An approach to first principles electronic structure calculation by symbolic-numeric computation
Year: 2013
Type: article
Abstract: This article is an introduction to a new approach to first principles electronic structure calculation. The starting point is the Hartree-Fock-Roothaan equation, in which molecular integrals are approximated by polynomials by way of Taylor expansion with respect to atomic coordinates and other variables. It leads to a set of polynomial equations whose solutions are eigenstate, which is designated as algebraic molecular orbital equation. Symbolic computation, especially, Gröbner bases theory, enables us to rewrite the polynomial equations into more trimmed and tractable forms with identical roots, from which we can unravel the relationship between physical parameters (wave function, atomic coordinates, and others) and numerically evaluate them one by one in order. Furthermore, this method is a unified way to solve the electronic structure calculation, the optimization of physical parameters, and the inverse problem as a forward problem.
Source: QScience Connect
Author: Akihito Kikuchi
Institution: Canon (Japan)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $995
OpenAlex ID: W1993843142