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We present an accurate and efficient formulation for the calculation of phonons in real-space Kohn-Sham density functional theory. Specifically, employing a local exchange-correlation functional, norm-conserving pseudopotential in the Kleinman-Bylander representation, and local form for the electrostatics, we derive expressions for the dynamical matrix and associated Sternheimer equation that are particularly amenable to the real-space finite-difference method, within the framework of density functional perturbation theory. In particular, the formulation is applicable to insulating as well as metallic systems of any dimensionality, enabling the efficient and accurate treatment of semi-infinite and bulk systems alike, for both orthogonal and nonorthogonal cells. We also develop an implementation of the proposed formulation within the high-order finite-difference method. Through representative examples, we verify the accuracy of the computed phonon dispersion curves and density of states, demonstrating excellent agreement with established plane-wave results.
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We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing Kohn-Sham density functional theory calculations within the local density and generalized gradient approximations. In particular, we develop a modular math-kernel based implementation for NVIDIA architectures wherein the computationally expensive operations are carried out on the GPUs, with the remainder of the workload retained on the central processing units (CPUs). Using representative bulk and slab examples, we show that relative to CPU-only execution, GPUs enable speedups of up to 6× and 60× in node and core hours, respectively, bringing time to solution down to less than 30 s for a metallic system with over 14 000 electrons and enabling significant reductions in computational resources required for a given wall time.
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Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.
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We study the effect of torsional deformations on the electronic properties of single-walled transition metal dichalcogenide (TMD) nanotubes. In particular, considering forty-five select armchair and zigzag TMD nanotubes, we perform symmetry-adapted Kohn-Sham density functional theory calculations to determine the variation in bandgap and effective mass of charge carriers with twist. We find that metallic nanotubes remain so even after deformation, whereas semiconducting nanotubes experience a decrease in bandgap with twist-originally direct bandgaps become indirect-resulting in semiconductor to metal transitions. In addition, the effective mass of holes and electrons continuously decrease and increase with twist, respectively, resulting in n-type to p-type semiconductor transitions. We find that this behavior is likely due to rehybridization of orbitals in the metal and chalcogen atoms, rather than charge transfer between them. Overall, torsional deformations represent a powerful avenue to engineer the electronic properties of semiconducting TMD nanotubes, with applications to devices like sensors and semiconductor switches.
RESUMEN
We calculate the torsional moduli of single-walled transition metal dichalcogenide (TMD) nanotubes usingab initiodensity functional theory (DFT). Specifically, considering forty-five select TMD nanotubes, we perform symmetry-adapted DFT calculations to calculate the torsional moduli for the armchair and zigzag variants of these materials in the low-twist regime and at practically relevant diameters. We find that the torsional moduli follow the trend: MS2> MSe2> MTe2. In addition, the moduli display a power law dependence on diameter, with the scaling generally close to cubic, as predicted by the isotropic elastic continuum model. In particular, the shear moduli so computed are in good agreement with those predicted by the isotropic relation in terms of the Young's modulus and Poisson's ratio, both of which are also calculated using symmetry-adapted DFT. Finally, we develop a linear regression model for the torsional moduli of TMD nanotubes based on the nature/characteristics of the metal-chalcogen bond, and show that it is capable of making reasonably accurate predictions.
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We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 106 K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.
RESUMEN
We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham density functional theory calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling expression for the stress tensor that is applicable to simulations with unit cells of arbitrary symmetry, semilocal exchange-correlation functionals, and Brillouin zone integration. In particular, we rewrite the contributions arising from the self-energy and the nonlocal pseudopotential energy to make them amenable to the real-space finite-difference discretization, achieving up to three orders of magnitude improvement in the accuracy of the computed stresses. Using examples representative of static and dynamic calculations, we verify the accuracy and efficiency of the proposed formulation. In particular, we demonstrate high rates of convergence with spatial discretization, consistency between the computed energy and the stress tensor, and very good agreement with reference planewave results.