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We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
The need for large-scale electronic structure calculations arises recently in the field of material physics and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the…
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…
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…
We propose a self-consistent method for electronic structure calculations of correlated systems, which combines the local spin-density approximation (LSDA) and the dynamical mean field theory (DMFT). The LSDA part is based on the exact…
In recent years, two-dimensional twisted systems have gained increasing attention. However, the calculation of electronic structures in twisted material has remained a challenge. To address this, we have developed a general computational…
We have developed a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods permit efficient calculations on ill-conditioned systems with long…
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…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
We show how to adapt the quasi-Newton method to the electronic-structure calculations using systematic basis sets. Our implementation requires less iterations than the conjugate gradient method, while the computational cost per iteration is…
A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are…
One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
A brief review of the SIESTA project is presented in the context of linear-scaling density-functional methods for electronic-structure calculations and molecular-dynamics simulations of systems with a large number of atoms. Applications of…
We present a method for the calculation of electronic structure of systems that contain tens of thousands of atoms. The method is based on the division of the system into mutually overlapping fragments and the representation of the…
We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer complexes, in order to…