On an "interaction by moments" property of four center integrals
Dietrich Foerster
Abstract
The four center integrals needed in the Hartree Fock approximation and in TDDFT linear response are known to be difficult to calculate for orbitals of the Slater type or of finite range. We show that the interaction of pairs of products that do not mutually intersect may be replaced by the interaction of their moments, of which there are O(N). Only quadruplets of orbitals 'close' to one another need an explicit calculation and the total calculational effort therefore scales as O(N). We provide a new and concise proof of this "interaction by moments" property.
Create a lesson
Related papers
Real-Time Emergence of Charge-Transfer-to-Solvent States from Core Excitation
Jiří Suchan, B. Scott Fales, Benjamin G. Levine et al.
ElemCo.jl: A Julia package for electron-correlation methods
Daniel Kats, Charlotte Rickert, Thomas Schraivogel et al.
Franson-Interferometric Bounds on Entangled Two-Photon Absorption
Albin Hedse, Sankaran Ramesh, Luis Matheis et al.
The off-diagonal low rank property: new opportunities for low-scaling computational chemistry methods
Zikuan Wang
Core-valence double ionization of SF6 involving S2p, F1s and S1s inner shells
Veronica Daver Ideböhn, Daniel M. Pereira, Lucas M. Cornetta et al.
Benchmark of Multi-Channel Dyson Equation and Algebraic Diagrammatic Construction Methods for molecules
Mike Keizer, Stefano Paggi, J. Arjan Berger et al.