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Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron…

Chemical Physics · Physics 2025-06-23 Hongji Gao , Xiangmin Jiao , Benjamin G. Levine

We study the decomposition of the Coulomb integrals of periodic systems into a tensor contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small…

Chemical Physics · Physics 2017-04-05 Felix Hummel , Theodoros Tsatsoulis , Andreas Grüneis

We present a novel multi-scale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that…

In this paper we present a mixed EIM-SVD tensor decomposition for bivariate functions. This method is composed, as its name suggests, of two main steps. The first one, provides an approximate representation of a function $f$ in separate…

Numerical Analysis · Mathematics 2017-11-07 Florian De Vuyst , Asma Toumi

Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…

Computational Physics · Physics 2023-10-25 Yang Kuang , Yedan Shen , Guanghui Hu

We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our…

Chemical Physics · Physics 2024-06-19 Edward G. Hohenstein , B. Scott Fales , Robert M. Parrish , Todd J. Martinez

We construct range-separated double-hybrid schemes which combine coupled-cluster or random-phase approximations with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron…

Chemical Physics · Physics 2020-01-29 Cairedine Kalai , Bastien Mussard , Julien Toulouse

We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are…

Numerical Analysis · Mathematics 2015-08-25 Fabien Casenave

Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. Quick generation of high-quality interatomic potentials is of urgent need under present circumstances,…

Materials Science · Physics 2016-11-23 Kun Wang , Wenjun Zhu , Shifang Xiao , Jun Chen , Wangyu Hu

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…

Computational Finance · Quantitative Finance 2019-02-13 Kathrin Glau , Daniel Kressner , Francesco Statti

A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…

Numerical Analysis · Mathematics 2022-09-22 Herbert Egger , Bogdan Radu

We compare three model-free numerical methods for inverting structural data to obtain interaction potentials, namely iterative Boltzmann inversion (IBI), test-particle insertion (TPI), and a machine-learning (ML) approach called ActiveNet.…

We introduce a systematic method for constructing polytope approximations to the quantum set in a variety of device-independent quantum random number generation (DI-QRNG) protocols. Our approach relies on two general-purpose algorithms that…

Quantum Physics · Physics 2026-03-11 Hyejung H. Jee , Florian J. Curchod , Mafalda L. Almeida

The calculation of two- and four-particle observables is addressed within the framework of the truncated polynomial expansion method (TPEM). The TPEM replaces the exact diagonalization of the one-electron sector in models for fermions…

Strongly Correlated Electrons · Physics 2009-11-11 G. Alvarez , T. C. Schulthess

Quantum generative modeling is emerging as a powerful tool for advancing data analysis in high-energy physics, where complex multivariate distributions are common. However, efficiently learning and sampling these distributions remains…

A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…

Atomic Physics · Physics 2024-10-08 Evgeny Z. Liverts

A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Shintaro Nomura , Toshiaki Iitaka

We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the…

Mesoscale and Nanoscale Physics · Physics 2013-01-29 Tuukka Hiltunen , Juha Ritala , Oona Kupiainen , Topi Siro , Ari Harju

An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…

Computational Physics · Physics 2015-11-17 M. S. Litsarev , I. V. Oseledets

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A…

Computational Physics · Physics 2020-08-07 Chengming He , Yicheng Chi , Peng Zhang