Related papers: Practical Methods for Ab Initio Calculations on Th…
In physics, it is sometimes desirable to compute the so-called \emph{Density Of States} (DOS), also known as the \emph{spectral density}, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient…
A theory is presented for a novel recursion method for O(N) ab initio tight-binding calculations. A long-standing problem of generalizing the recursion method to a non-orthogonal basis, which is a crucial step to make the recursion method…
A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a…
Accurately calculating energies and atomic forces with linear-scaling methods is a crucial approach to accelerating and improving molecular dynamics simulations. In this paper, we introduce HamGNN-DM, a machine learning model designed to…
An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
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 propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements $f(H)_{ij}$ decay rapidly…
Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…
Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…
We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the…
We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and…
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…
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The…
To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit…
Electron density is a fundamental quantity, which can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a…