Rodríguez Juan I, Thompson David C, Ayers Paul W, Köster Andreas M
Department of Chemistry, McMaster University, Hamilton, Ontario, L8S 4M1, Canada.
J Chem Phys. 2008 Jun 14;128(22):224103. doi: 10.1063/1.2931563.
A new numerical integration procedure for exchange-correlation energies and potentials is proposed and "proof of principle" results are presented. The numerical integration grids are built from sparse-tensor product grids (constructed according to Smolyak's prescription [Dokl. Akad. Nauk. 4, 240 (1963)] ) on the unit cube. The grid on the unit cube is then transformed to a grid over real space with respect to a weight function, which we choose to be the promolecular density. This produces a "whole molecule" grid, in contrast to conventional integration methods in density-functional theory, which use atom-in-molecule grids. The integration scheme was implemented in a modified version of the DEMON2K density-functional theory program, where it is used to evaluate integrals of the exchange-correlation energy density and the exchange-correlation potential. Ground-state energies and molecular geometries are accurately computed. The biggest advantages of the grid are its flexibility (it is easy to change the number and distribution of grid points) and its whole molecule nature. The latter feature is potentially helpful for basis-set-free computational algorithms.
提出了一种用于交换关联能和势的新数值积分方法，并给出了“原理验证”结果。数值积分网格基于单位立方体上的稀疏张量积网格（根据斯莫利亚克法则[《苏联科学院通报》4, 240 (1963)]构建）。然后，相对于一个权重函数（我们选择为前分子密度），将单位立方体上的网格变换为实空间上的网格。这产生了一个“全分子”网格，与密度泛函理论中使用分子内原子网格的传统积分方法形成对比。该积分方案在DEMON2K密度泛函理论程序的一个修改版本中实现，用于评估交换关联能密度和交换关联势的积分。准确计算了基态能量和分子几何结构。该网格的最大优点是其灵活性（易于改变网格点的数量和分布）以及全分子特性。后一个特性对于无基组计算算法可能有帮助。
