基于团簇状态张量积的选择组态相互作用
Selected Configuration Interaction in a Basis of Cluster State Tensor Products
摘要：
选择组态相互作用（SCI）的方法目前正在享受复苏，由于最近的几个发展，提高整体的计算效率或所得到的SCI矢量的紧凑性。与传统方法相比，这些最新进展使得有可能在大得多的轨道活动空间获得完全CI（FCI）质量的结果。然而，由于FCI向量只有少量重要的斯莱特行列式的起始假设，SCI对于具有强相关性的系统变得难以处理。本文介绍了一种开发SCI算法的方法，利用局部分子结构，显着减少SCI变量的数量。所提出的方法是通过首先将轨道分组为簇，在簇上我们可以定义许多粒子簇状态来定义的。然后，我们直接执行SCI算法的基础上的张量积的集群状态，而不是斯莱特行列式。虽然该方法是一般的任意定义的集群状态，我们发现通过定义集群状态通过塔克分解的全球（和稀疏）SCI向量显着提高性能。为了证明这种方法的潜力，称为张量积选择组态相互作用（TPSCI），我们提出了一组不同的例子的数值结果：1）改进的哈伯德模型，增加了不同的团簇间和团簇内跳跃项，2）N2和F2中键断裂的可聚性不明显，（3）42个电子在42个轨道上的大平面π共轭体系的基态能量。这些数值结果表明，TPSCI可以用来显着减少SCI变量的变分空间中的数量，从而铺平了道路，这些确定性和变分SCI方法扩展到更广泛的物理系统。
英文摘要：
Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces, compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: 1) modified Hubbard model with different inter- and intra-cluster hopping terms, 2) less obviously clusterable cases of bond breaking in N2 and F2, and 3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.
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