13)C NMR chemical shifts. For thymol, the method yields a crystal structure for the powdered sample, which differs by an atomic root-mean-square-deviation (all atoms except methyl group protons) of only 0.07 A from the single crystal X-ray diffraction structure with DFT-optimized proton positions.