Related papers: A proposal to first principles electronic structur…

In computational physics and materials science, first-principles methods, particularly density functional theory, have become central tools for electronic structure prediction and materials design. Recently, rapid advances in artificial…

A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via…

The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…

Silicon quantum computing has the potential to revolutionize technology with capabilities to solve real-life problems that are computationally complex or even intractable for modern computers [1] by offering sufficient high quality qubits…

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…

We develop a discontinuous Galerkin (DG) framework for automatically constructing adaptive basis sets for electronic structure calculations. By allowing basis functions to be discontinuous across element interfaces, our approach supports…

An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…

By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…

Simplified Hartree-Fock computations are carried out on the atoms He through Ne, using orthonormalized basis functions for the 1s, 2s and 2p orbitals dependent on three parameters. Using Mathematica with the new Apple M1 chip, computations…

To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural methods exploiting a dependency graph for this task was…

Base inertial parameters constitute a minimal inertial parametrization of mechanical systems that is of interest, for example, in parameter estimation and model reduction. Numerical and symbolic methods are available to determine their…

We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…

This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…

We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…

A new approach, motivated by Fock space localization, for constructing a reduced many-particle Hilbert space is proposed and tested. The self-consistent Hartree-Fock (SCHF) approach is used to obtain a single-electron basis from which the…

We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve…

In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…

We introduce a new framework for the low-energy nuclear structure calculations, which describes the single-particle wave function as a superposition of localized Gaussians. It is a hybrid of the Hartree-Fock and antisymmetrized molecular…

We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…