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Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our…

We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized…

We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of…

The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…

The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…

We present a method for total energy minimizations and molecular dynamics simulations based either on tight-binding or on Kohn-Sham hamiltonians. The method leads to an algorithm whose computational cost scales linearly with the system…

In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equations of independent particles that move in an effective…

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…

We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…

We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization…

In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…

Within the framework of linear-scaling Kohn-Sham density functional theory, a robust method for maintaining compact localized orbitals close to the ground state is coupled with nuclear dynamics. This allows to obviate the commonly employed…

We introduce a method for solving a self consistent electronic calculation within localized atomic orbitals, that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our…

The recently developed selected columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463, 2015] is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of…

As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only…

In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…

With the aim of future applications in quantum mechanical embedding in extended systems such as crystals, we suggest a simple and computationally efficient method which enables construction of a set of nonorthogonal highly localized…

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids…

We present an approach to the DFT+U method (Density Functional Theory + Hubbard model) within which the computational effort for calculation of ground state energies and forces scales linearly with system size. We employ a formulation of…

A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-quartz crystal…