Stewart J. Clark

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.

Structure and elasticity of MgO at high pressure

Abstract The structural and elastic properties of MgO periclase were studied up to 150 GPa with the first-principles pseudopotential method within the local density approximation. The calculated lattice constant of the B1 phase over the pressure range studied is within 1% of experimental values. The observed B1 phase of MgO was found to be stable up to 450 GPa, precluding the B1-B2 phase transition within the lower mantle. The calculated transition pressure is less than one-half of the previous pseudopotential prediction but is very close to the linearized augmented plane-wave result. All three independent elastic constants, c11, c12, and c44, for the B1 phase are calculated from direct computation of stresses generated by small strains. The calculated zero-pressure values of the elastic moduli and wave velocities and their initial pressure dependence are in excellent agreement with experiments. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 15 GPa and then increasing from 15 to 150 GPa. Longitudinal and shear-wave velocities were found to vary by 23 and 59%, respectively, with propagation direction at 150 GPa. The character of the anisotropy changes qualitatively with pressure. At zero pressure longitudinal and shear-wave propagations are fastest along [111] and [100], respectively, whereas above 15 GPa, the corresponding fast directions are [100] and [110]. The Cauchy condition was found to be strongly violated in MgO, reflecting the importance of noncentral many-body forces.

Defect energy levels in HfO2 high-dielectric-constant gate oxide

This letter presents calculations of the energy levels of the oxygen vacancy and oxygen interstitial defects in HfO2 using density functional methods that do not need an empirical band gap correction. The levels are aligned to those of the Si channel using the known band offsets. The oxygen vacancy gives an energy level nearer the HfO2 conduction band and just above the Si gap, depending on its charge state. It is identified as the main electron trap in HfO2. The oxygen interstitial gives levels just above the oxide valence band.

Band gap and Schottky barrier heights of multiferroic BiFeO3

BiFeO3 is an interesting multiferroic oxide and a potentially important Pb-free ferroelectric. However, its applications can be limited by large leakage currents. Its band gap is calculated by the density-functional based screened exchange method to be 2.8eV, similar to experiment. The Schottky barrier height on Pt or SrRuO3 is calculated in the metal induced gap state model to be over 0.9eV. Thus, its leakage is not intrinsic.

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.

Passivation of oxygen vacancy states in HfO2 by nitrogen

Nitrogen is known to reduce leakage currents and charge trapping in high-dielectric-constant gate oxides such as HfO2. We show that this occurs because nitrogen, substituting for oxygen atoms next to oxygen vacancy sites, repels the occupied gap states due to the neutral and positively charged oxygen vacancies out of the band gap into its conduction band. The state of the negatively charge vacancy is also repelled upwards but remains as a shallow gap state. This occurs because the vacancy becomes effectively positively charged; the adjacent Hf ions relax outwards from the vacancy and shift its states upwards. We show this using ab initio calculation methods which do not require an empirical correction to the band gap.

Arene–perfluoroarene interactions in crystal engineering 8: structures of 1∶1 complexes of hexafluorobenzene with fused-ring polyaromatic hydrocarbons

A series of 1∶1 complexes of hexafluorobenzene (HFB) with naphthalene, anthracene, phenanthrene, pyrene and triphenylene were prepared and their X-ray crystal structures determined at low temperatures. Each structure contains infinite mixed stacks of alternating nearly-parallel molecules of HFB and arene, which display various ‘slip’ distortions and form different 3-dimensional motifs. The naphthalene, anthracene and pyrene complexes show polymorphism. Crystal packing of HFB complexes is compared with that of corresponding octafluoronaphthalene complexes. Ab initio DFT calculations on the infinite lattices give lattice parameters and ‘slip’ parameters in close agreement with the experimental crystal structures, while showing that intermolecular cohesion is predominantly of electrostatic, rather than van der Waals, origin.

Band gap modification of single-walled carbon nanotube and boron nitride nanotube under a transverse electric field

The electronic structures of carbon (C) and boron nitride (BN) nanotubes under a transverse electric field were investigated through the first-principles pseudopotential density-functional theory (DFT) calculations. It was found that band gap modifications occur both in the semiconducting C and BN nanotubes under an external electric field by inducing a semiconductor–metal transition. The variations of the band gap sizes with transverse electric fields are very different between C and BN nanotubes. In the semiconducting C nanotube, a sharp semiconductor–metal transition does not occur until a threshold electric field is achieved; the BN nanotube, on the other hand, shows a gradual reduction of the band gap size once an external electric field is applied due to the larger ionicity of BN bonds. In addition, the semiconductor–metal transition in both C and BN nanotubes occurs at a lower value of electric field with increasing diameter. The ability to tune the band gap in both C and BN nanotubes by an external electric field provides the possibility for future electronic and electro-optic nanodevice applications.

Nature of the electronic band gap in lanthanide oxides

Accurate electronic structures of the technologically important lanthanide/rare-earth sesquioxides (Ln2O3, with Ln=La, ⋯,Lu) and CeO2have been calculated using hybrid density functionals HSE03, HSE06, and screened exchange (sX-LDA). We find that these density functional methods describe the strongly correlated Ln f electrons as well as the recent G0W0@LDA+U results, generally yielding the correct band gaps and trends across the Ln period. For HSE, the band gap between O 2p states and lanthanide 5d states is nearly independent of the lanthanide, while the minimum gap varies as filled or empty Ln 4f states come into this gap. sX-LDA predicts the unoccupied 4f levels at higher energies, which leads to a better agreement with experiments for Sm2O3, Eu2O3, and Yb2O3.