Related papers: An approach to first principles electronic structu…

We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…

In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…

In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological…

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…

In the first order of the perturbation theory, the correction to the electronic terms of a diatomic molecule is calculated taking into account the Pauli principle.

Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…

Accurate electronic structure calculations might be one of the most anticipated applications of quantum computing.The recent landscape of quantum simulations within the Hartree-Fock approximation raises the prospect of substantial theory…

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent…

Considering the emblematic Hartree-Fock (HF) energy expression with single Slater determinant and the ortho-normal molecular orbits (MO) in it, expressed as a linear combination (LC) of atomic orbits (LCAO) basis set functions, the HF…

By the use of integer and noninteger n-Slater Type Orbitals in combined Hartree-Fock-Roothaan method, self consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell…

Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…

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 develop a numerical approach based on the sinc basis set for first-principles electronic structure calculations in one-dimensional systems. The method exploits the inherent accuracy and non-local character of the sinc functions to handle…

We developed a fast numerical methodfor complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronic-structure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate…

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…

We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the…

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi…

The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…