Røeggen I, Johansen Tor
Department of Physics and Technology, Centre for Theoretical and Computational Chemistry, University of Tromso, 9037 Tromso, Norway.
J Chem Phys. 2008 May 21;128(19):194107. doi: 10.1063/1.2925269.
A standard Cholesky decomposition of the two-electron integral matrix leads to integral tables which have a huge number of very small elements. By neglecting these small elements, it is demonstrated that the recursive part of the Cholesky algorithm is no longer a bottleneck in the procedure. It is shown that a very efficient algorithm can be constructed when family type basis sets are adopted. For subsequent calculations, it is argued that two-electron integrals represented by Cholesky integral tables have the same potential for simplifications as density fitting. Compared to density fitting, a Cholesky decomposition of the two-electron matrix is not subjected to the problem of defining an auxiliary basis for obtaining a fixed accuracy in a calculation since the accuracy simply derives from the choice of a threshold for the decomposition procedure. A particularly robust algorithm for solving the restricted Hartree-Fock (RHF) equations can be speeded up if one has access to an ordered set of integral tables. In a test calculation on a linear chain of beryllium atoms, the advocated RHF algorithm nicely converged, but where the standard direct inversion in iterative space method converged very slowly to an excited state.
双电子积分矩阵的标准Cholesky分解会产生包含大量极小元素的积分表。通过忽略这些小元素，证明了Cholesky算法的递归部分不再是该过程的瓶颈。结果表明，采用族类型基组时可以构建一种非常高效的算法。对于后续计算，有人认为由Cholesky积分表表示的双电子积分与密度拟合具有相同的简化潜力。与密度拟合相比，双电子矩阵的Cholesky分解不存在为在计算中获得固定精度而定义辅助基组的问题，因为精度仅源于分解过程阈值的选择。如果能够获得有序的积分表集，那么求解受限Hartree-Fock（RHF）方程的一种特别稳健的算法可以得到加速。在对铍原子线性链的测试计算中，所倡导的RHF算法很好地收敛了，但标准的迭代空间直接反演方法收敛到激发态的速度非常慢。
