Session T7: Focus Session: Computational Design of Materials: Electronic Structure Methods for Materials - Faster and More Accurate

How accurate is Density Functional Theory in Predicting Reaction Energies Relevant to Phase Stability?

Density Functional Theory (DFT) computations can be used to build computational phase diagrams that are used to understand the stability of known phases but also to assess the stability of novel, predicted compounds. The quality and predictive power of those phase diagrams rely on the accuracy of DFT in modeling reaction energies and we will present in this talk the results of a large scale comparison between experimentally measured and DFT computed reaction energies. For starters, we will show that only certain reaction energies are directly relevant to phase stability of multicomponent systems and that very often those reaction energies are not the commonly studied reactions from the elements. Using data from different experimental thermochemical tables and DFT high-throughput computing, we will present the results of a statistical study based on more than 130 reaction energies relevant to phase stability and from binary oxides to ternary oxides. We will show that the typical error are around 30 meV/at and therefore an order of magnitude lower than the errors in reaction energies from the elements. Finally, we will discuss the broad implications of our results on the evaluation of ab initio phase diagrams and on the computational prediction of new solid phases.   

Correcting Density Functional Theory for Accurate Predictions of Compound Enthalpies of Formation:Fitted elemental-phase Reference Energies (FERE)

The first step in the Inverse Design of materials is the assessment of their thermodynamic stability and the needed growth conditions. The compound enthalpy of formation ($\Delta \mbox{H}_f$) is a quantity that provides these information. However, standard ab-initio approaches are known for their large errors in calculating $\Delta \mbox{H}_f$ of semiconducting and insulating compounds. In this talk I will present an approach, based on GGA+U total energies for compounds and fitted elemental-phase reference energies (FERE), that corrects GGA+U for the incomplete error cancellation between compound total energies and those of the pure elements, thereby resulting in $\Delta \mbox{H}_f$ values for insulating and semiconducting solids calculated with chemical accuracy. The FERE for 50 chemical elements we fit to a set of 252 measured $\Delta \mbox{H}_f$ of binary compounds (pnictides, chalcogenides and halides) and show accurate predictions also when applied to ternary compounds. I will discuss the application of the FERE approach in predicting new compounds, assess the accuracy of such predictions as well as comment on experimental efforts of our collaborators in growing some of the predicted materials.   

Correction to DFT Interaction Energies by an Empirical Dispersion Term Valid for a Range of Intermolecular Distances

The computation of intermolecular interaction energies via commonly used density functionals is hindered by their inaccurate inclusion of medium and long range dispersion interactions. Computation of inter- and intra-molecule interaction energies as well as computational design of (bio)materials, requires a fairly accurate yet not overly expensive methodology. It is also desirable to compute intermolecular energies not only at their equilibrium (lowest energy) configurations but also over a range of distances. We present a method to compute intermolecular interaction energies by including an empirical correction for dispersion which is valid over a range of intermolecular distances. This is achieved by optimizing parameters that moderate the empirical correction by explicit comparison of density functional (GGA) energies with distance-dependent (DD) reference values obtained at the CCSD(T)/CBS limit. The resulting GGA-DD method yields interaction energies with an accuracy generally better than 1 kcal/mol for different types of noncovalent complexes, over a range of intermolecular distances and interaction strengths, relative to the expensive CCSD(T)/CBS standard   

Accurate predictions of biomolecular interactions using density functional theory based semi-empirical alchemical derivatives in chemical compound space

A small but relevant sub-set of chemical compound space is explored in terms of biomolecular interaction energies, and using analytical derivatives. When transmutating any two iso-electronic ligands their intermolecular energies are not necessarily monotonic functions, consequently the corresponding Hellmann-Feynman derivatives can fail to predict the right trends. Semi-empirical corrections, effectively linearizing the intermolecular energy in the interpolation parameter, promise to drastically improve the predictive power of these first order derivatives. For various biomolecules, including ellipticine interacting with DNA, we show that these semi-empirical derivatives yield predictions superior to alternative prediction schemes that are additive and derivative-free. As such, new evidence is presented in support of the conclusion that quantitative estimates of relevant properties of new molecules can be made without additional self-consistency calculations.   

