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Related papers: On the Evaluation of the electron repulsion integr…

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Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic…

Atomic Physics · Physics 2009-11-13 Krzysztof Pachucki , Mariusz Puchalski

The resistance coefficients in screen Coulomb potential of stellar plasma are evaluated in high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of…

Solar and Stellar Astrophysics · Physics 2017-01-18 Q. S. Zhang

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…

Quantum Physics · Physics 2012-08-01 Christian B. Mendl

Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…

Chemical Physics · Physics 2007-12-27 I. I. Guseinov

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer n STOs derived in this study with the help of - exponential type orbitals (-ETOs, the general formulas are…

Chemical Physics · Physics 2007-06-13 I. I. Guseinov

Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…

Chemical Physics · Physics 2025-10-20 Alexander Stark , Nathan Meier , Jeffrey Hatch , Joshua Kammeraad , Duy-Khoi Dang , Paul Zimmerman

In a recent publication (Telhat Ozdogan, Int. J. Quantum Chem., 92 (2003) 419), we presented a unified algorithm for the evaluation of multicenter multielectron integrals over Slater type orbitals with noninteger principal quantum numbers,…

Chemical Physics · Physics 2007-05-23 Telhat Ozdogan

The author suggests an approach based on the separation of total energy of multielectron systems into the semi-classical Coulomb part and the non-classical additional part. This approach allows on the one hand to simplify calculations and…

Atomic Physics · Physics 2008-11-04 Vadim Kavera

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…

Mathematical Physics · Physics 2018-04-03 Md Fazlul Hoque , Ian Marquette , Sarah Post , Yao-Zhong Zhang

A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij}…

Atomic Physics · Physics 2016-09-02 Bholanath Padhy

We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed…

Other Condensed Matter · Physics 2009-11-11 Carlo A. Rozzi , Daniele Varsano , Andrea Marini , Eberhard K. U. Gross , Angel Rubio

An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the…

Strongly Correlated Electrons · Physics 2009-11-10 Masahiko Higuchi , Hiroshi Yasuhara

Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and…

Chemical Physics · Physics 2016-05-25 Giuseppe M. J. Barca , Pierre-François Loos , Peter M. W. Gill

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the…

Chemical Physics · Physics 2017-05-17 Michal Lesiuk , Aleksandra M. Tucholska , Robert Moszynski

Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves and Coulomb potentials, and the…

General Mathematics · Mathematics 2026-01-27 Jack C. Straton

Electron repulsion integral tensor has ubiquitous applications in quantum chemistry calculations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor hypercontraction format with…

Numerical Analysis · Mathematics 2015-06-18 Jianfeng Lu , Lexing Ying

Coulomb repulsion can, counterintuitively, mediate Cooper pairing via the Kohn-Luttinger mechanism. However, it is commonly believed that observability of the effect requires special circumstances -- e.g., vicinity of the Fermi level to van…

Superconductivity · Physics 2025-05-01 Gal Shavit , Jason Alicea

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…

Chemical Physics · Physics 2022-05-16 Jerry L. Whitten

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…

Chemical Physics · Physics 2009-02-04 I. I. Guseinov

We represent in this note the solutions of the electronic Schr\"odinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction potential but comes at the price of a degenerate elliptic…

Mathematical Physics · Physics 2022-08-09 Harry Yserentant