Order-N first-principles calculation method for self-consistent ground-state electronic structures of semi-infinite systems

Finite Difference Interpolation for Reduction of Grid-Related Errors in Real-Space Pseudopotential Density Functional Theory

The real-space pseudopotential approach is a well-known method for large-scale density functional theory (DFT) calculations. One of its main limitations, however, is the introduction of errors associated with the positioning of the underlying real-space grid, a phenomenon usually known as the "egg-box" effect. The effect can be controlled by using a finer grid, but this raises the cost of the calculations or even undermines their feasibility altogether. Therefore, there is ongoing interest in the reduction of the effect per a given real-space grid. Here, we present a finite difference interpolation of electron orbitals as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. We implement the method in PARSEC, a finite difference real-space pseudopotential DFT code, and demonstrate error mitigation and improved convergence at a low additional computational cost.

General Approach for Reducing Continuous Translational Symmetry Errors in Finite Difference Real-Space Calculations

We provide a new scheme for representing pseudopotentials on a finite real-space grid, designed to significantly reduce the "egg box" (also known as the "egg carton") effect, i.e., unphysical fluctuations of computed quantities upon real-space translation. Instead of interpolating the electron-ion potential onto the grid, our scheme starts at a reference position and then uses a weighted sum of translation operators to account for the positions of atoms in real space. This results in a nonlocal but banded representation (even for local potentials) which is fully compatible with nonlocal pseudopotential operators. As a demonstration, this scheme is tested in one dimension for three types of potentials: a local pseudopotential, a nonlocal pseudopotential, and a local pseudopotential with self-consistent Hartree and exchange-correlation potentials. This scheme is found to reduce fluctuations of examined quantities by at least three orders of magnitude. The approach requires neither grid adaptation nor pseudopotential modification and can be readily extended to the three-dimensional case.

First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation

We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state.

O(N) methods in electronic structure calculations

Linear-scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers. The linear-scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas are then discussed. The applications of linear-scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear-scaling methods are discussed.

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

Real-space calculations for electron transport properties of nanostructures

Recent developments in the fabrication and investigation of conductors of atomic dimensions have stimulated a large number of experimental and theoretical studies on these nanoscale devices. In this paper, we introduce examples presenting the efficiencies and advantages of a first-principles transport calculation scheme based on the real-space finite-difference (RSFD) formalism and the overbridging boundary-matching (OBM) method. The RSFD method does not suffer from the artificial periodicity problems that arise in methods using plane-wave basis sets or the linear dependence problems that occur in methods using atomic basis sets. Moreover, the algorithm of the RSFD method is suitable for massively parallel computers and, thus, the combination of the RSFD and OBM methods enables us to execute first-principles transport calculations using large models. To demonstrate the advantages of this method, several applications of the transport calculations in various systems ranging from jellium nanowires to the tip and surface system of scanning tunneling microscopy are presented.

Total-energy minimization of few-body electron systems in the real-space finite-difference scheme

A practical and high-accuracy computation method to search for ground states of few-electron systems is presented on the basis of the real-space finite-difference scheme. A linear combination of Slater determinants is employed as a many-electron wavefunction, and the total-energy functional is described in terms of overlap integrals of one-electron orbitals without the constraints of orthogonality and normalization. In order to execute a direct energy minimization process of the energy functional, the steepest-descent method is used. For accurate descriptions of integrals which include bare-Coulomb potentials of ions, the time-saving double-grid technique is introduced. As an example of the present method, calculations for the ground state of the hydrogen molecule are demonstrated. An adiabatic potential curve is illustrated, and the accessibility and accuracy of the present method are discussed.

Relationship between the geometric structure and conductance oscillation in nanowires

A theoretical analysis of the electron transport properties of plain and bumpy jellium nanowires suspended between semi-infinite jellium electrodes is carried out, and the possibility of the experimental observation of the conductance oscillation with a period longer than the two-atom length is discussed. In both the nanowires, the transmission trace as a function of the nanowire length exhibits oscillatory behaviour. The period of the oscillation of the plain nanowire corresponds to π divided by the Bloch wavenumber of the electrons in the nanowire region. However, the period of the oscillation of the bumpy nanowire results in the least common multiple of π divided by the Bloch wavenumber and the geometric period of the nanowire. Our result indicates that the conductance oscillation with a period longer than the two-atom length can be experimentally observed if nanowires without any defects are formed in experiments.