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An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…

Numerical Analysis · Mathematics 2025-07-25 Daniel Appelo , Jeffrey W. Banks , William D. Henshaw , Ngan Le , Donald W. Schwendeman

In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we…

Numerical Analysis · Mathematics 2022-07-15 Pieter Appeltans , Wim Michiels

We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…

Quantum Physics · Physics 2023-03-29 Nicholas H. Stair , Cristian L. Cortes , Robert M. Parrish , Jeffrey Cohn , Mario Motta

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the…

Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…

Other Condensed Matter · Physics 2010-08-16 Michal Bajdich , Lubos Mitas

The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is $O(N^4)$ in the…

Chemical Physics · Physics 2021-04-21 Jan Wilhelm , Dorothea Golze , Leopold Talirz , Jürg Hutter , Carlo A. Pignedoli

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…

The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…

Strongly Correlated Electrons · Physics 2007-05-23 Igor Sandalov , Borje Johansson , Olle Eriksson

In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum…

Atomic Physics · Physics 2007-05-23 G. Gaigalas

In (relativistic) electronic structure methods, the quaternion matrix eigenvalue problem and the linear response (Bethe-Salpeter) eigenvalue problem for excitation energies are two frequently encountered structured eigenvalue problems.…

Chemical Physics · Physics 2021-12-01 Zhendong Li

Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…

Numerical Analysis · Mathematics 2007-05-23 Anton Leykin , Jan Verschelde , Ailing Zhao

With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational methods are required to take advantage of such extreme-scale machines. In this…

Materials Science · Physics 2012-11-13 Truong Vinh Truong Duy , Taisuke Ozaki

We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…

Computational Physics · Physics 2020-07-15 Benedikt Hartl , Shubham Sharma , Oliver Brügner , Stijn F. L. Mertens , Michael Walter , Gerhard Kahl

In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…

Numerical Analysis · Mathematics 2026-03-05 Amin Faghih , Michele Rinelli , Marc Van Barel , Raf Vandebril , Robbe Vermeiren

Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…

Chemical Physics · Physics 2023-01-11 Xiang Li , Zhe Li , Ji Chen

We present a method (the Aufbau/Abbau method) for optimizing the structure of a whole series of clusters without making any assumptions on the structure. Subsequently, the method is combined with the embedded-atom method in determining the…

Atomic and Molecular Clusters · Physics 2009-11-10 V. G. Grigoryan , M. Springborg

Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…

Quantum Physics · Physics 2007-05-23 Yuri I. Ozhigov

This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic…

Chemical Physics · Physics 2020-02-18 Aleksandra Leszczyk , Paweł Tecmer , Katharina Boguslawski

Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…

Condensed Matter · Physics 2009-11-07 Torkel D. Engeness , T. A. Arias

A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb-Breit Hamiltonian aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei…

Quantum Physics · Physics 2024-06-19 Péter Jeszenszki , Dávid Ferenc , Edit Mátyus