J. K. Dewhurst

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.

Reduced density matrix functional for many-electron systems

Reduced density matrix functional theory for the case of solids is presented and an exchange-correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this produces more accurate behavior for total energies as a function of particle number for finite systems. Moreover, it captures the correct band-gap behavior for conventional semiconductors, as well as strongly correlated Mott insulators, where a gap is obtained in the absence of any magnetic ordering.

Bootstrap Approximation for the Exchange-Correlation Kernel of Time-Dependent Density-Functional Theory

A new parameter-free approximation for the exchange-correlation kernel f(xc) of time-dependent density-functional theory is proposed. This kernel is expressed as an algorithm in which the exact Dyson equation for the response, as well as an approximate expression for f(xc) in terms of the dielectric function, are solved together self-consistently, leading to a simple parameter-free kernel. We apply this to the calculation of optical spectra for various small band gap (Ge, Si, GaAs, AlN, TiO(2), SiC), large band gap (C, LiF, Ar, Ne), and magnetic (NiO) insulators. The calculated spectra are in very good agreement with the experiment for this diverse set of materials, highlighting the universal applicability of the new kernel.

Density-matrix-power functional: Performance for finite systems and the homogeneous electron gas

An exchange-correlation energy functional involving fractional power of the one-body reduced density matrix [S. Sharma, J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, Phys. Rev. B 78, 201103(R) (2008)] is applied to finite systems and to the homogeneous electron gas. The performance of the functional is assessed for the correlation and atomization energies of a large set of molecules and for the correlation energy of the homogeneous electron gas. High accuracy is found for these two very different types of systems.

Spectral density and metal-insulator phase transition in Mott insulators within reduced density matrix functional theory.

We present a method for calculating the spectrum of periodic solids within reduced density matrix functional theory. This method is validated by a detailed comparison of the angular momentum projected spectral density with that of well-established many-body techniques, finding very good agreement in all cases. The physics behind the pressure induced insulator-metal phase transition in MnO is investigated. The driving mechanism of this transition is identified as increased crystal field splitting with pressure, resulting in a charge redistribution between the Mn e(g) and t(2)g symmetry projected states.

Laser-induced demagnetization at ultrashort time scales: predictions of TDDFT.

Time-dependent density functional theory (TDDFT) is implemented in an all electron solid-state code for the case of fully unconstrained noncollinear spins. We use this to study intense, short, laser pulse-induced demagnetization in bulk Fe, Co, Ni and find that demagnetization can take place on time scales of <20 fs. It is demonstrated that this form of demagnetization is a two-step process: excitation of a fraction of electrons followed by spin-flip transitions mediated by spin–orbit coupling of the remaining localized electrons. We further show that it is possible to control the moment loss by tunable laser parameters, including frequency, duration, and intensity.

Optimal control of laser-induced spin–orbit mediated ultrafast demagnetization

Laser induced ultrafast demagnetization is the process whereby the magnetic moment of a ferromagnetic material is seen to drop significantly on a timescale of 10–100 s of femtoseconds due to the application of a strong laser pulse. If this phenomenon can be harnessed for future technology, it offers the possibility for devices operating at speeds several orders of magnitude faster than at present. A key component to successful transfer of such a process to technology is the controllability of the process, i.e. that it can be tuned in order to overcome the practical and physical limitations imposed on the system. In this paper, we demonstrate that the spin–orbit mediated form of ultrafast demagnetization recently investigated (Krieger et al 2015 J. Chem. Theory Comput. 11 4870) by ab initio time-dependent density functional theory (TDDFT) can be controlled. To do so we use quantum optimal control theory (OCT) to couple our TDDFT simulations to the optimization machinery of OCT. We show that a laser pulse can be found which maximizes the loss of moment within a given time interval while subject to several practical and physical constraints. Furthermore we also include a constraint on the fluence of the laser pulses and find the optimal pulse that combines significant demagnetization with a desire for less powerful pulses. These calculations demonstrate optimal control is possible for spin–orbit mediated ultrafast demagnetization and lays the foundation for future optimizations/simulations which can incorporate even more constraints.

Lithiation of InSb and Cu

In this work the mechanism of Li insertion/intercalation in the anode materials InSb and Cu

_2

_2

Sb : A Theoretical Investigation

Sb is investigated by means of the first principles total energy calculations. The total charge densities for the lithiated products of the two compounds are presented. Based on these results the change in the bonding character on lithiation is discussed. Further, the isomer shift for InSb and Cu