Ab-initio Methods in the Mechanics of MaterialsCopyright (c) 2024 Purdue University All rights reserved.
https://docs.lib.purdue.edu/ses2014/mms/ammm
Recent Events in Ab-initio Methods in the Mechanics of Materialsen-usSun, 14 Jan 2024 18:58:09 PST3600Overcoming the cubic-scaling bottleneck: linear-scaling density functional theory
https://docs.lib.purdue.edu/ses2014/mms/ammm/9
https://docs.lib.purdue.edu/ses2014/mms/ammm/9
Electronic structure calculations based on Density Functional Theory (DFT) have been remarkably successful in describing material properties and behavior. In conventional formulations and implementations of DFT, the orthogonality constraint on the orbitals results in a cubic-scaling with respect to the number of atoms. The inherent nonlocality of such approaches also makes them unsuitable for high performance computing. Consequently, the length and time scales for which DFT is practical is severely restricted. In this discussion, earlier and current efforts of the speaker to overcome the aforementioned limitations will be discussed. In particular, the presentation will focus on the development of (i) linear-scaling DFT methods, including those based on purification, spectral quadrature and maximally localized Wannier functions; (ii) a better than linear-scaling technique to coarse-grain DFT, whereby crystal defects can be accurately and efficiently studied. The discussion will conclude with a discussion on possible future directions.
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Phanish SuryanarayanaA Tensor-product approach for large scale electronic structure calculations using Kohn–Sham density functional theory
https://docs.lib.purdue.edu/ses2014/mms/ammm/8
https://docs.lib.purdue.edu/ses2014/mms/ammm/8
Quantum-mechanical calculations based on Kohn–Sham density functional theory (DFT) played a significant role in accurately predicting various aspects of materials behavior over the past decade. The Kohn–Sham approach to DFT reduces the many-body Schrodinger (eigen value) problem of interacting electrons into an equivalent problem of noninteracting electrons in an effective mean field that is governed by electron-density. Despite the reduced computational complexity of Kohn–Sham DFT, large-scale DFT calculations are still computationally very demanding with the resulting computational complexity scaling cubically with number of atoms in a given materials system. Numerical algorithms with reduced scaling behavior which are robust, computationally efficient and scalable on parallel computing architectures are always desirable to enable simulations at larger scales and on more complex systems. Following this line of thought, this study explores the use of tensor structured methods for ab-initio numerical solution of Kohn–Sham equations arising in DFT calculations. Earlier studies on tensor-structured methods have been quite successful in the accurate calculation of Hartree and the nonlocal exchange operators arising in the Hartree–Fock equations. A recent investigation of low-rank Tucker-type decomposition of the electron-density of large aluminum clusters (obtained from the finite-element discretization of orbital free DFT) shows the exponential decay of approximation error with respect to Tucker rank (number of tensor-basis functions in Tucker type representation). The results also indicate a smaller Tucker rank for the accurate representation of the electron density and is only weakly dependent on the system sizes studied. The promising success of tensor-structured techniques in resolving the electronic structure of material systems has enabled us to take a step further. In this study, we propose a systematic way of computing a globally adapted Tucker-type basis for solving the Kohn–Sham DFT problem by using a separable approximation of the Kohn–Sham Hamiltonian. Further, the resulting Kohn–Sham eigenvalue problem is projected into the aforementioned Tucker basis and is solved for ground-state energy using a self-consistent field iteration. The rank of the resulting Tucker representation and the computational complexity of the calculation are examined on representative benchmark examples involving metallic and insulating systems.
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Phani Motamarri et al.Mechanical strain can switch the sign of quantum capacitance from positive to negative
https://docs.lib.purdue.edu/ses2014/mms/ammm/7
https://docs.lib.purdue.edu/ses2014/mms/ammm/7
Quantum capacitance is a fundamental quantity that can directly reveal many interactions among electrons and is expected to play a critical role in nanoelectronics. One of many tantalizing recent physical revelations about quantum capacitance is that it can posses a negative value, hence allowing for the possibility of enhancing the overall capacitance in some particular material systems beyond the scaling predicted by classical electrostatics. Using detailed quantum mechanical simulations, we find an intriguing result that mechanical strains can tune both signs and values of quantum capacitance. We use a small coaxially-gated carbon nanotube as a paradigmatical capacitor system and show that, for the range of mechanical strain considered, quantum capacitance can be adjusted from very large positive to very large negative values (in the order of plus/minus hundreds of at-to farads), compared with the corresponding classical geometric value (0.31035 aF). We elucidate the mechanisms underpinning the switching of the sign of quantum capacitance due to strain. This finding opens novel avenues in designing quantum capacitance for applications in nanosensors, energy storage, and nanoelectronics.
