Analytic evaluation of Coulomb integrals for one, two and three-electron distance operators

07 September 2017, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

The state of the art for integral evaluation is that analytical solutions to integrals are far more useful than numerical solutions. We evaluate certain integrals analytically that are necessary in some approaches in quantum chemistry. In the title, where R stands for nucleus-electron and r for electron-electron distances, the (n,m)=(0,0) case is trivial, the (n,m)=(1,0) and (0,1) cases are well known, fundamental milestone in integration and widely used in computation chemistry, as well as based on Laplace transformation with integrand exp(-a2t2). The rest of the cases are new and need the other Laplace transformation with integrand exp(-a2t) also, as well as the necessity of a two dimensional version of Boys function comes up in case. These analytic expressions (up to Gaussian function integrand) are useful for manipulation with higher moments of inter-electronic distances, for example in correlation calculations.

Keywords

Analytic evaluation of Coulomb integrals for one, two and three-electron operators
Higher moment Coulomb operators RC1-nRD1-m, RC1-nr12-m and r12-nr13-m with n, m=0,1,2
Chemistry

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.