Related papers: Practical error bounds for properties in plane-wav…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
Materials with optimized band gap are needed in many specialized applications. In this work, we demonstrate that Hellmann-Feynman forces associated with the gap states can be used to find atomic coordinates with a desired electronic density…
The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational…
We address the problem of bounding rigorously the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, (iii) the propagation of…
Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a…
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they…
We analyze a data set comprising 370 GW band structures composed of 61716 quasiparticle (QP) energies of two-dimensional (2D) materials spanning 14 crystal structures and 52 elements. The data results from PAW plane wave based one-shot…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We present a set of efficient techniques in first-principles electronic-structure calculations utilizing the real-space finite-difference method. These techniques greatly reduce the overhead for performing integrals that involve…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution processes are typically not explicitly known and numerical…
In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…
We study the half-plane problem for the elastic wave equation subject to a free surface boundary condition, with particular emphasis on almost incompressible materials. A normal mode analysis is developed to estimate the solution in terms…
We show that quasiparticle (QP) energies as calculated in the $GW$ approximation converge to the wrong value using the projector augmented wave (PAW) method, since the overlap integrals between occupied orbitals and high energy, plane wave…
Atomic effective pseudopotentials enable atomistic calculations at the level of accuracy of density functional theory for semiconductor nanostructures with up to fifty thousand atoms. Since they are directly derived from ab-initio…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
In this article, we derive fully guaranteed error bounds for the energy of convex nonlinear mean-field models. These results apply in particular to Kohn-Sham equations with convex density functionals, which includes the reduced Hartree-Fock…
We present a novel "linear combination of atomic orbitals"-type of approximation, enabling accurate electronic structure calculations for systems of up to 20 or more electronically coupled quantum dots. Using realistic single quantum dot…
Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-- to third--…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…