Preliminary results in data mining for materials

In recent years, materials scientists have started exploiting data mining techniques, i.e., methods for extracting meaningful information and patterns from data, for the discovery and design of materials. One of the grand challenges in this methodology is to establish correlations and intrinsic features in materials database in order to facilitate the extraction of useful information that can be exploited to discover new hypothetical materials. Using an atomic properties database of 110 elements, obtained from quantum mechanical calculations and several macroscopic properties database of binary compounds, we explored several sample data mining techniques to study the correlations among them with the goal of predicting macroscopic properties from knowledge of the atomic constituents. In this talk, preliminary results of such efforts will be presented to demonstrate how simple data mining can be applied in materials science and what they can achieve. These preliminary results indicate a good potential for data mining applications in materials science.   

Expediting Solutions for the Electronic Structure of Large Systems: A Spectrum Slicing Algorithm

Solving the Kohn-Sham equation requires computing a set of low lying eigenpairs. The standard methods for computing such eigenpairs require two procedures: (a) maintaining the orthogonality of an approximation space, and (b) forming approximate eigenpairs with the Rayliegh-Ritz method. These two procedures scale cubically with the number of desired eigenpairs. We present a method, applicable to {\it any} large Hermitian eigenproblem, by which the spectrum is partitioned among distinct groups of processors. This ``divide and conquer'' approach serves as a parallelization scheme at the level of the solver, making it compatible with existing schemes that parallelize at a physical level, {\it e.g.}, {\bf k}-points or symmetric representations, and at the level of primitive operations, matrix-vector multiplication. In addition, among all processor sets, the size of any approximation subspace is reduced, thereby reducing the cost of orthogonalization and the Rayleigh-Ritz method. We will explain the key aspects of the algorithm that give reliability, and demonstrate the accuracy of the algorithm by computing the electronic structure of a core-shell nanocrystal and a DNA segment. Overall scaling and the utility of the method for a wide variety of applications will be discussed.   

Density Functional Theory using Multiresolution Analysis with MADNESS

We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for the nuclear potential, and an implementation for Hartree-Fock exchange.   

GPU speedup of the plane wave pseudopotential density functional theory calculations

Plane wave (PW) pseudopotential density functional theory (DFT) calculation is the most widely used method for computational design of new materials. In this talk, we will present our recent work in using the graphics processing unit (GPU) to accelerate the PW-DFT calculations. Compared with the pure CPU calculation, the GPU machine with CUDA coding can speed up the calculation by 20 times for systems with a few hundred atoms, while still being able to scale to hundreds of CPU/GPU units. However, to reach this speedup, some algorithm changes are necessary. We will discuss these algorithm changes, and various computational kernels in a PW-DFT code, and their speedups in the GPU code. These include the FFT, the nonlocal projector, the orthogonalization and the diagonalization. We will also discuss the computational times for MPI communication, CPU/GPU memory copy, and floating point operation. We will present the hardware and library requirement to further speed up the calculations. Finally, the implication of the GPU speed up for new material design will be discussed.   

Linear-scaling DFT+U applied to hole localization and Friedel oscillations in very dilute (Ga,Mn)As

System-size and strong electronic correlation are two factors inhibiting the routine first-principles simulation of transition-metal doped nanostructures. Tackling these issues simultaneously, we have developed a linear-scaling implementation of the DFT+$U$ method within the ONETEP code,\footnote{Hine, Haynes, Mostofi, Skylaris \& Payne, {\it Comp. Phys. Commun.,} {\bf 180}, 1041 (2009).} demonstrating scaling upto $7,000$ atoms. Our implementation allows for nonorthogonal projectors,\footnote{O'Regan, Payne \& Mostofi, {\it PRB} {\bf 83}, 245124 (2011).} which may be self-consistently optimized.\footnote{O'Regan, Hine, Payne \& Mostofi, {\it PRB} {\bf 82}, 081102(R) (2010).} We apply our approach to the prototypical dilute magnetic semiconductor (Ga,Mn)As. The ferromagnetic interaction between distant localized magnetic moments in (Ga,Mn)As is mediated by defect-induced holes, whose long-range character is critical. Our large-scale calculations on $1,728$ atom super-cells enable us to study the localization and symmetry of the magnetization and hole in the very dilute ($0.1\%$) limit, and to analyze the long-range Friedel oscillations.   

