Related papers: Spectral finite-element formulation of the optimiz…
We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron…
LibRPA is a software package designed for efficient calculations of random phase approximation (RPA) electron correlation energies from first principles using numerical atomic orbital (NAOs). Leveraging a localized resolution of identity…
The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both…
The $hp$-version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed in one- and two-dimensional domains with analytic boundary. On suitably designed \emph{Spectral Boundary Layer meshes},…
We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version…
The Virtual Element Method (VEM) is a very effective framework to design numerical approximations with high global regularity to the solutions of elliptic partial differential equations. In this paper, we review the construction of such…
We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded…
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are…
We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress…
In wavefunction-based $\textit{ab-initio}$ quantum mechanical calculations, achieving absolute convergence with respect to the one-electron basis set is a long-standing challenge. In this work, using the random phase approximation (RPA)…
We introduce the proper orthogonal descriptors for efficient and accurate interatomic potentials of multi-element chemical systems. The potential energy surface of a multi-element system is represented as a many-body expansion of…
The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and…
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
Quantum mechanical calculations require the repeated solution of a Schr\"odinger equation for the wavefunctions of the system. Recent work has shown that enriched finite element methods significantly reduce the degrees of freedom required…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
We present the finite amplitude method (FAM) for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasi-particle-random-phase approximation (QRPA) with simple modifications. This technique has…
We show that the finite-basis optimized effective potential (OEP) equations exhibit previously unknown singular behavior.Imposing continuity, we derive new well-behaved finite-basis-set OEP equations that determine OEP for any orbital and…
We propose a practical method to solve the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing finite…
Practical applications of fragment embedding and closely related local correlation methods critically depend on a judicious choice of a low-level theory to define the local embedding subspace and to capture long-range electrostatic and…