Linear scaling computation of the Fock matrix. V. Hierarchical cubature for numerical integration of the exchange-correlation matrix
Linear scaling computation of the Fock matrix. V. Hierarchical cubature for numerical integration of the exchange-correlation matrix
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DOI：
10.1063/1.1316012
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发表时间：
2000-12-08
影响因子：
4.4
通讯作者：
Challacombe, M
中科院分区：
文献类型：
--
作者：
Challacombe, M
层次体积法是一种新的方法，用于实现密度泛函理论中交换相关矩阵的线性标度计算。分层体积法结合了二叉搜索树的k维推广与涉及完全笛卡尔网格的自适应数值积分。分级容积克服了强烈的变化，通过多分辨率，而不是球极坐标变换与核尖点的电子密度。这种独特的笛卡尔表示允许在网格构建期间使用精确的积分误差，支持利用基于笛卡尔高斯的电子密度的局部性的O（log N）范围查询。收敛由τ（r）控制，其限制电子密度的局部积分误差。对于水分子团簇的RB 3LYP/6- 31 G ** 计算，观察到线性标度的早期开始，从（H2O）（30）开始，并随着tau（r）值的减小而持续。与核重量计划的比较表明，新方法是有竞争力的基础上，每个原子的网格点。RPBE 0/6- 31 G ** Ne-2结合曲线的系统收敛性相对于tau（r）被证明。(C)2000年美国物理学会。[S0021-9606（00）32442-4]。
Hierarchical cubature is a new method for achieving linear scaling computation of the exchange-correlation matrix central to Density Functional Theory. Hierarchical cubature combines a k-dimensional generalization of the binary search tree with adaptive numerical integration involving an entirely Cartesian grid. Hierarchical cubature overcomes strong variations in the electron density associated with nuclear cusps through multiresolution rather than spherical-polar coordinate transformations. This unique Cartesian representation allows use of the exact integration error during grid construction, supporting O(log N) range-queries that exploit locality of the Cartesian Gaussian based electron density. Convergence is controlled by tau (r), which bounds the local integration error of the electron density. An early onset of linear scaling is observed for RB3LYP/6-31G** calculations on water clusters, commencing at (H2O)(30) and persisting with decreasing values of tau (r). Comparison with nuclear weight schemes suggests that the new method is competitive on the basis of grid points per atom. Systematic convergence of the RPBE0/6-31G** Ne-2 binding curve is demonstrated with respect to tau (r). (C) 2000 American Institute of Physics. [S0021-9606(00)32442-4].