We outline a generic, flexible, modular, yet efficient framework to the computation of energies and states for general nanoscopic systems with a focus on semiconductor quantum dots. The approach utilizes the configuration interaction method, in principal obtaining all many-body correlations in the system. The approach exploits the powerful abstracting mechanisms of C++'s template facility to produce efficient yet general code. The primary utility of the present approach is not in the resulting raw computational speed, but rather in minimizing the time from initial idea to final results.
An efficient method for calculating the electronic structure in large systems with a fully converged BZ sampling is presented. The method is based on a k.p-like approximation developed in the framework of the density functional perturbation theory. The reliability and efficiency of the method are demostrated in test calculations on Ar and Si supercells.
A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing direct comparison with conventional cubically scaling algorithms. The method has, to date, the lowest complexity of any algorithm for an exact calculation. A simple one-dimensional model system is used to thoroughly test the numerical stability of the algorithm and results for a real physical system are also given.
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 cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eige…
We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods.
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare sequential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential ap…
A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K computer. The algorithms are Krylov-subspace solvers for generalized shifted linear equations and were implemented in our order-N calculation code ELSES (http://www.elses.jp/). Moreover, a method for calculating eigen states is presented as a theoretical extension.
To get insight into the electronic properties of PrFe4P12 skutterudite, band electronic structure calculations, Total and Projected Density of States, Crystal Orbital Overlap Population and Mulliken Population Analysis were performed. The energy bands yield a semi metallic behavior with a direct gap (at gamma) of 0.02 eV. Total and Projected Density of States provided information of the contribution from each orbital of each atom to the total Density of States. Moreover, the bonding strength between some atoms within the unit cell was obtained. Mulliken Population analysis suggests ionic behav…
An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from k.p-approximation theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analysed for a test calculation on a 16-atom Na supercell.
The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computation…
We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the representation insures minimization of digital storage requirements for the computational data, while the code-independence makes the data ready for "big data" analytics. Our approach allows to minimize differences between original and the new representation, and is in principle information-lossless. The procedure for obtaining the wavefunction representation is closel…
We present an implicit solvent model for ab initio electronic structure calculations which is fully self-consistent and is based on direct solution of the nonhomogeneous Poisson equation. The solute cavity is naturally defined in terms of an isosurface of the electronic density according to the formula of Fattebert and Gygi (J. Comp. Chem. 23, 6 (2002)). While this model depends on only two parameters, we demonstrate that by using appropriate boundary conditions and dispersion-repulsion contributions, solvation energies obtained for an extensive test set including neutral and charged molecules…
Use of density-functional theory in a $Δ$self-consistent field framework result in both the ground- and two lowest electronicly excited states of the NaCl and LiCl. The accuracy of this method is confirmed using a multi-configuration self-consistent field method to obtain the same states. The overall good agreement between the calculated ground and excited potential-energy surfaces speaks promising for the computationally simple $Δ$self-consistent field method.
We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophis…
A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was realized on the K computer with upto 98,304 processor cores. The mathematical foundation is a novel linear algebraic algorithm for the generalized shifted linear equation. The calculation was carried out by our code ' ELSES ' (www.elses.jp) with modelled (tight-binding-form) systems based on ab initio calculations. (2) A post-calculation analysis method, called …
Moving beyond traditional 2D materials is now desirable to have switching capabilities (e.g., transistors). Here we propose using graphyne because, as we will show in this letter, obtaining regions of the electronic bandstructure which act as valence and conduction bands, with an apparent bandgap, is found. Here for particular allotropes of graphyne, density of states (DOS) and electronic bandstructure diagrams with E(k) vs k are found for the graphyne allotropes graphyne-1 and graphyne-2 having, respectively, one and two triple C-C carbon-carbon bonds between adjoining benzene rings. The ab i…
The methods which are actively used for electronic structure calculations of low-lying states of heavy- and superheavy-element compounds are briefly described. The advantages and disadvantages of calculations with the Dirac-Coulomb-Breit Hamiltonian, Huzinaga-type pseudopotential, shape-consistent Relativistic Effective Core Potential (RECP) and Generalized RECP are discussed. The nonvariational technique of the electronic structure restoration in atomic cores after the RECP calculation of a molecule is presented. The features of some approaches accounting for electron correlation, the configu…
We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient, systematically improvable, discontinuous basis spanning the occupied subspace and project the real-space Hamiltonian onto the span. In calculations on a range of systems, we find that accurate energies and forces are obtained with 8--25 basis functions per atom, reducing the dimension of the associated real-space eigenproblems by 1--3 orders of magnitude.
In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the "black-box" solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [2]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within t…
The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to simulate defected and disordered systems. This work studies the MST methods from a numerical point of view and shows the convergence with respect to the truncation of the angular momentum summations, which is a fundamental approximation parameter for all MST methods. We provide both rigorous analysis and numerical experiments to illustrate the efficiency of…
Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease …
