Related papers: Systematically improvable optimized atomic basis s…

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…

We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling…

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…

Calculating dipole moments with high-order basis sets is generally only possible for the light molecules, such as water. A simple, yet highly effective strategy of obtaining high-order dipoles with small, computationally less expensive…

A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly…

Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…

Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…

In this work we present a new basis set for electronic structures (Density Functional Theory (DFT)) calculations. This basis set extends Soler Williams Linearized Augmented Plane Wave (SLAPW) basis sets by allowing variable Muffin Tin (MT)…

We present SPARC-atomSFE, a spectral finite-element package for accurate and efficient atomic structure calculations within the framework of Kohn-Sham density functional theory. The package supports both all-electron and norm conserving…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…

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…

We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of…

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…

We present an approach for augmenting Gaussian atomic orbitals with correct nuclear cusps. Like the atomic orbital basis set itself, and unlike previous cusp corrections, this approach is independent of the many-body method used to prepare…