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Xiaobao Li et al.Finite elements for accurate, large-scale quantum mechanical materials calculations: from classical to enriched to discontinuous
https://docs.lib.purdue.edu/ses2014/mms/ammm/6
https://docs.lib.purdue.edu/ses2014/mms/ammm/6
We discuss recent developments in finite-element (FE) based methods for the solution of the Kohn-Sham equations that have made possible smaller basis sets and larger calculations than possible by current state-of-the-art planewave based methods, in some cases by an order of magnitude or more. We begin with classical FE based approaches, demonstrating optimal convergence rates and micro-Hartree agreement with established PW based methods. We then discuss recent enriched partition-of-unity FE methods, which build known atomic physics into the basis while retaining strict locality and systematic improvability. By incorporating known physics, these bases can achieve the required accuracies with an order of magnitude fewer degrees of freedom (DOF) than required by traditional PW based methods, for “hard atom” calculations in particular. However, with such enrichment comes more expensive quadrature and some degree of ill-conditioning, which must be addressed. By incorporating not only local-atomic but also environmental physics into the basis, recent Discontinuous Galerkin (DG) based approaches can achieve larger reductions in DOFs still, while retaining both strict locality and systematic improvability. Crucially, however, the DG formulation allows for orthonormality as well, alleviating conditioning issues and allowing for the solution of standard rather than generalized discrete eigenproblems in the critical N3 scaling step of the Kohn-Sham solution. Accurate quantum mechanical forces have also been demonstrated. We conclude with an outlook and particular applications interests going forward.
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John PaskSurface terminated germanene as emerging nanomaterials
https://docs.lib.purdue.edu/ses2014/mms/ammm/5
https://docs.lib.purdue.edu/ses2014/mms/ammm/5
Using first principle calculations, we propose functionalized germanene (GeX, X = H, F, Cl, Br, I, OH, CH3) as emerging nanomaterials. Although germanene has no band gap, complete functionalization with H induces band gap of ~1.80 eV. A 50% H functionalization shows a dangling band at the Fermi level. Germanene I (GeI) is a 2D Topological Insulators (TI). GeH, GeF, GeCl, and GeBr can be transformed into TI by applying strain.The methyl-functionalized two-dimensional germanium monolayer sheets have been synthesized with a facile, one-step metathesis approach from CaGe2 crystals. We find that tensile strain can induce topological phase transition with band inversion at Gamma point. The band gap opened by spin-orbit coupling in this quantum spin Hall insulator can be as large as 0.1 eV ample for practical applications at room temperature.
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Dibakar Datta et al.Coarse-Graining KS-DFT
https://docs.lib.purdue.edu/ses2014/mms/ammm/4
https://docs.lib.purdue.edu/ses2014/mms/ammm/4
In this study, we develop and implement a Coarse-Grained version of the Kohn-Sham Density Funtional -(CG-KS-DFT) method to predict the evolution of crystal defects. The CG-KS-DFT method used in this study is based on the Linear Scaling Spectral Gauss Quadrature (LSSGQ) method, which proposes a reformulation of the traditional DFT equations. One of the main advantages of the LSSGQ method is that eliminates the need to explicitly compute orbitals. This property is achieved by using integral representation of the electronic quantities over the spectrum of the linear Hamiltonian operator. In addition, the evaluation of these integrals can be performed using spectral Gaussian quadrature rules. Therefore, the spectral nodes and weights of the quadrature rule are obtained using an efficient Lanczos type iteration, which are computed independently for each point in the domain. This property allows us to apply a systematic coarse graining description of the LSSGQ method, for example, using the Quasi-Continuum (QC) framework. Within this technique, a systematically coarsening of the domain is performed by applying judicious kinematic constraints, reducing the total number of degrees of freedom of the system. Finally, the combination of the LSSGQ method and the coarse graining approximation of the QC method enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. In this study, we introduce the fundamental equations to develop a coarse graining description. Then, we compute the formation energies of different defects in Mg, such us vacancies, divacancies, dislocations, and twin boundaries for crystals with large number of atoms. In addition, the parallel performance of the implementation and some experiment for massively large parallel programing are also going to be presented.
