Implementation of the full CCSDT electronic structure model with tensor decompositions
Implementation of the full CCSDT electronic structure model with tensor decompositions
复制标题
通过张量分解实现完整的 CCSDT 电子结构模型
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Lesiuk
中科院分区：
文献类型：
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作者：
M. Lesiuk
我们报告了一个完整的实现耦合集群方法与单，双，三重激发（CCSDT），张量分解，以减少其规模和整体计算成本。对于电子排斥积分的分解，使用标准密度拟合（或乔莱斯基分解）格式。对耦合团簇的单振幅和双振幅作了常规处理，对三振幅张量则采用Tucker-3压缩公式：tabc ijk tXY Z UX ai UY bj UZ ck.辅助量UXai来自基于微扰理论的近似三倍振幅张量的奇异值分解（SVD）。所提出的方法的效率依赖于观察到的“压缩”张量tXY Z的尺寸足以提供恒定的相对精度的相关能量仅线性增长的系统的大小，N。这一事实，结合适当的因式分解的耦合簇方程，导致实际上N6缩放的计算成本所提出的方法，如数值所示的直链烷烃的链长增加。这构成了对传统（未压缩）CCSDT理论的N8标度的相当大的改进。通过对几个小分子体系的总能量和相对能量的基准计算，并与1 ar X iv：1 91 0进行比较，验证了该方法的准确性。00 50 6v 1 [phys ic s. CHEM-PH] 10 ct 2019的精确CCSDT方法。1 kJ/mol的精度水平是很容易实现与合理的SVD子空间大小，甚至更苛刻的精度水平，可以达到一个相当大的减少计算成本。扩展所提出的方法，包括更高的激励简要讨论，沿着可能的战略，减少其他残留误差。
We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the electron repulsion integrals the standard density fitting (or Cholesky decomposition) format is used. The coupled-cluster single and double amplitudes are treated conventionally, and for the triple amplitudes tensor we employ the Tucker-3 compression formula, tabc ijk ≈ tXY Z UX ai UY bj UZ ck. The auxiliary quantities UX ai come from singular value decomposition (SVD) of an approximate triple amplitudes tensor based on perturbation theory. The efficiency of the proposed method relies on an observation that the dimension of the “compressed” tensor tXY Z sufficient to deliver a constant relative accuracy of the correlation energy grows only linearly with the size of the system, N . This fact, combined with proper factorization of the coupled-cluster equations, leads to practically N6 scaling of the computational costs of the proposed method, as illustrated numerically for linear alkanes with increasing chain length. This constitutes a considerable improvement over the N8 scaling of the conventional (uncompressed) CCSDT theory. The accuracy of the proposed method is verified by benchmark calculations of total and relative energies for several small molecular systems and comparison with 1 ar X iv :1 91 0. 00 50 6v 1 [ ph ys ic s. ch em -p h] 1 O ct 2 01 9 the exact CCSDT method. The accuracy levels of 1 kJ/mol are easily achievable with reasonable SVD subspace size, and even more demanding levels of accuracy can be reached with a considerable reduction of the computational costs. Extensions of the proposed method to include higher excitations are briefly discussed, along with possible strategies of reducing other residual errors.