scholarly journals Multipole-based distance-dependent screening of Coulomb integrals

2019 ◽  
Vol 151 (8) ◽  
pp. 084111 ◽  
Author(s):  
Andreas Irmler ◽  
Fabian Pauly
Keyword(s):  
Coulomb Integrals

Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals

2017 ◽  
Vol 13 (3) ◽  
pp. 1199-1208 ◽  
Author(s):  
Ivan Duchemin ◽  
Jing Li ◽  
Xavier Blase
Keyword(s):  
Coulomb Integrals

Two-centre Coulomb integrals over STOs from analytical evaluation of k-integrals by contour integration in the complex plane

1990 ◽  
Vol 167 (6) ◽  
pp. 547-554 ◽  
Author(s):  
Giuseppe Figari ◽  
Camilla Costa ◽  
Roberto Pratolongo ◽  
Valerio Magnasco
Keyword(s):  
Complex Plane ◽  
Contour Integration ◽  
Analytical Evaluation ◽  
Coulomb Integrals

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

Electric-hexadecapole (24-pole) Coulomb integrals

1996 ◽  
Vol 53 (3) ◽  
pp. 1519-1524 ◽  
Author(s):  
Marita C. Chidichimo ◽  
Marek Stastna
Keyword(s):  
Coulomb Integrals
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