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Mauricio Ponga et al.An ab-initio analysis of the influence of knock-on-atom induced damage on the peak tensile strength of 3C-SiC grain boundaries
https://docs.lib.purdue.edu/ses2014/mms/ammm/3
https://docs.lib.purdue.edu/ses2014/mms/ammm/3
The effect of knock-on atom induced damage on the peak tensile strength of cubic silicon carbide (3C-SiC) is examined using an ab initio simulation framework based on Car Parrinello Molecular Dynamics method. The framework examines the effect of impact damage caused by a knock-on atom with velocities corresponding to four different kinetic energy levels (50 eV, 500 eV, 1 keV, and 2 keV) in three different SiC structure samples with different grain boundary (GB) configurations. Analyses show that peak tensile strength of the examined structures decreases by up to 37% in samples with GBs due to the impact damage caused by knock-on atom when compared with the case of single crystalline SiC under similar conditions. Analyses reveal new insights regarding the influence of bond strength change under knock-on atom induced impact damage on peak tensile strength of the examined structures. It is found that the peak tensile strength of the examined structures is a function of change in temperature, impact energy, and GB configuration. In order to extend the observed correlation of the peak tensile strength with atomic configurations to other structure types, a fractal dimension-based approach is adopted to predict structure peak tensile strength as a function of knock-on atom impact energy, temperature, and GB configuration. Analyses show that the tensile strength of the examined SiC structures increases as a function of their fractal dimension increase. Fractal dimensions also change as a function of change in impact energy level and the corresponding damage in an inversely proportional manner. Based on the observed correlations, an empirical relation to predict structure peak tensile strength as a function of simulation parameters is developed. The developed relation is found to predict strength data of structures not included in the fitting with good accuracy.
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Yousung Han et al.Spectral scheme for abinitio simulations of clusters
https://docs.lib.purdue.edu/ses2014/mms/ammm/2
https://docs.lib.purdue.edu/ses2014/mms/ammm/2
We formulate and implement a spectral scheme designed towards solving the Kohn–Sham equations for clusters in this study. This is motivated by the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane wave method – is a spectral method based on eigenfunction expansion. Our spectral solution method allows for efficient calculation of the electronic structure of clusters with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in our method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. We compute the occupied eigenstates of the discretized Kohn–Sham Hamiltonian using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. We highlight several algorithmic and computational aspects of our method, including computation of the electrostatics terms and parallelization. We present results from a variety of benchmark calculations employing local and nonlocal pseudopotentials and compare these to the literature. To illustrate the efficacy of our method, we demonstrate computations involving large systems that contain thousands of electrons. Finally, we briefly discuss the use of our method to study clusters with arbitrary point group symmetries.
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Amartya Banerjee et al.The relationship between core structure of dislocation and material defect energies in fcc metals
https://docs.lib.purdue.edu/ses2014/mms/ammm/1
https://docs.lib.purdue.edu/ses2014/mms/ammm/1
This research uses an ab initio density functional theory (DFT) informed phase field dislocation dynamics (PFDD) model to investigate the relationship between the dislocation equilibrium core width and the material surface for nine fcc metals. Furthermore, we show that due to an anomalous feature in its -surface, platinum has a fundamentally different core structure than other fcc metals and a much wider equilibrium core width than expected. Based on ab initio valence charge density difference calculations, we attribute this anomaly to distinct differences in the directionality of charge transfer in platinum. Advantageously, the DFT–PFDD model can account for the entire surface (a material dependent energy landscape that describes the energy maxima and minima that atoms must overcome as they shear pass one another on {111} planes) developed for specific materials through direct connections to ab initio DFT. This incorporates a dependence on unstable SFEs in addition to the commonly used intrinsic SFE. In addition, this establishes a link between atomic-scale numerical methods and the DFT–PFDD model that enables us to follow the dynamics of several nucleating and interacting dislocations based on appropriate calculation of their stacking fault widths and accurately probe the physics that underlies plastic deformation of even the smallest volumes.
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Abigail Hunter et al.