Rates of Convergence, Error Estimation Formulas, and Improved Basis Sets for Variational Methods in Atomic and Molecular Physics

这项工作的主要目标是发展 技术的有效，可靠的计算原子和 分子性质，充分考虑电子关联 方面的影响. 这些技术将通过高精度边界进行测试 小原子系统的状态计算。 的主要工具 使用的是主要研究者的工作延伸 Charles Schwartz和Klahn和Morgan的利率 Rayleigh Ritz变分法的收敛性 的 最近开发的公式分析评估三个 电子矩阵元积分，这是基于较早的 博纳姆的工作，现在已经用FORTRAN编程， 也将被使用。 在准确性和 可靠性，减少计算机时间的消耗， 预期 这项工作的初始阶段将引起以下人士的兴趣 应用数学家和原子理论家 小系统的高精度束缚态计算。 后续扩展到更大的系统应该是感兴趣的， 其他原子和分子理论家以及量子化学家。

The principal goal of this work is the development of techniques for the efficient, reliable calculation of atomic and molecular properties, taking full account of electron correlation effects. The techniques will be tested via high accuracy bound state calculations on small atomic systems. The principal tool used will be the principal investigator's extension of the work of Charles Schwartz and of Klahn and Morgan on rates of convergence for the Rayleigh Ritz variational method. The recently developed formulas for the analytic evaluation of three electron matrix element integrals, which are based on earlier work of Bonham, and which have now been programmed in FORTRAN, will also be used. Significant improvements in accuracy and reliability with a reduced expenditure of computer time are expected. The initial stages of the work would be of interest to applied mathematicians and to atomic theorists concerned with high accuracy bound state calculations on small systems. Subsequent extensions to larger systems should be of interest to other atomic and molecular theorists and to quantum chemists.