第一性原理电子结构的符号-数值计算方法
An approach to first principles electronic structure calculation by symbolic-numeric computation
摘要：
本文介绍了第一性原理电子结构计算的一种新方法。出发点是Hartree-Fock-Roothaan方程，其中分子积分通过关于原子坐标和其他变量的泰勒展开的多项式近似。它导出了一组多项式方程，其解是本征态，称为代数分子轨道方程。符号计算，特别是Gröbner基理论，使我们能够将多项式方程改写成具有相同根的更修剪和更易处理的形式，从中我们可以解开物理参数（波函数，原子坐标等）之间的关系，并按顺序逐一进行数值计算。此外，该方法是将电子结构计算、物理参数优化、反问题作为正问题求解的统一方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