G0W0 implementation using Lanczos algorithm and Sternheimer equation

The G0W0 approach is an accurate method to give a physical meaning to the eigenvalues obtained in adensity-functional theory (DFT) calculation.However, the calculation of such corrections with plane wave codes is currently prohibitive for systems with more than a few hundreds of electrons. What limits calculations to this system size is the need in current implementations to invert the dielectric matrix and the need to carry out summations over conduction bands. This talk presents a strategy to avoid both of these bottlenecks. In traditional plane wave implementations of G0W0, the dielectric matrix is expressed in a plane wave basis, which needs to be relatively big to properly describe the matrix. Here, we will explain how a Lanczos basis can be generated to substantially reduce the size of the matrix. Also, the number of conduction bands needed to reach convergence in the summations is usually an order of magnitude larger than the number of valence bands. Here, the calculation of the conduction states is avoided by reformulating the summations into linear equation problems (Sternheimer equations), which also substantially reduces the computation time. Preliminary results will be presented.   

Dynamical Cluster Approximation: Cluster Extension of CPA for Disordered System

The dynamical mean-field approximation (DMFA) or the coherent potential approximation (CPA) provides a convenient and effective method for studying disordered systems; however, non-local short range correlations of the disorder potential are neglected leading to a self-consistent single-site approximation. We combine the recently developed first principles method of Wei Ku and co-workers for the simulation of disordered systems with the dynamical cluster approximation (DCA) to develop a highly efficient means to treat disordered systems. We solve this model system using the DCA, which systematically incorporates short-range nonlocal correlations to the CPA. We apply this method to a number of model systems to illustrate where the DCA or a finite size simulation is more appropriate.   

Analyzing electron-electron correlations at nanoscale: a DFT+DMFT code for nanosystems

We propose a DFT+DMFT approach to study electron-electron correlation effects in nanosized systems containing atoms with localized d- and f-electron states. For the purpose we have developed a nanoDFT+DMFT code which allows one to study the properties of systems containing up to several hundred atoms. The system geometry is first optimized using ab-initio electron structure calculations based on density-functional theory (DFT), and correlation effects are analyzed employing nonhomogeneous Dynamical Mean-Field Theory (DMFT) calculations with the iterated perturbation theory (IPT) approximation for the quantum impurity solver. To test the formalism we have evaluated the magnetic properties of several transition metal atom clusters and compared the results with those obtained from the exact diagonalization method (a few-atom clusters) and available experimental data (2-19 atom clusters). In particular, we find that the IPT-DMFT gives magnetic moments much closer to experimental values as compared to DFT calculations. We discuss possible extensions of the approach including application of more accurate quantum impurity solvers, such as Hirsch-Fye and Continuous-Time Quantum Monte Carlo. The application of the methodology to the nonequilibrium case is in progress.   

Using Machine Learning to Accelerate Complex Atomic Structure Elucidation

Workers in various scientific disciplines seek to develop chemical models for extended and molecular systems. The modeling process revolves around the gradual refinement of model assumptions, through comparison of experimental and computational results. Solid state Nuclear Magnetic Resonance (NMR) is one such experimental technique, providing great insight into chemical order over Angstrom length scales. However, interpretation of spectra for complex materials is difficult, often requiring intensive simulations. Similarly, working forward from the model in order to produce experimental quantities via ab initio is computationally demanding. The work involved in these two significant steps, compounded by the need to iterate back and forth, drastically slows the discovery process for new materials. There is thus great motivation for the derivation of structural models directly from complex experimental data, the subject of this work. Using solid state NMR experimental datasets, in conjunction with ab initio calculations of measurable NMR parameters, a network of machine learning kernels are trained to rapidly yield structural details, on the basis of input NMR spectra. Results for an environmentally relevant material will be presented, and directions for future work.