A proposal to first principles electronic structure calculation: Symbolic-Numeric method
Abstract
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular integrals in analytic forms and approximate them as a set of polynomial equations. By use of the Grobner bases technique, the polynomial equations are transformed into other ones which have identical roots. The converted equations take more convenient forms which will simplify numerical procedures, from which we can derive necessary physical properties in order, in an a la carte way. This method enables us to solve the electronic structure calculation, the optimization of any kind, or the inverse problem as a forward problem in a unified way, in which there is no need for iterative self-consistent procedures with trials and errors.
Keywords
Cite
@article{arxiv.1209.5127,
title = {A proposal to first principles electronic structure calculation: Symbolic-Numeric method},
author = {Akihito Kikuchi},
journal= {arXiv preprint arXiv:1209.5127},
year = {2013}
}
Comments
49 pages. This paper is originally written in Japanese and published in a Japanese journal "bussei-kenkyu". The author submits here the original Japanese text, accompanied with a brief (almost full) English translation. In this revised version, the author has corrected some typos. If the reader would like to get the complete full translation, contact the author [ kikuchi.akihito@canon.co.jp ]