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Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)]…
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured…
We present an efficient post-processing method for calculating the electronic structure of nanosystems based on the divide-and-conquer approach to density functional theory (DC-DFT), in which a system is divided into subsystems whose…
We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single…
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 have developed a linear scaling algorithm for calculating maximally-localized Wannier functions (MLWFs) using atomic orbital basis. An O(N) ground state calculation is carried out to get the density matrix (DM). Through a projection of…
The past years have witnessed impressive advances in electronic structure calculation, especially in the complexity and size of the systems studied, as well as in computation time. Linear scaling methods based on empirical tight-binding…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
The FIND algorithm is a fast algorithm designed to calculate certain entries of the inverse of a sparse matrix. Such calculation is critical in many applications, e.g., quantum transport in nano-devices. We extended the algorithm to other…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
We propose an efficient reduced-order technique for electronic structure calculations of semiconductor nanostructures, suited for inclusion in full-band quantum transport simulators. The model is based on the linear combination of bulk…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
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…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
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…
Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need. In this paper, we present an approach to calculate the charge density in…
Ga$_2$O$_3$ and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga$_2$O$_3$ offers potential for electronic structure engineering, which is of particular interest for a…
We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…